![Page 1: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/1.jpg)
Design of “RNA-seq”
Experiments
RabadanLab
06/29/2015
Albert Lee
![Page 2: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/2.jpg)
Motivation
![Page 3: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/3.jpg)
Motivation
• RNAseq is getting cheaper (~$600 per sample) and more sophisticated analyses are being/will be called for.
![Page 4: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/4.jpg)
Motivation• RNAseq is getting cheaper (~$600 per sample) and more sophisticated
analyses are being/will be called for.• Multifactorial analysis (multiple treatments, multiple tissues , multiple time points)
![Page 5: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/5.jpg)
Motivation• RNAseq is getting cheaper (~$600 per sample) and more sophisticated
analyses are being/will be called for.• Multifactorial analysis (multiple treatments, multiple tissues , multiple time points)• Repeated measures (more than one samples from the same individual)
![Page 6: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/6.jpg)
Motivation• RNAseq is getting cheaper (~$600 per sample) and more sophisticated
analyses are being/will be called for.• Multifactorial analysis (multiple treatments, multiple tissues , multiple time points)• Repeated measures (more than one samples from the same individual)
![Page 7: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/7.jpg)
Motivation• RNAseq is getting cheaper (~$600 per sample) and more sophisticated analyses
are being/will be called for.• Multifactorial analysis (multiple treatments, multiple tissues , multiple time points)• Repeated measures (more than one samples from the same individual)
• Currently, the majority of RNAseq tools heavily focus on comparing two classes
![Page 8: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/8.jpg)
Motivation• RNAseq is getting cheaper (~$600 per sample) and more sophisticated
analyses are being/will be called for.• Multifactorial analysis (multiple treatments, multiple tissues , multiple time points)• Repeated measures (more than one samples from the same individual)
• Currently, the majority of RNAseq tools heavily focus on comparing two classes
• edgeR & DESeq : Modified Fisher Exact test for NB distribution
![Page 9: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/9.jpg)
Motivation• RNAseq is getting cheaper (~$600 per sample) and more sophisticated analyses
are being/will be called for.• Multifactorial analysis (multiple treatments, multiple tissues , multiple time points)• Repeated measures (more than one samples from the same individual)
• Currently, the majority of RNAseq tools heavily focus on comparing two classes• edgeR & DESeq : Modified Fisher Exact test for NB distribution• Cuffdiff : z-score based on the log-transformed ratio of expression divided by the variance
of the transformed ratio
![Page 10: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/10.jpg)
Motivation• RNAseq is getting cheaper (~$600 per sample) and more sophisticated analyses
are being/will be called for.• Multifactorial analysis (multiple treatments, multiple tissues , multiple time points)• Repeated measures (more than one samples from the same individual)
• Currently, the majority of RNAseq tools heavily focus on comparing two classes• edgeR & DESeq : Modified Fisher Exact test for NB distribution• Cuffdiff : z-score based on the log-transformed ratio of expression divided by the variance
of the transformed ratio
![Page 11: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/11.jpg)
Motivation• RNAseq is getting cheaper (~$600 per sample) and more sophisticated analyses are being/will be
called for.• Multifactorial analysis (multiple treatments, multiple tissues , multiple time points)• Repeated measures (more than one samples from the same individual)
• Currently, the majority of RNAseq tools heavily focus on comparing two classes• edgeR & DESeq : Modified Fisher Exact test for NB distribution• Cuffdiff : z-score based on the log-transformed ratio of expression divided by the variance of the transformed ratio
• One-factor-at-a-time method is ineffective. •
![Page 12: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/12.jpg)
Motivation• RNAseq is getting cheaper (~$600 per sample) and more sophisticated analyses are being/will be
called for.• Multifactorial analysis (multiple treatments, multiple tissues , multiple time points)• Repeated measures (more than one samples from the same individual)
• Currently, the majority of RNAseq tools heavily focus on comparing two classes• edgeR & DESeq : Modified Fisher Exact test for NB distribution• Cuffdiff : z-score based on the log-transformed ratio of expression divided by the variance of the transformed ratio
• One-factor-at-a-time method is ineffective. •
![Page 13: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/13.jpg)
Motivation• RNAseq is getting cheaper (~$600 per sample) and more sophisticated analyses are being/will be
called for.• Multifactorial analysis (multiple treatments, multiple tissues , multiple time points)• Repeated measures (more than one samples from the same individual)
• Currently, the majority of RNAseq tools heavily focus on comparing two classes• edgeR & DESeq : Modified Fisher Exact test for NB distribution• Cuffdiff : z-score based on the log-transformed ratio of expression divided by the variance of the transformed ratio
• One-factor-at-a-time method is ineffective. • Multifactorial options in edgeR/DESeq/Limma-Voom may be difficult to understand in the beginning
![Page 14: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/14.jpg)
Aim• Goal is to identify a subset of genes ranked by interestingness while
accounting for the structure of the experimental design
![Page 15: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/15.jpg)
Aim• Goal is to identify a subset of genes ranked by interestingness while
accounting for the structure of the experimental design
Example questions
![Page 16: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/16.jpg)
Aim• Goal is to identify a subset of genes ranked by interestingness while
accounting for the structure of the experimental design
• (Level 1) What are the genes that are differentially expressed in tumor vs normal?
Example questions
![Page 17: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/17.jpg)
Aim• Goal is to identify a subset of genes ranked by interestingness while
accounting for the structure of the experimental design
• (Level 1) What are the genes that are differentially expressed in tumor vs normal?
• (Level 2) What are the genes that are differentially expressed in tumor vs normal while controlling for batch effects?
Example questions
![Page 18: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/18.jpg)
Aim• Goal is to identify a subset of genes ranked by interestingness while
accounting for the structure of the experimental design
• (Level 1) What are the genes that are differentially expressed in tumor vs normal?
• (Level 2) What are the genes that are differentially expressed in tumor vs normal while controlling for batch effects?
• (Level 3) What are the genes that are differentially expressed only in testis and not in other tissues?
Example questions
![Page 19: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/19.jpg)
Aim• Goal is to identify a subset of genes ranked by interestingness while
accounting for the structure of the experimental design
• (Level 1) What are the genes that are differentially expressed in tumor vs normal?
• (Level 2) What are the genes that are differentially expressed in tumor vs normal while controlling for batch effects?
• (Level 3) What are the genes that are differentially expressed only in testis and not in other tissues?
• (Level 3) What are the genes that are differentially expressed between time 3 and time2 in drugged samples while controlling for vehicle effects?
Example questions
![Page 20: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/20.jpg)
There are many problems in RNAseq, but…
![Page 21: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/21.jpg)
There are many problems in RNAseq, but…Let’s assume that:
![Page 22: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/22.jpg)
There are many problems in RNAseq, but…Let’s assume that:
1. All heavy biological & computational work(sequencing, preprocessing, alignment, and counting ) have been done.
![Page 23: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/23.jpg)
There are many problems in RNAseq, but…Let’s assume that:
1. All heavy biological & computational work(sequencing, preprocessing, alignment, and counting ) have been done.
data generation problem
![Page 24: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/24.jpg)
There are many problems in RNAseq, but…Let’s assume that:
1. All heavy biological & computational work(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.
data generation problem
![Page 25: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/25.jpg)
There are many problems in RNAseq, but…Let’s assume that:
1. All heavy biological & computational work(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.
data generation problem
non-normality problem
![Page 26: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/26.jpg)
There are many problems in RNAseq, but…Let’s assume that:
1. All heavy biological & computational work(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).
data generation problem
non-normality problem
![Page 27: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/27.jpg)
There are many problems in RNAseq, but…Let’s assume that:
1. All heavy biological & computational work(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).
data generation problem
non-normality problem
small replicate size problem
![Page 28: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/28.jpg)
There are many problems in RNAseq, but…Let’s assume that:
1. All heavy biological & computational work(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.
data generation problem
non-normality problem
small replicate size problem
![Page 29: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/29.jpg)
There are many problems in RNAseq, but…Let’s assume that:
1. All heavy biological & computational work(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.
data generation problem
non-normality problem
small replicate size problem
normalization problem
![Page 30: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/30.jpg)
There are many problems in RNAseq, but…Let’s assume that:
1. All heavy biological & computational work(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
non-normality problem
small replicate size problem
normalization problem
![Page 31: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/31.jpg)
There are many problems in RNAseq, but…Let’s assume that:
1. All heavy biological & computational work(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problem
![Page 32: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/32.jpg)
Level 1
![Page 33: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/33.jpg)
Level 1 “What are the genes that are differentially expressed in tumor vs normal?”
