VERONIQUE STORME

SAS and SAS/EG at the Plant Systems Biology Department

Using the mixed procedure to analyze data with empty cells

random coefficient model with a fitted periodic function

invoke SAS in batch mode in a unix environment passing through environment variables

SAS Enterprise Guide: using prompts

SAS information

outline

Using the mixed procedure to analyze data with empty cells

Leaf area data on 6 different plant varieties

Clustered data

Leaf series analysis: Leaf area was measured on 11 leaves from a single plant

Some varieties have less than 11 leaves

The experiment was performed 3 times

Problem setting

Subject plots

Frequency tables

Table of Line by Leaf

Line Leaf

Frequency 0 1 3 4 5 6 7 8 9 10 11 Total

AA1_H 30 30 30 30 30 30 30 28 12 1 0 251

AA1_WT 30 30 30 30 30 30 30 30 23 4 0 267

AA2_H 28 28 28 28 28 28 28 28 25 5 1 255

AA2_WT 28 28 28 28 28 28 28 28 25 4 0 253

AA3_H 24 24 24 24 24 24 24 23 17 4 0 212

AA3_WT 30 30 30 30 30 30 30 30 28 14 5 287

Total 170 170 170 170 170 170 170 167 130 32 6 1525

Analysis 1:

model Area= Line|Leaf / ddfm = KR ;

repeated leaf/type=un subject=PlantID ;

random int /subject=experiment ;

Analysis 2:

model Area= Line|Leaf / ddfm = KR ;

repeated leaf/type=ar(1) subject=PlantID ;

random int /subject=experiment ;

Analysis 3:

model Area= Line|Leaf ;

repeated leaf/type=ar(1) subject=PlantID ;

random int /subject=experiment

Proc mixed analyses

Results type 3 tests of fixed effects ANALYSIS 1 (KR UN)

Analysis 1:

model Area= Line|Leaf / ddfm = KR ;

repeated leaf/type=un subject=PlantID ;

random int /subject=experiment ;

Analysis 2:

model Area= Line|Leaf / ddfm = KR ;

repeated leaf/type=ar(1) subject=PlantID ;

random int /subject=experiment ;

Analysis 3:

model Area= Line|Leaf ;

repeated leaf/type=ar(1) subject=PlantID ;

random int /subject=experiment

Proc mixed analyses

ANALYSIS 2 (KR AR(1))

Results type 3 tests of fixed effects ANALYSIS 1 (KR UN)

Analysis 1:

model Area= Line|Leaf / ddfm = KR ;

repeated leaf/type=un subject=PlantID ;

random int /subject=experiment ;

Analysis 2:

model Area= Line|Leaf / ddfm = KR ;

repeated leaf/type=ar(1) subject=PlantID ;

random int /subject=experiment ;

Analysis 3:

model Area= Line|Leaf ;

repeated leaf/type=ar(1) subject=PlantID ;

random int /subject=experiment

Proc mixed analyses

ANALYSIS 3 (CONTAINMENT AR(1)) ANALYSIS 2 (KR AR(1))

Results type 3 tests of fixed effects ANALYSIS 1 (KR UN)

Option 1: truncate the data

Option 2: tune the sensitivity in sweeping with the singular option

model Area= Line|Leaf / ddfm = KR singular = 1E-7;

repeated leaf/type=ar(1) subject=PlantID ;

The singular option

random coefficient model with a fitted periodic function

2 Arabidopsis varieties

4 treatment conditions

High-througput phenotyping (IGIS)

Phenotype: compactness

Compactness describes if the leaves are nearer around the centroid or farther away from it, e. g. by having longer stipes

rhythmic leaf movements (circadian clock)

Problem setting

Research question:

Is there an effect of the variety and/or treatment on the amplitude

Mean line plot

Fit a model with a fundamental sine wave

Allow sinusodal deviations for each plant

Assume these random coefficients come from the same normal distribution

Use a single variance component for all the trigonometric components

model compactness =

S C G(enotype) T(reatment) time S*G C*G S*T C*T G*time T*time

S*G*T C*G*T G*T*time/ ddfm=Satterthwaite;

random plantID;

random S*plantID C*plantID /type=toep(1) ;

