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BIOS 101 Week 1, Lecture 1Overview

• Teaching Method:– Lecture, readings and some hands on exercise– More Concept based learning, What, When, Where and How ?

• Tentative Planning: About 17 lectures (twice a month)• Books

– Biostatistics: A methodology for health Sciences (Second edition) by van Belle, Fisher, Heagerty and Lumley, Wiley-Interscience.

– Fundamentals of Biostatistics (Seventh Edition) by Bernard Rosner, Duxbury Press

• Slides will loaded on to this site – https://ephpublic.aecom.yu.edu/sites/SViswanathan/default.aspx

• We will cover basically from Descriptive statistics to Multivariable methods

• Software: R

Article Discussion

• Chang et.al “Treatment results of hypopharyngeal cancer by different treatment startegies and its secondary primary- experience in Taiwan”, Radiation oncology, 2010, 5:91

• WHAT is the study about and what is important in the article

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BIOS 101 Week 1, Lecture 1An Introduction to R

• R is a statistical language and environment for data analysis and display.

• The syntax of R is almost the same as that of S (or S-Plus).• R is free! It is open-source and involves many developers.• R is object-oriented• R/Splus are good packages for certain kinds of graphics and

data exploration• R is flexible, but also pretty low level for certain types of

tasks. Thus you might take longer to set up a regression analysis in R than in, say, SAS. But other types of analysis or plots can be much simpler in R.

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• Main page at http://www.r-project.org/

In the words of the developers, R is/has:• an effective data handling and storage facility, • a suite of operators for calculations on arrays, in

particular matrices, • a large, coherent, integrated collection of intermediate

tools for data analysis, • graphical facilities for data analysis and display either

on-screen or on hardcopy, and • a well-developed, simple and effective programming

language which includes conditionals, loops, user-defined recursive functions and input and output facilities.

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Links for downloads

Pre-compiled binaries for most systems of interest

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• Many useful R packages are not included in the base distribution, and must be added

• Students are responsible for getting R on a machine they can use (ask me if you need help!). It’s a snap to install on a PC

• E.g., Start->Programs->Statistical Applications->R or something similar

• I will follow some parts from “An Introduction to R” (Venables/Smith/Gentleman R Core Development Team) at http://cran.r-project.org/doc/manuals/R-intro.pdf and “R for Beginners” (Paridis) http://cran.r-project.org/doc/contrib/Paradis-rdebuts_en.pdf

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• I will describe the interactive shell mode (text window) command-line use of R.

• For windows machines, a graphical interface appears, but here I will use the “console” window, so it’s pretty much the same as with the Unix machines.

• I will follow some parts from “An Introduction to R” (Venables/Smith/Gentleman R Core Development Team) at http://cran.r-project.org/doc/manuals/R-intro.pdf and “R for Beginners” (Paridis) http://cran.r-project.org/doc/contrib/rdebuts_en.pdf

• Also I will make comments about things I have found useful

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A schematic view of R (from E. Paridis, R for Beginners, 2002)

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• Object-oriented means that variables, data, functions, results, etc, are stored in the active memory of the computer in the form of objects which have a name. The user can do actions on these objects with operators (arithmetic, logical, and comparison) and functions (which are themselves objects)

• Let’s illustrate by starting with the command line in a new session. You’ll see “>” starting each line

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> nError: Object "n" not found> n<-10> n[1] 10> n=15> n[1] 15

I typed “n” and hit returnDoesn’t exist yet

Now I assign (using <-) the value 10 to object n

Now it exists

Alternate way of assigning. However this is a bit dangerous, if you intended a comparison query.

If the object already exists, its previous value is erased (the modification affects only the objectsin the active memory, not the data on the disk).

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> n==20[1] FALSE> n==15[1] TRUE> n<10[1] FALSE> n>10[1] TRUE> n==n[1] TRUE> a<-15> a< -15[1] FALSE> n==a[1] TRUE

An assignment.A query.