![Page 34: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/34.jpg)
1. Completely randomized design
• Completely randomized design:• the simplest experimental design. • With this design, experimental units are randomly assigned to
treatments.
![Page 35: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/35.jpg)
1. Completely randomized design
• Completely randomized design:• the simplest experimental design. • With this design, experimental units are randomly assigned to
treatments.Control Drug
![Page 36: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/36.jpg)
1. Completely randomized design
• Completely randomized design:• the simplest experimental design. • With this design, experimental units are randomly assigned to
treatments.Control Drug
![Page 37: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/37.jpg)
1. Completely randomized design
• Completely randomized design:• the simplest experimental design. • With this design, experimental units are randomly assigned to
treatments.Control Drug
![Page 38: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/38.jpg)
1. Completely randomized design
• Completely randomized design:• the simplest experimental design. • With this design, experimental units are randomly assigned to
treatments.Control Drug
![Page 39: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/39.jpg)
1. Completely randomized design
• Completely randomized design:• the simplest experimental design. • With this design, experimental units are randomly assigned to
treatments.Control Drug
![Page 40: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/40.jpg)
1. Completely randomized design
• Completely randomized design:• the simplest experimental design. • With this design, experimental units are randomly assigned to
treatments.Control Drug
![Page 41: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/41.jpg)
1. Completely randomized design
• Completely randomized design:• the simplest experimental design. • With this design, experimental units are randomly assigned to
treatments.Control Drug
![Page 42: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/42.jpg)
1. Completely randomized design
• Completely randomized design:• the simplest experimental design. • With this design, experimental units are randomly assigned to
treatments.Control Drug
![Page 43: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/43.jpg)
1. Completely randomized design
• Completely randomized design:• the simplest experimental design. • With this design, experimental units are randomly assigned to
treatments.Control Drug
![Page 44: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/44.jpg)
1. Completely randomized design
• Completely randomized design:• the simplest experimental design. • With this design, experimental units are randomly assigned to
treatments.Control Drug
![Page 45: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/45.jpg)
1. Completely randomized design
• Completely randomized design:• the simplest experimental design. • With this design, experimental units are randomly assigned to
treatments.Control Drug
![Page 46: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/46.jpg)
![Page 47: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/47.jpg)
The typical matrix you will see
![Page 48: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/48.jpg)
The typical matrix you will see
![Page 49: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/49.jpg)
Condition AThe typical matrix you will see
![Page 50: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/50.jpg)
Condition BCondition AThe typical matrix you will see
![Page 51: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/51.jpg)
Condition BCondition AThe typical matrix you will see
“Condition” factor
![Page 52: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/52.jpg)
Condition BCondition AThe typical matrix you will see
“Condition” factor
N Experimental units
![Page 53: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/53.jpg)
Condition BCondition AThe typical matrix you will see
“Condition” factor
N Experimental units
Each experimental unit is represented as a vector of gene expressions
![Page 54: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/54.jpg)
Condition BCondition AThe typical matrix you will see
“Condition” factor
N Experimental units
Each experimental unit is represented as a vector of gene expressions
Expressionmeasurement
![Page 55: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/55.jpg)
Condition BCondition AThe typical matrix you will see
![Page 56: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/56.jpg)
One thing to keep in mind
![Page 57: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/57.jpg)
One thing to keep in mind
![Page 58: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/58.jpg)
One thing to keep in mind
“In designing a microarray experiment,
![Page 59: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/59.jpg)
One thing to keep in mind
“In designing a microarray experiment, or RNA-seq
![Page 60: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/60.jpg)
One thing to keep in mind
“In designing a microarray experiment, we should concentrate on getting it right for one gene.
or RNA-seq
![Page 61: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/61.jpg)
One thing to keep in mind
“In designing a microarray experiment, we should concentrate on getting it right for one gene. As the other 53, 999 data points are measured on subsamples of the experimental unit(!),
or RNA-seq
![Page 62: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/62.jpg)
One thing to keep in mind
“In designing a microarray experiment, we should concentrate on getting it right for one gene. As the other 53, 999 data points are measured on subsamples of the experimental unit(!), they have no bearing on constructing a good design.”
or RNA-seq
![Page 63: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/63.jpg)
One thing to keep in mind
“In designing a microarray experiment, we should concentrate on getting it right for one gene. As the other 53, 999 data points are measured on subsamples of the experimental unit(!), they have no bearing on constructing a good design.”
-- George Casella, “Statistical Design”, Springer 2008
or RNA-seq
![Page 64: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/64.jpg)
Condition BCondition A
![Page 65: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/65.jpg)
Condition BCondition A
![Page 66: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/66.jpg)
Condition BCondition A
![Page 67: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/67.jpg)
Condition BCondition A
![Page 68: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/68.jpg)
Condition BCondition A
expression22
113433247
1226799
14522
![Page 69: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/69.jpg)
Condition BCondition A
expression22
113433247
1226799
14522
conditionA
AAAABBBBB
![Page 70: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/70.jpg)
expression22
113433247
1226799
14522
conditionA
AAAABBBBB
factor
Experimental units
![Page 71: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/71.jpg)
expression22
113433247
1226799
14522
conditionA
AAAABBBBB
factor
Experimental units
a level of the factor
![Page 72: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/72.jpg)
expression22
113433247
1226799
14522
conditionA
AAAABBBBB
factor
Experimental units
a level of the factor
another level of the factor
![Page 73: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/73.jpg)
expression22
113433247
1226799
14522
conditionA
AAAABBBBB
You can compute sample means and sample standard deviations for two groups
![Page 74: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/74.jpg)
expression22
113433247
1226799
14522
conditionA
AAAABBBBB
You can compute sample means and sample standard deviations for two groups
![Page 75: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/75.jpg)
expression22
113433247
1226799
14522
conditionA
AAAABBBBB
,
You can compute sample means and sample standard deviations for two groups
![Page 76: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/76.jpg)
expression22
113433247
1226799
14522
conditionA
AAAABBBBB
,
You can compute sample means and sample standard deviations for two groups
![Page 77: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/77.jpg)
expression22
113433247
1226799
14522
conditionA
AAAABBBBB
,
,
You can compute sample means and sample standard deviations for two groups
![Page 78: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/78.jpg)
expression22
113433247
1226799
14522
conditionA
AAAABBBBB
,
,
You can compute sample means and sample standard deviations for two groups
Null Hypothesis : =
![Page 79: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/79.jpg)
expression22
113433247
1226799
14522
conditionA
AAAABBBBB
,
,
You can compute sample means and sample standard deviations for two groups
Null Hypothesis : =
Alternative Hypothesis :
![Page 80: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/80.jpg)
expression22
113433247
1226799
14522
conditionA
AAAABBBBB
,
,
You can compute sample means and sample standard deviations for two groups
Null Hypothesis : =
Alternative Hypothesis :
+=Compute test-statistic :
![Page 81: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/81.jpg)
expression22
113433247
1226799
14522
conditionA
AAAABBBBB
,
,
You can compute sample means and sample standard deviations for two groups
Null Hypothesis : =
Alternative Hypothesis :
+=Compute test-statistic :
Compare with critical value & compute p value
![Page 82: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/82.jpg)
Image source: http://www.beingencouraged.com/
![Page 83: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/83.jpg)
Expression22
113433247
1226799
14522
conditionA
AAAABBBBB
You can describe the same thing with linear modeling
![Page 84: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/84.jpg)
Expression22
113433247
1226799
14522
conditionA
AAAABBBBB
You can describe the same thing with linear modeling
![Page 85: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/85.jpg)
Expression22
113433247
1226799
14522
conditionA
AAAABBBBB
You can describe the same thing with linear modeling
![Page 86: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/86.jpg)
Expression22
113433247
1226799
14522
conditionA
AAAABBBBB
You can describe the same thing with linear modeling
Instead of focusing comparison of two groups,
![Page 87: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/87.jpg)
Expression22
113433247
1226799
14522
conditionA
AAAABBBBB
You can describe the same thing with linear modeling
![Page 88: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/88.jpg)
Expression22
113433247
1226799
14522
conditionA
AAAABBBBB
You can describe the same thing with linear modeling
![Page 89: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/89.jpg)
Expression22
113433247
1226799
14522
conditionA
AAAABBBBB