Where S = sin(2*constant('pi')*time/24)

C = cos(2*constant('pi')*time/24)

The analysis model

b0 + b1*S + b2*C + b3*G1 + b4*T1 + b5*T2 + b6*T3 + b7*time +

b8*S*G1 + b9*C*G1 +

b10*S*T1 + b11*S*T2 + b12*S*T3 + b13*C*T1 + b14*C*T2 + b15*C*T3 +

b16*time*G1 + b17*time*T1 + b18*time*T2 + b19*time*T3 +

b20*S*G1*T1 + b21*S*G1*T2 + b22*S*G1*T3 +

b23*C*G1*T1 + b24*C*G1*T2 + b25*C*G1*T3 +

b26*time*G1*T1 + b27*time*G1*T1 + b28*time*G1*T1

The regression model

Amplitude:

1 + 82 + 2 + 9

2

GT1 AND REF TREATMENT

b0 + b1*S + b2*C + b7*time

Amplitude: 12 + 2

2

REF GT AND REF TREATMENT

Mean predicted amplitude

Amplitude:

1 + 102 + 2 + 13

2

REF GT AND TREATMENT T 1

Amplitude:

1 + 8 + 10 + 202 + 2 + 9 + 13 + 23

2

GT1 AND TREATMENT T 1

Parametric bootstrap (ie resampling residuals)

Fit the model

Bootstrap sample from the residuals

Add the randomly resampled e to Y-hat

Fit the model for each of the B reps

Compute bootstrap estimates

Difficulty: unbalanced clustered data

Standard errors ?

invoke SAS in batch mode in a unix environment passing through environment variables

%let path=%sysget(fullpath); * returns the value as string;

%let libname=%sysget(wkd);

libname &libname "&path";

%include "&path.m_NameConversions.sas" /source2;

%include "&path.m_selectSNPs.sas" /source2;

%include "&path.m_selectPheno.sas" /source2;

%NameConversions(libname=wkd,traitfile=file);

%selectSNPs(libname=wkd);

%selectPheno(libname=wkd);

Main code

[vesto@midas TEST]$ sas

-set fullpath "/group/biostat/myGWASprojects/SNP_ARAB/GCEP/GALAXY/TEST/"

-set wkd "stem"

-set file "stems3.txt"

-sysin workflow_unix.sas

set : defines an environment variable

sysin: specifies an external file

Invoke SAS in batch mode (Red Hat Enterprise LINUX 6)

SAS Enterprise Guide: using prompts

Way to automate your project

Prompts pass parameters to macro variables

Example:

routine two-way analysis of variance where the whole experiment was repeated 3 times independently

Performing simple tests of effects with the plm procedure

SAS Enterprise Guide Prompts

Open the sas program

Create prompts

Assign the prompts to the program

Steps

libname dir "&path";

ods graphics on;

proc mixed data =dir.&inputdata scoring = 3;

class &F1 &F2 █

model &Y=&F1 &F2 &F1.*&F2 /ddfm= satterthwaite solution vciry

outp=out singular=1E-7;

random █

lsmeans &F1.*&F2 ;

repeated /group = &F2 ;

store work.result;

run;

ods graphics off;

proc plm restore = work.result;

slice &F1.*&F2/sliceby=&F2 diff adjust=&method;

effectplot;

lsmeans &F1.*&F2 ;

run;

path

Give the path where the inputdata is located

Name of the

macro

variable

proc plm restore = work.result;

slice &F1.*&F2/sliceby=&F2 diff

adjust=&method;

SAS provides a wealth of information

Koen Knapen

SAS Technical Support:

Aditya

Bart

ACKNOWLEDGEMENTS

Proc mixed manual

Schaalje et al (SAS Paper 262-26)

Cassell D.L. SAS paper 183-2007

Morris J.S., 2002

Shang S and Cavanaugh J.E., 2008

Hettinger P. SAS paper DV-03

REFERENCES

references

Default algorithm to optimize the likelihood function:

ridge-stabilized Newton-Raphson algorithm

Possible problems

covariance parameters are on a different scale

Rescale the effects

poor MIVQUE(0) starting values

Use the Fisher scoring algorithm in the first 3 steps

Proc mixed data = input scoring = 3;

Other convergence problems