You can describe the same thing with linear modeling
![Page 90: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/90.jpg)
Expression22
113433247
1226799
14522
conditionA
AAAABBBBB
You can describe the same thing with linear modeling
Focus on modeling the expression as a function of factors
![Page 91: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/91.jpg)
Expression22
113433247
1226799
14522
conditionA
AAAABBBBB
You can describe the same thing with linear modeling
![Page 92: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/92.jpg)
Expression22
113433247
1226799
14522
conditionA
AAAABBBBB
You can describe the same thing with linear modeling
Expression
![Page 93: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/93.jpg)
Expression22
113433247
1226799
14522
conditionA
AAAABBBBB
You can describe the same thing with linear modeling
Expression
A Effect
![Page 94: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/94.jpg)
Expression22
113433247
1226799
14522
conditionA
AAAABBBBB
You can describe the same thing with linear modeling
Expression
A Effect B Effect
![Page 95: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/95.jpg)
Expression22
113433247
1226799
14522
conditionA
AAAABBBBB
You can describe the same thing with linear modeling
Expression
A Effect B Effect Error
![Page 96: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/96.jpg)
Expression22
113433247
1226799
14522
conditionA
AAAABBBBB
You can describe the same thing with linear modeling
Expression
A Effect B Effect Error
Expression = default effect + B Effect + Error
![Page 97: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/97.jpg)
Expression(Y)22
113433247
1226799
14522
+ B+ B+ B+ B+ B
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1
Use dummy variables to indicate a membership
![Page 98: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/98.jpg)
Expression(Y)22
113433247
1226799
14522
Expression = default effect + B Effect + Error
+ B+ B+ B+ B+ B
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1
Use dummy variables to indicate a membership
![Page 99: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/99.jpg)
Expression(Y)22
113433247
1226799
14522
Expression = default effect + B Effect + Error
+ B+ B+ B+ B+ B
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1
Use dummy variables to indicate a membership
[ | ] = +~ (0, )
Assume
![Page 100: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/100.jpg)
Expression(Y)22
113433247
1226799
14522
Expression = default effect + B Effect + Error
+ B+ B+ B+ B+ B
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1
Use dummy variables to indicate a membership
[ | ] = +~ (0, )
Assume
Estimate parameters, ,
![Page 101: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/101.jpg)
Expression(Y)22
113433247
1226799
14522
Expression = default effect + B Effect + Error
+ B+ B+ B+ B+ B
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1
Use dummy variables to indicate a membership
In R: lm ( expression ~ condition, data=data)
[ | ] = +~ (0, )
Assume
Estimate parameters, ,
![Page 102: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/102.jpg)
Expression22
113433247
1226799
14522
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1
=
“Design matrix”“Response variable”
![Page 103: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/103.jpg)
Expression22
113433247
1226799
14522
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1
=
“Design matrix”“Response variable”
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Expression22
113433247
1226799
14522
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1
=
“Design matrix”“Response variable”
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Expression22
113433247
1226799
14522
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1
=
“Design matrix”“Response variable”
![Page 106: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/106.jpg)
Expression22
113433247
1226799
14522
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1
=
“Design matrix”“Response variable” “Coefficients”
![Page 107: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/107.jpg)
Expression22
113433247
1226799
14522
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1
=
“Design matrix”“Response variable” “Coefficients”
![Page 108: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/108.jpg)
Expression22
113433247
1226799
14522
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1S
=
“Design matrix”“Response variable” “Coefficients”
![Page 109: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/109.jpg)
Expression22
113433247
1226799
14522
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1S
=
“Design matrix”“Response variable” “Coefficients”
![Page 110: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/110.jpg)
Expression22
113433247
1226799
14522
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1S
=
=“Design matrix”“Response variable” “Coefficients”
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Expression22
113433247
1226799
14522
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1S
=
=“Design matrix”“Response variable” “Coefficients”
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Expression22
113433247
1226799
14522
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1S
=
=“Design matrix”“Response variable” “Coefficients”
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Expression22
113433247
1226799
14522
Effect of B0
000011111
Default(A)
1
1
1
1
1
1
1
1
1
1S
=
=
Solve for
“Design matrix”“Response variable” “Coefficients”
![Page 114: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/114.jpg)
S
=
Solve for
![Page 115: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/115.jpg)
S
=
Solve for
![Page 116: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/116.jpg)
S
==
Solve for
![Page 117: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/117.jpg)
S
=== ( )
Solve for
![Page 118: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/118.jpg)
S
=== ( )=
Solve for
![Page 119: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/119.jpg)
Expression = + +
Expr
essi
on
![Page 120: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/120.jpg)
Expression = + +
Expr
essi
on
![Page 121: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/121.jpg)
Expression = + +
Expr
essi
on
![Page 122: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/122.jpg)
Expression = + +
Expr
essi
on
![Page 123: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/123.jpg)
Baseline effect
Expression = + +
Expr
essi
on
![Page 124: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/124.jpg)
Baseline effect
Expression = + +
Expr
essi
on
![Page 125: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/125.jpg)
Baseline effect
Expression = + +
Expr
essi
on
![Page 126: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/126.jpg)
Baseline effect
Expression = + +
Expr
essi
on
![Page 127: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/127.jpg)
Baseline effect
Drug effect
Expression = + +
Expr
essi
on
![Page 128: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/128.jpg)
Baseline effect
Drug effect
Expression = + +
![Page 129: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/129.jpg)
Baseline effect
Drug effect
Expression = + +
![Page 130: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/130.jpg)
Expression = + +
Baseline effect
Drug effect
![Page 131: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/131.jpg)
Expression = + +
Baseline effect
Drug effect
![Page 132: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/132.jpg)
Expression = + +
Baseline effect
Drug effect
![Page 133: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/133.jpg)
Expression = + +
Baseline effect
Drug effect
Here, we partitioned thevariance of expression into three parts:Baseline, drug effect, and residuals
![Page 134: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/134.jpg)
Expression = + +
Baseline effect
Drug effect
Here, we partitioned thevariance of expression into three parts:Baseline, drug effect, and residuals
Now we can do analyze each term separately
![Page 135: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/135.jpg)
Expression = + +
Baseline effect
Drug effect
Here, we partitioned thevariance of expression into three parts:Baseline, drug effect, and residuals
Now we can do analyze each term separately
For example, we can check if drug effect is significant
![Page 136: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/136.jpg)
Expression = + +
Baseline effect
Drug effect
: = 0
Here, we partitioned thevariance of expression into three parts:Baseline, drug effect, and residuals
Now we can do analyze each term separately
For example, we can check if drug effect is significant
![Page 137: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/137.jpg)
Expression = + +
Baseline effect
Drug effect
: = 0: 0
Here, we partitioned thevariance of expression into three parts:Baseline, drug effect, and residuals
Now we can do analyze each term separately
For example, we can check if drug effect is significant
![Page 138: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/138.jpg)
Expression = + +
Baseline effect
Drug effect
: = 0: 0
~Here, we partitioned thevariance of expression into three parts:Baseline, drug effect, and residuals
Now we can do analyze each term separately
For example, we can check if drug effect is significant
![Page 139: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/139.jpg)
Expression = + +
Baseline effect
Drug effect
: = 0: 0
~Here, we partitioned thevariance of expression into three parts:Baseline, drug effect, and residuals
Now we can do analyze each term separately
For example, we can check if drug effect is significant
![Page 140: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/140.jpg)
![Page 141: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/141.jpg)
= Least square
![Page 142: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/142.jpg)
=
( ) = ( )
Least square
![Page 143: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/143.jpg)
=
( ) = ( )=
Least square
Since ( ) =
![Page 144: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/144.jpg)
=
( ) = ( )=
=
Least square
Since ( ) =
Since Var(Y) =
![Page 145: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/145.jpg)
=
( ) = ( )=
=
Least square
Since ( ) =
Since Var(Y) =
Since = and ==
![Page 146: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/146.jpg)
=
( ) = ( )=
=
=
Least square
Since ( ) =
Since Var(Y) =
Since = and ==
Since =
![Page 147: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/147.jpg)
=
( ) = ( )=
=
=
=
Least square
Since ( ) =
Since Var(Y) =
Since = and ==
Since =
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=
( ) = ( )=
=
=
=
= =
Least square
Since ( ) =
Since Var(Y) =
Since = and ==
Since =
![Page 149: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/149.jpg)
![Page 150: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/150.jpg)
“Are the two means different?”
![Page 151: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/151.jpg)
“Are the two means different?” =+
![Page 152: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/152.jpg)
“Are the two means different?” =+
![Page 153: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/153.jpg)
“Are the two means different?”
“Is there a additional effect of B (if we have A as a baseline)?”
=+
![Page 154: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/154.jpg)
“Are the two means different?”
“Is there a additional effect of B (if we have A as a baseline)?”
=+
= +
![Page 155: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/155.jpg)
Limitations of CRD
• If experimental units are heterogeneous, there might be high false positives or false negatives
![Page 156: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/156.jpg)
Level 2 “What are the genes that are differentially expressed in tumor vs normal while controlling for batch effects?”
![Page 157: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/157.jpg)
2. Randomized block design Control Drug
Batch 1
Batch 2
Batch 3
![Page 158: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/158.jpg)
2. Randomized block design Control Drug
Batch 1
Batch 2
Batch 3
![Page 159: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/159.jpg)
2. Randomized block design Control Drug
Batch 1
Batch 2
Batch 3
![Page 160: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/160.jpg)
2. Randomized block design Control Drug
Batch 1
Batch 2
Batch 3
![Page 161: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/161.jpg)
2. Randomized block design Control Drug
Batch 1
Batch 2
Batch 3
![Page 162: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/162.jpg)
2. Randomized block design Control Drug
Batch 1
Batch 2
Batch 3
![Page 163: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/163.jpg)
2. Randomized block design Control Drug
Batch 1
Batch 2
Batch 3
![Page 164: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/164.jpg)
2. Randomized block design Control Drug
Batch 1
Batch 2
Batch 3
![Page 165: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/165.jpg)
2. Randomized block design Control Drug
Batch 1
Batch 2
Batch 3
![Page 166: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/166.jpg)
2. Randomized block design Control Drug
Batch 1
Batch 2
Batch 3
![Page 167: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/167.jpg)
2. Randomized block design Control Drug
Batch 1
Batch 2
Batch 3
![Page 168: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/168.jpg)
2. Randomized block design Control Drug
Batch 1
Batch 2
Batch 3
![Page 169: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/169.jpg)
2. Randomized block design Control Drug
Batch 1
Batch 2
Batch 3
![Page 170: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/170.jpg)
2. Randomized block design Control Drug
Batch 1
Batch 2
Batch 3
![Page 171: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/171.jpg)
2. Randomized block design
expression22
113433247
1226799
145223221
conditionA
AAAAABBBBBB
batch1
122331
12233
1st factor 2nd factor
![Page 172: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/172.jpg)
2. Randomized block design
expression22
113433247
1226799
145223221
conditionA
AAAAABBBBBB
batch1
122331
12233
1st factor 2nd factor
![Page 173: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/173.jpg)
2. Randomized block design
expression22
113433247
1226799
145223221
conditionA
AAAAABBBBBB
batch1
122331
12233
1st factor 2nd factor
~ +
![Page 174: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/174.jpg)
2. Randomized block design
expression22
113433247
1226799
145223221
conditionA
AAAAABBBBBB
batch1
122331
12233
1st factor 2nd factor
~ +
![Page 175: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/175.jpg)
2. Randomized block design
![Page 176: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/176.jpg)
![Page 177: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/177.jpg)
![Page 178: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/178.jpg)
Expr
essio
n
![Page 179: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/179.jpg)
Expr
essio
n
BaselineControl & batch 1
![Page 180: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/180.jpg)
Expr
essio
n
BaselineControl & batch 1
Effect of Drug
![Page 181: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/181.jpg)
Expr
essio
n
Effect of batch 2BaselineControl & batch 1
Effect of Drug
![Page 182: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/182.jpg)
Expr
essio
n
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
![Page 183: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/183.jpg)
Expr
essio
n
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
![Page 184: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/184.jpg)
Expr
essio
n
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
![Page 185: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/185.jpg)
Expr
essio
n
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
Effect of drug + batch 2 effect
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Expr
essio
n
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
Effect of drug + batch 2 effect
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Expr
essio
n
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
Effect of drug + batch 2 effect
![Page 188: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/188.jpg)
Expr
essio
n
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
Effect of drug + batch 2 effect
![Page 189: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/189.jpg)
Expr
essio
n
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
Effect of drug + batch 2 effect
Effect of drug +batch 3 effect
![Page 190: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/190.jpg)
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
![Page 191: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/191.jpg)
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
![Page 192: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/192.jpg)
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
![Page 193: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/193.jpg)
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
![Page 194: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/194.jpg)
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
![Page 195: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/195.jpg)
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
![Page 196: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/196.jpg)
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
![Page 197: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/197.jpg)
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
![Page 198: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/198.jpg)
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
We effectively have partitioned the variance.
![Page 199: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/199.jpg)
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
We effectively have partitioned the variance.That is, we separated batch effects from treatment
![Page 200: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/200.jpg)
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
We effectively have partitioned the variance.
Now we can test if there is a effect of drug and if it’s significantThat is, we separated batch effects from treatment
![Page 201: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/201.jpg)
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
We effectively have partitioned the variance.
Null hypothesis : : = 0
Now we can test if there is a effect of drug and if it’s significantThat is, we separated batch effects from treatment
![Page 202: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/202.jpg)
Effect of batch 2
Effect of batch 3
BaselineControl & batch 1
Effect of Drug
We effectively have partitioned the variance.
Null hypothesis : : = 0 Test statistics: ~
Now we can test if there is a effect of drug and if it’s significantThat is, we separated batch effects from treatment
![Page 203: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/203.jpg)
Effect of Drug
We effectively have partitioned the variance.
Null hypothesis : : = 0 Test statistics: ~
Now we can test if there is a effect of drug and if it’s significantThat is, we separated batch effects from treatment
![Page 204: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/204.jpg)
Effect of Drug
We effectively have partitioned the variance.
Null hypothesis : : = 0 Test statistics: ~
Now we can test if there is a effect of drug and if it’s significant
33.6132
That is, we separated batch effects from treatment
![Page 205: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/205.jpg)
Effect of Drug
We effectively have partitioned the variance.
Null hypothesis : : = 0 Test statistics: ~
Now we can test if there is a effect of drug and if it’s significant
( )0.710233.6132
That is, we separated batch effects from treatment
![Page 206: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/206.jpg)
Effect of Drug
We effectively have partitioned the variance.
Null hypothesis : : = 0 Test statistics: ~
Now we can test if there is a effect of drug and if it’s significant
t-statistic
47.33( )
0.710233.6132
That is, we separated batch effects from treatment
![Page 207: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/207.jpg)
Effect of Drug
We effectively have partitioned the variance.
Null hypothesis : : = 0 Test statistics: ~
Now we can test if there is a effect of drug and if it’s significant
t-statistic
47.33
p-value
<2e-16( )
0.710233.6132
That is, we separated batch effects from treatment
![Page 208: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/208.jpg)
Level 3 “What are the genes that are differentially expressed between drugged mice in time 2 and in time1 while controlling for vehicle effects?”
![Page 209: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/209.jpg)
Research Question
• Setting: Mice are randomly assigned to drug and vehicle groups and their expression measures are obtained at time 1, time 2, and time3 (not repeated measure design)
![Page 210: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/210.jpg)
3. Time seriesControl Drug
Time 1
Time 2
Time 3
![Page 211: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/211.jpg)
3. Time seriesControl Drug
Time 1
Time 2
Time 3
![Page 212: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/212.jpg)
3. Time seriesControl Drug
Time 1
Time 2
Time 3
![Page 213: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/213.jpg)
3. Time seriesControl Drug
Time 1
Time 2
Time 3
![Page 214: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/214.jpg)
3. Time seriesControl Drug
Time 1
Time 2
Time 3
![Page 215: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/215.jpg)
3. Time seriesControl Drug
Time 1
Time 2
Time 3
![Page 216: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/216.jpg)
3. Time seriesControl Drug
Time 1
Time 2
Time 3
![Page 217: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/217.jpg)
3. Time seriesControl Drug
Time 1
Time 2
Time 3
![Page 218: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/218.jpg)
3. Time seriesControl Drug
Time 1
Time 2
Time 3
![Page 219: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/219.jpg)
3. Time seriesControl Drug
Time 1
Time 2
Time 3
![Page 220: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/220.jpg)
3. Time seriesControl Drug
Time 1
Time 2
Time 3
![Page 221: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/221.jpg)
3. Time seriesControl Drug
Time 1
Time 2
Time 3
![Page 222: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/222.jpg)
3. Time seriesControl Drug
Time 1
Time 2
Time 3
![Page 223: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/223.jpg)
Data and model
![Page 224: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/224.jpg)
Data and model
![Page 225: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/225.jpg)
Data and model
![Page 226: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/226.jpg)
Data and model
Model :
![Page 227: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/227.jpg)
~ +
Data and model
Model :
![Page 228: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/228.jpg)
~ + + :
Data and model
Model :
![Page 229: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/229.jpg)
~ + + :
Data and model
Interaction term
Model :
![Page 230: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/230.jpg)
~ + + :
Data and model
Interaction term
Interaction : the effect of a factor on the response variable isdifferent depending on the level of another factor
Model :
![Page 231: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/231.jpg)
~ + + :
Data and model
Interaction term
Interaction : the effect of a factor on the response variable isdifferent depending on the level of another factor
Model :
Ex) drug will act differently in t2 from control in t2
![Page 232: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/232.jpg)
In R..
![Page 233: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/233.jpg)
In R..
![Page 234: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/234.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
![Page 235: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/235.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
![Page 236: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/236.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
![Page 237: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/237.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
![Page 238: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/238.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
![Page 239: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/239.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
![Page 240: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/240.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
Time3 effect
![Page 241: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/241.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
Time3 effect
Drug effect
![Page 242: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/242.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
Time3 effect
Drug effect
![Page 243: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/243.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
Time3 effect
Drug effect
![Page 244: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/244.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
Time3 effect
Drug effect
Time 2effect
![Page 245: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/245.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
Time3 effect
Drug effect
Drug & time2 interaction
Time 2effect
![Page 246: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/246.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
Time3 effect
Drug effect
Drug & time2 interaction
Time 2effect
![Page 247: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/247.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
Time3 effect
Drug effect
Drug & time2 interaction
Time 2effect
Time3 effect
![Page 248: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/248.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
Time3 effect
Drug effect
Drug & time2 interaction
Time 2effect
Time3 effect
![Page 249: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/249.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
Time3 effect
Drug effect
Drug & time2 interaction
Drug & time3interaction
Time 2effect
Time3 effect
![Page 250: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/250.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
Time3 effect
Drug effect
Drug & time2 interaction
Drug & time3interaction
Time 2effect
Time3 effect
How do we interpretInteraction terms?
![Page 251: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/251.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Drug & time2 interaction
Time 2effect
This segment corresponds tothe difference betweendrug_t2 and drug_t1
![Page 252: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/252.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
![Page 253: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/253.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
![Page 254: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/254.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Because
![Page 255: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/255.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Becausethis
![Page 256: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/256.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Becausethis
![Page 257: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/257.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Becausethis
![Page 258: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/258.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Becausethis
minus
![Page 259: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/259.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Becausethis
minus
that
![Page 260: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/260.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Becausethis
minus
that
![Page 261: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/261.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Becausethis
minus
that
![Page 262: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/262.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Becausethis
minus
that equals
![Page 263: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/263.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Becausethis
minus
that equals this
![Page 264: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/264.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Drug & time2 interaction
Time 2effect
This segment corresponds todrug_t2 – drug_t1
![Page 265: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/265.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
![Page 266: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/266.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
![Page 267: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/267.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
By the same token,
![Page 268: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/268.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
By the same token,
this corresponds to
![Page 269: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/269.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
By the same token,
this corresponds to
![Page 270: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/270.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
By the same token,
this corresponds to the difference between ctrl_t2 and ctrl_t1
![Page 271: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/271.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
By the same token,
this corresponds to the difference between ctrl_t2 and ctrl_t1
![Page 272: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/272.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
By the same token,
this corresponds to the difference between ctrl_t2 and ctrl_t1
![Page 273: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/273.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
By the same token,
this corresponds to the difference between ctrl_t2 and ctrl_t1
![Page 274: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/274.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Baseline effects
Time 2effect
By the same token,
this corresponds to the difference between ctrl_t2 and ctrl_t1
![Page 275: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/275.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Drug & time2 interaction
Time 2effect
Time 2effect Therefore,
the interaction corresponds to
(drug_t2 – drug_t1) –(ctrL_t2 – ctrl_t1)
![Page 276: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/276.jpg)
Drug & time2 interaction
Time 2effect
Time 2effect
Interaction: Difference of Differences
![Page 277: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/277.jpg)
Drug & time2 interaction
Time 2effect
Time 2effect
Interaction: Difference of Differences
![Page 278: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/278.jpg)
Drug & time2 interaction
Time 2effect
Time 2effect
(drug_t2 – drug_t1) (ctrL_t2 – ctrl_t1)
Interaction: Difference of Differences
![Page 279: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/279.jpg)
Drug & time2 interaction
Time 2effect
Time 2effect
minus
(drug_t2 – drug_t1) (ctrL_t2 – ctrl_t1)-
Interaction: Difference of Differences
![Page 280: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/280.jpg)
Drug & time2 interaction
Time 2effect
Time 2effect
minus =
(drug_t2 – drug_t1) (ctrL_t2 – ctrl_t1)-
Interaction: Difference of Differences
![Page 281: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/281.jpg)
Drug & time2 interaction
Time 2effect
Time 2effect
minus
Drug & time2 interaction
=
(drug_t2 – drug_t1) (ctrL_t2 – ctrl_t1)-
Interaction: Difference of Differences
![Page 282: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/282.jpg)
Drug & time2 interaction
Time 2effect
Time 2effect
minus
Drug & time2 interaction
=
(drug_t2 – drug_t1) (ctrL_t2 – ctrl_t1)-
Interaction: Difference of Differences
Does this gene respond differently to drug at time t2 vs time1 than to placebo at time2 vs time1?
![Page 283: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/283.jpg)
nxhExpression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
Drug & time3interaction
Time3 effect
What about this one?
Time3 effect
![Page 284: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/284.jpg)
What if we want to compute(drug_t3 – drug_t2) - (ctrl_t3 – ctrl_t2) ?
![Page 285: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/285.jpg)
What if we want to compute(drug_t3 – drug_t2) - (ctrl_t3 – ctrl_t2) ?
“What are the genes that are differentially expressed between drugged mice in time3 and in time2 while controlling for vehicle effects?”
![Page 286: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/286.jpg)
What if we want to compute
We know that drug:time2 corresponds to?
(drug_t3 – drug_t2) - (ctrl_t3 – ctrl_t2) ?
“What are the genes that are differentially expressed between drugged mice in time3 and in time2 while controlling for vehicle effects?”
![Page 287: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/287.jpg)
What if we want to compute
We know that drug:time2 corresponds to?
drug:time2:
(drug_t3 – drug_t2) - (ctrl_t3 – ctrl_t2) ?
“What are the genes that are differentially expressed between drugged mice in time3 and in time2 while controlling for vehicle effects?”
![Page 288: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/288.jpg)
What if we want to compute
We know that drug:time2 corresponds to?
(drug_t2 – drug_t1) - (ctrl_t2 – ctrl_t1) drug:time2:
(drug_t3 – drug_t2) - (ctrl_t3 – ctrl_t2) ?
“What are the genes that are differentially expressed between drugged mice in time3 and in time2 while controlling for vehicle effects?”
![Page 289: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/289.jpg)
What if we want to compute
We know that drug:time2 corresponds to?
drug:time3(drug_t2 – drug_t1) - (ctrl_t2 – ctrl_t1) drug:time2:
(drug_t3 – drug_t2) - (ctrl_t3 – ctrl_t2) ?
“What are the genes that are differentially expressed between drugged mice in time3 and in time2 while controlling for vehicle effects?”
![Page 290: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/290.jpg)
What if we want to compute
We know that drug:time2 corresponds to?
drug:time3(drug_t2 – drug_t1) - (ctrl_t2 – ctrl_t1) drug:time2: (drug_t3 – drug_t1) - (ctrl_t3 – ctrl_t1)
(drug_t3 – drug_t2) - (ctrl_t3 – ctrl_t2) ?
“What are the genes that are differentially expressed between drugged mice in time3 and in time2 while controlling for vehicle effects?”
![Page 291: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/291.jpg)
What if we want to compute
We know that drug:time2 corresponds to?
drug:time3(drug_t2 – drug_t1) - (ctrl_t2 – ctrl_t1) drug:time2: (drug_t3 – drug_t1) - (ctrl_t3 – ctrl_t1)
So,
(drug_t3 – drug_t2) - (ctrl_t3 – ctrl_t2) ?
“What are the genes that are differentially expressed between drugged mice in time3 and in time2 while controlling for vehicle effects?”
![Page 292: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/292.jpg)
What if we want to compute
We know that drug:time2 corresponds to?
drug:time3(drug_t2 – drug_t1) - (ctrl_t2 – ctrl_t1) drug:time2: (drug_t3 – drug_t1) - (ctrl_t3 – ctrl_t1)
So, drug:time3 - drug:time2:
(drug_t3 – drug_t2) - (ctrl_t3 – ctrl_t2) ?
“What are the genes that are differentially expressed between drugged mice in time3 and in time2 while controlling for vehicle effects?”
![Page 293: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/293.jpg)
What if we want to compute
We know that drug:time2 corresponds to?
drug:time3(drug_t2 – drug_t1) - (ctrl_t2 – ctrl_t1) drug:time2: (drug_t3 – drug_t1) - (ctrl_t3 – ctrl_t1)
So, drug:time3 - drug:time2:
(drug_t3 – drug_t2) - (ctrl_t3 – ctrl_t2)
(drug_t3 – drug_t2) - (ctrl_t3 – ctrl_t2) ?
“What are the genes that are differentially expressed between drugged mice in time3 and in time2 while controlling for vehicle effects?”
![Page 294: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/294.jpg)
Use contrast matrix for arbitrary comparison
Expression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
![Page 295: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/295.jpg)
Use contrast matrix for arbitrary comparison
Expression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
![Page 296: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/296.jpg)
Use contrast matrix for arbitrary comparison
Expression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
InterceptDrugTime2Time3Drug:time2Drug:time3
coefficients
![Page 297: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/297.jpg)
Use contrast matrix for arbitrary comparison
Expression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
[0, 0, 0, 0, -1, 1] InterceptDrugTime2Time3Drug:time2Drug:time3
contrast coefficients
![Page 298: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/298.jpg)
Use contrast matrix for arbitrary comparison
Expression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
[0, 0, 0, 0, -1, 1] InterceptDrugTime2Time3Drug:time2Drug:time3
=
contrast coefficients
![Page 299: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/299.jpg)
Use contrast matrix for arbitrary comparison
Expression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
[0, 0, 0, 0, -1, 1] InterceptDrugTime2Time3Drug:time2Drug:time3
= Drug:time3 - Drug:time2
contrast coefficients
![Page 300: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/300.jpg)
Use contrast matrix for arbitrary comparison
Expression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
[0, 0, 0, 0, -1, 1] InterceptDrugTime2Time3Drug:time2Drug:time3
= Drug:time3 - Drug:time2
contrast coefficients result
![Page 301: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/301.jpg)
Use contrast matrix for arbitrary comparison
Expression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
![Page 302: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/302.jpg)
Use contrast matrix for arbitrary comparison
Expression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
![Page 303: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/303.jpg)
Use contrast matrix for arbitrary comparison
Expression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
![Page 304: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/304.jpg)
Use contrast matrix for arbitrary comparison
Expression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
![Page 305: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/305.jpg)
Use contrast matrix for arbitrary comparison
Expression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
![Page 306: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/306.jpg)
Use contrast matrix for arbitrary comparison
Expression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
general linear hypothesis test
![Page 307: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/307.jpg)
Use contrast matrix for arbitrary comparison
Expression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
general linear hypothesis test
![Page 308: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/308.jpg)
Use contrast matrix for arbitrary comparison
Expression = Intercept + drug+ time2 + time3+ drug:time2+ drug:time3
![Page 309: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/309.jpg)
If using interaction is confusing…
![Page 310: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/310.jpg)
If using interaction is confusing…
Make combined factor
![Page 311: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/311.jpg)
If using interaction is confusing…
Make combined factor
![Page 312: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/312.jpg)
If the interaction is confusing…
![Page 313: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/313.jpg)
Fit classtime instead, and use contrast
![Page 314: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/314.jpg)
Fit classtime instead, and use contrast
lm ( expression ~ classtime ,data = data)
![Page 315: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/315.jpg)
Fit classtime instead, and use contrast
lm ( expression ~ classtime ,data = data)
![Page 316: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/316.jpg)
nxhExpression = control_t1 + control_t2+ control_t3 + drug_t1 + drug_t2 + drug_t3
![Page 317: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/317.jpg)
nxhExpression = control_t1 + control_t2+ control_t3 + drug_t1 + drug_t2 + drug_t3
![Page 318: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/318.jpg)
Expression = control_t1 + control_t2+ control_t3 + drug_t1 + drug_t2 + drug_t3
![Page 319: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/319.jpg)
Expression = control_t1 + control_t2+ control_t3 + drug_t1 + drug_t2 + drug_t3
![Page 320: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/320.jpg)
Expression = control_t1 + control_t2+ control_t3 + drug_t1 + drug_t2 + drug_t3
To compute , (drug_t3- drug_t2) – (control_t3 – control_t2)
![Page 321: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/321.jpg)
Expression = control_t1 + control_t2+ control_t3 + drug_t1 + drug_t2 + drug_t3
To compute , (drug_t3- drug_t2) – (control_t3 – control_t2)
Use contrast:
![Page 322: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/322.jpg)
Expression = control_t1 + control_t2+ control_t3 + drug_t1 + drug_t2 + drug_t3
To compute , (drug_t3- drug_t2) – (control_t3 – control_t2)
Use contrast: [ 0, 1, -1 , 0, -1, 1 ]
![Page 323: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/323.jpg)
To compute , (drug_t3- drug_t2) – (control_t3 – control_t2)
Use contrast: [ 0, 1, -1 , 0, -1, 1 ]
![Page 324: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/324.jpg)
To compute , (drug_t3- drug_t2) – (control_t3 – control_t2)
Use contrast: [ 0, 1, -1 , 0, -1, 1 ]
![Page 325: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/325.jpg)
To compute , (drug_t3- drug_t2) – (control_t3 – control_t2)
Use contrast: [ 0, 1, -1 , 0, -1, 1 ]
![Page 326: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/326.jpg)
To compute , (drug_t3- drug_t2) – (control_t3 – control_t2)
Use contrast: [ 0, 1, -1 , 0, -1, 1 ]
![Page 327: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/327.jpg)
To compute , (drug_t3- drug_t2) – (control_t3 – control_t2)
Use contrast: [ 0, 1, -1 , 0, -1, 1 ]
![Page 328: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/328.jpg)
To compute , (drug_t3- drug_t2) – (control_t3 – control_t2)
Use contrast: [ 0, 1, -1 , 0, -1, 1 ]
![Page 329: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/329.jpg)
To compute , (drug_t3- drug_t2) – (control_t3 – control_t2)
Use contrast: [ 0, 1, -1 , 0, -1, 1 ]
Previous method
![Page 330: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/330.jpg)
To compute , (drug_t3- drug_t2) – (control_t3 – control_t2)
Use contrast: [ 0, 1, -1 , 0, -1, 1 ]
Previous method
![Page 331: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/331.jpg)
Level 4 “Pre-Post-Control” Design
![Page 332: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/332.jpg)
Study design
• Pre-post-control study design
control
Drug
pre treatment post treatment
![Page 333: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/333.jpg)
Study design
• Pre-post-control study design
control
Drug
pre treatment post treatment
![Page 334: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/334.jpg)
Study design
• Pre-post-control study design
control
Drug
pre treatment post treatment
![Page 335: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/335.jpg)
TIMTOADY(There’s more than one way to do it)
![Page 336: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/336.jpg)
TIMTOADY(There’s more than one way to do it)
![Page 337: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/337.jpg)
TIMTOADY(There’s more than one way to do it)
• Using Interaction
![Page 338: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/338.jpg)
TIMTOADY(There’s more than one way to do it)
• Using Interaction • Use expression as dependent variable and use treatment, Patient and treatment interaction, and time
and treatment interaction as independent variables
![Page 339: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/339.jpg)
TIMTOADY(There’s more than one way to do it)
• ~ + : + :
• Using Interaction • Use expression as dependent variable and use treatment, Patient and treatment interaction, and time
and treatment interaction as independent variables~ + : + :
![Page 340: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/340.jpg)
TIMTOADY(There’s more than one way to do it)
• ~ + : + :
• Using Interaction • Use expression as dependent variable and use treatment, Patient and treatment interaction, and time
and treatment interaction as independent variables~ + : + :
![Page 341: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/341.jpg)
TIMTOADY(There’s more than one way to do it)
• ~ + : + :
• Using Interaction • Use expression as dependent variable and use treatment, Patient and treatment interaction, and time
and treatment interaction as independent variables~ + : + :
![Page 342: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/342.jpg)
TIMTOADY(There’s more than one way to do it)
• ~ + : + :
• Using Interaction • Use expression as dependent variable and use treatment, Patient and treatment interaction, and time
and treatment interaction as independent variables~ + : + :
![Page 343: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/343.jpg)
TIMTOADY(There’s more than one way to do it)
• ~ + : + :
• Using Interaction • Use expression as dependent variable and use treatment, Patient and treatment interaction, and time
and treatment interaction as independent variables• Using Mixed model
![Page 344: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/344.jpg)
TIMTOADY(There’s more than one way to do it)
• ~ + : + :
• Using Interaction • Use expression as dependent variable and use treatment, Patient and treatment interaction, and time
and treatment interaction as independent variables• Using Mixed model
• Use expression as dependent variable and use treatment and treatment and time interaction as fixed effects and patients as random effects.
![Page 345: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/345.jpg)
TIMTOADY(There’s more than one way to do it)
• + : 1+ 1+ 1+)
• ~ + : + :
• Using Interaction • Use expression as dependent variable and use treatment, Patient and treatment interaction, and time
and treatment interaction as independent variables• Using Mixed model
• Use expression as dependent variable and use treatment and treatment and time interaction as fixed effects and patients as random effects.
~ + : + 1 + )
![Page 346: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/346.jpg)
TIMTOADY(There’s more than one way to do it)
• + : 1+ 1+ 1+)
• ~ + : + :
• Using Interaction • Use expression as dependent variable and use treatment, Patient and treatment interaction, and time
and treatment interaction as independent variables• Using Mixed model
• Use expression as dependent variable and use treatment and treatment and time interaction as fixed effects and patients as random effects.
~ + : + 1 + )
![Page 347: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/347.jpg)
TIMTOADY(There’s more than one way to do it)
• + : 1+ 1+ 1+)
• ~ + : + :
• Using Interaction • Use expression as dependent variable and use treatment, Patient and treatment interaction, and time
and treatment interaction as independent variables• Using Mixed model
• Use expression as dependent variable and use treatment and treatment and time interaction as fixed effects and patients as random effects.
~ + : + 1 + )
Assume Patients are random samples (from the hypothetical population)
![Page 348: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/348.jpg)
TIMTOADY(There’s more than one way to do it)
~
~ +
![Page 349: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/349.jpg)
TIMTOADY(There’s more than one way to do it)
~
~ +
![Page 350: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/350.jpg)
TIMTOADY(There’s more than one way to do it)
• Using Gain of score
~
~ +
![Page 351: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/351.jpg)
TIMTOADY(There’s more than one way to do it)
• Using Gain of score• Compute the difference between post and pre expression as a response variable
(Diff Expression) and use treatment as a independent variable~
~ +
![Page 352: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/352.jpg)
TIMTOADY(There’s more than one way to do it)
• ~ • Using Gain of score
• Compute the difference between post and pre expression as a response variable (Diff Expression) and use treatment as a independent variable
~
~ +
![Page 353: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/353.jpg)
TIMTOADY(There’s more than one way to do it)
• ~ • Using Gain of score
• Compute the difference between post and pre expression as a response variable (Diff Expression) and use treatment as a independent variable
~
~ +
![Page 354: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/354.jpg)
TIMTOADY(There’s more than one way to do it)
• ~ • Using Gain of score
• Compute the difference between post and pre expression as a response variable (Diff Expression) and use treatment as a independent variable
~
~ +
![Page 355: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/355.jpg)
TIMTOADY(There’s more than one way to do it)
• ~ • Using Gain of score
• Compute the difference between post and pre expression as a response variable (Diff Expression) and use treatment as a independent variable
~
~ +
![Page 356: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/356.jpg)
TIMTOADY(There’s more than one way to do it)
• ~ • Using Gain of score
• Compute the difference between post and pre expression as a response variable (Diff Expression) and use treatment as a independent variable
~
~ +
![Page 357: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/357.jpg)
TIMTOADY(There’s more than one way to do it)
• ~ • Using Gain of score
• Compute the difference between post and pre expression as a response variable (Diff Expression) and use treatment as a independent variable
~
~ +
![Page 358: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/358.jpg)
TIMTOADY(There’s more than one way to do it)
• ~ • Using Gain of score
• Compute the difference between post and pre expression as a response variable (Diff Expression) and use treatment as a independent variable
~
~ +
![Page 359: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/359.jpg)
TIMTOADY(There’s more than one way to do it)
• ~ • Using Gain of score
• Compute the difference between post and pre expression as a response variable (Diff Expression) and use treatment as a independent variable
• Using ANCOVA
~ +
![Page 360: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/360.jpg)
TIMTOADY(There’s more than one way to do it)
• ~ • Using Gain of score
• Compute the difference between post and pre expression as a response variable (Diff Expression) and use treatment as a independent variable
• Using ANCOVA • Use post as a response variable (Y) and fit the linear/general linear model
using factors and also pre as a covariate
~ +
![Page 361: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/361.jpg)
TIMTOADY(There’s more than one way to do it)
• +
• ~ • Using Gain of score
• Compute the difference between post and pre expression as a response variable (Diff Expression) and use treatment as a independent variable
• Using ANCOVA • Use post as a response variable (Y) and fit the linear/general linear model
using factors and also pre as a covariate~ +~ +
![Page 362: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/362.jpg)
TIMTOADY(There’s more than one way to do it)
• +
• ~ • Using Gain of score
• Compute the difference between post and pre expression as a response variable (Diff Expression) and use treatment as a independent variable
• Using ANCOVA • Use post as a response variable (Y) and fit the linear/general linear model
using factors and also pre as a covariate~ +~ +
![Page 363: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/363.jpg)
TIMTOADY(There’s more than one way to do it)
• +
• ~ • Using Gain of score
• Compute the difference between post and pre expression as a response variable (Diff Expression) and use treatment as a independent variable
• Using ANCOVA • Use post as a response variable (Y) and fit the linear/general linear model
using factors and also pre as a covariate~ +~ +
![Page 364: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/364.jpg)
In the real world…
![Page 365: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/365.jpg)
We have assumed that
![Page 366: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/366.jpg)
We have assumed that
![Page 367: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/367.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
![Page 368: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/368.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
data generation problem
![Page 369: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/369.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.
data generation problem
![Page 370: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/370.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.
data generation problem
non-normality problem
![Page 371: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/371.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).
data generation problem
non-normality problem
![Page 372: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/372.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).
data generation problem
non-normality problem
small replicate size problem
![Page 373: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/373.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).
data generation problem
non-normality problem
small replicate size problem
![Page 374: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/374.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.
data generation problem
non-normality problem
small replicate size problem
![Page 375: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/375.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.
data generation problem
non-normality problem
small replicate size problem
normalization problem
![Page 376: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/376.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
non-normality problem
small replicate size problem
normalization problem
![Page 377: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/377.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problem
![Page 378: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/378.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. e have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemD
![Page 379: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/379.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. e have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemD
![Page 380: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/380.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. e have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemD
Gee. Tophat takes hours and hours
![Page 381: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/381.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. e have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemD
Gee. Tophat takes hours and hours
Remedy:
![Page 382: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/382.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. e have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemD
Gee. Tophat takes hours and hours
Remedy:1) Use STAR aligner instead. It should take 4 to 8 minutes.
![Page 383: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/383.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. e have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemD
Gee. Tophat takes hours and hours
Remedy:1) Use STAR aligner instead. It should take 4 to 8 minutes. 2) Utilize multithreads.
![Page 384: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/384.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. e have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemD
Gee. Tophat takes hours and hours
Remedy:1) Use STAR aligner instead. It should take 4 to 8 minutes. 2) Utilize multithreads.
Ex) What could takes 30 minutes can be done in 30 seconds
![Page 385: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/385.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. e have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemD
![Page 386: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/386.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. e have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemD
![Page 387: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/387.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. e have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemD
“Not really. RNAseq is usually measured in counts”
![Page 388: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/388.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. e have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemD
“Not really. RNAseq is usually measured in counts”
Remedy:
![Page 389: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/389.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. e have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemD
1) Assume negative binomial and fit generalized linear model
“Not really. RNAseq is usually measured in counts”
Remedy:
![Page 390: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/390.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. e have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemD
1) Assume negative binomial and fit generalized linear model
2) Transform your counts to log and fit linear model
“Not really. RNAseq is usually measured in counts”
Remedy:
![Page 391: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/391.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problem
![Page 392: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/392.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problem
![Page 393: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/393.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemNot really. RNAseq sample size is usually 2~ 3 per group
![Page 394: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/394.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemNot really. RNAseq sample size is usually 2~ 3 per group
Remedy:
![Page 395: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/395.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemNot really. RNAseq sample size is usually 2~ 3 per group
Remedy:Use some sort of shrinkage method to stabilize variance(borrowing information of all genes)
![Page 396: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/396.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problemNot really. RNAseq sample size is usually 2~ 3 per group
Remedy:Use some sort of shrinkage method to stabilize variance(borrowing information of all genes)Use edgeR, DESeq, Voom
![Page 397: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/397.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problem
![Page 398: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/398.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problem
![Page 399: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/399.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problem
Remedy:
![Page 400: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/400.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problem
Remedy:There are many normalization schemes. Choose one.
![Page 401: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/401.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problem
![Page 402: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/402.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problem
![Page 403: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/403.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problem
Remedy:
![Page 404: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/404.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problem
Remedy:1) Use Cufflinks, RSEM, Stringtie, etc.
![Page 405: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/405.jpg)
We have assumed that
1. All heavy biological & computational works(sequencing, preprocessing, alignment, and counting ) have been done.
2. Expression measurement follows normal distribution.3. We have a large size of experimental units(+100 samples).4. Normalization is taken care of.5. Expression measurements are collected at gene level.
data generation problem
Isoform problem
non-normality problem
small replicate size problem
normalization problem
Remedy:1) Use Cufflinks, RSEM, Stringtie, etc. 2) Exon level counting
![Page 406: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/406.jpg)
Big Picture
![Page 407: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/407.jpg)
Prof. Peter Sims’ Talks
Albert Lee’s Talk
Alexander Lachmann’s Talk
Prof. Friedman’s Talk
![Page 408: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/408.jpg)
Prof. Peter Sims’ Talks
Albert Lee’s Talk
Alexander Lachmann’s Talk
Prof. Friedman’s Talk
![Page 409: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/409.jpg)
RNA-seq
Prof. Peter Sims’ Talks
Albert Lee’s Talk
Alexander Lachmann’s Talk
![Page 410: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/410.jpg)
Cells to reads
RNA-seq
Albert Lee’s Talk
Alexander Lachmann’s Talk
![Page 411: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/411.jpg)
Cells to reads
RNA-seq
“How do you efficiently capture the high quality biological data with little cost yet high resolution?”
Albert Lee’s Talk
Alexander Lachmann’s Talk
![Page 412: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/412.jpg)
Cells to reads
RNA-seq
“How do you efficiently capture the high quality biological data with little cost yet high resolution?”
Albert Lee’s Talk
Alexander Lachmann’s Talk
![Page 413: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/413.jpg)
Cells to reads Reads to ranked gene list
RNA-seq
“How do you efficiently capture the high quality biological data with little cost yet high resolution?”
Alexander Lachmann’s Talk
![Page 414: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/414.jpg)
Cells to reads Reads to ranked gene list
RNA-seq
“How do you efficiently capture the high quality biological data with little cost yet high resolution?”
“What is the most interesting subset of genes within our experiment design?”
Alexander Lachmann’s Talk
![Page 415: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/415.jpg)
Cells to reads Reads to ranked gene list Gene list to knowledge
RNA-seq
“How do you efficiently capture the high quality biological data with little cost yet high resolution?”
“What is the most interesting subset of genes within our experiment design?”
![Page 416: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/416.jpg)
Cells to reads Reads to ranked gene list Gene list to knowledge
RNA-seq
“How do you efficiently capture the high quality biological data with little cost yet high resolution?”
“What is the most interesting subset of genes within our experiment design?”
“What’s the biological meaning of those genes that are affected?”
![Page 417: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/417.jpg)
Cells to reads Reads to ranked gene list Gene list to knowledge
RNA-seq
Biological question
![Page 418: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/418.jpg)
Cells to reads Reads to ranked gene list Gene list to knowledge
RNA-seq
Biological question
![Page 419: Design of “RNA-seq” Experiments - Columbia Universitysystemsbiology.columbia.edu/sites/default/files/Design_of_rnaseq... · Design of “RNA-seq” Experiments RabadanLab 06/29/2015](https://reader031.vdocuments.us/reader031/viewer/2022013014/5ad20db87f8b9a72118ca858/html5/thumbnails/419.jpg)
Cells to reads Reads to ranked gene list Gene list to knowledge
RNA-seq
Biological question
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On that note….
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Sir Ronald Aylmer FisherFather of “Design of Experiments”
On that note….
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Sir Ronald Aylmer FisherFather of “Design of Experiments”
“The statistician cannot evade the responsibility for understanding the process he applies or recommends”
On that note….
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THE END