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Functions need an argument, provided in parentheses

> a<-10

> sqrt(a)

> [1] 3.162278

Object names cannot start with digits or periods, but they can have periods (dots) and digits within them

Names are case sensitive

Names that are already in use by R (usually as functions) are a bad idea. Single letter names could be a problem, like “t” (used for the transpose function, etc.). But it’s easy to check.

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> dError: Object "d" not found> tfunction (x) UseMethod("t")<environment: namespace:base>

Variable data types – character, numeric, logical

> a<-"scooby doo"> a[1] "scooby doo"> is.character(a)[1] TRUE> typeof(a)[1] "character"

functions that start with “is” often can answer a question about an object

CHARACTER

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> a<-10> is.numeric(a)[1] TRUE> is.character(a)[1] FALSE> > a<-10/sqrt(2)> a[1] 7.071068> is.numeric(a)[1] TRUE> a^100[1] 8.881784e+84> a^1000[1] Inf> a^(-1000)[1] 0

NUMERIC

Too big

Too tiny

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LOGICAL

> a<-T> a[1] TRUE> a<-TRUE> a[1] TRUE> a+1[1] 2 Treats TRUE as 1, FALSE as zero

when numeric operations performed

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R as calculator

> a<-2> b<-10> c<-3> > (-b+sqrt(b^2-4*a*c))/(2*a)[1] -0.3205505> (-b-sqrt(b^2-4*a*c))/(2*a)[1] -4.679449

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R object types

• Vector: – a one-dimensional array of arbitrary length. Subsets

of the vector may be referenced. All elements of the vector must be of the same data type--numerical, character, etc.

• Matrix: – a two-dimensional array with an arbitrary number of

rows and columns. Subsets of the matrix may be referenced, and individual rows and columns of the matrix may be handled as vectors. Again all elements of the matrix must be of the same data type.

• Array: – as a matrix, but of arbitrary dimension.

Source: http://www.ma.hw.ac.uk/~stan/R/Rnotes.pdf

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So far we have assigned a single element to each object. This is a special case of a vector.

> a<-c(1,2,3,4)> a[1] 1 2 3 4> a<-(1:4)> a[1] 1 2 3 4> typeof(a)[1] "integer"> is.numeric(a)[1] TRUE> is.vector(a)[1] TRUE>

Special case of numeric type

The “c” function collects things into a single vector

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So far we have assigned a single element to each object. This is a special case of a vector.> a[1] 1 2 3 4> a<-a+1> a[1] 2 3 4 5> a<-c(a, "scooby doo")> a[1] "2" "3" "4" "5" "scooby doo"> typeof(a)[1] "character">

What does this do?

We say that a was “coerced” into the character data type

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I’m impatient. I want to see something cool.

> a<-2> b<-10> c<-3> x<-c(-50:50)/10> > y<-a*x^2+b*x+c> plot(x,y)> abline(0,0)

Vector from what value to what value?

Another vector

Simple scatterplot – two vectors must have elements in the same order

Draws a line on a plot with intercept 0 and slope 0

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> a<-c(1:11)> b<-c(-5:5)> c<-outer(a,b,FUN="*")> c [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [1,] -5 -4 -3 -2 -1 0 1 2 3 4 5 [2,] -10 -8 -6 -4 -2 0 2 4 6 8 10 [3,] -15 -12 -9 -6 -3 0 3 6 9 12 15 [4,] -20 -16 -12 -8 -4 0 4 8 12 16 20 [5,] -25 -20 -15 -10 -5 0 5 10 15 20 25 [6,] -30 -24 -18 -12 -6 0 6 12 18 24 30 [7,] -35 -28 -21 -14 -7 0 7 14 21 28 35 [8,] -40 -32 -24 -16 -8 0 8 16 24 32 40 [9,] -45 -36 -27 -18 -9 0 9 18 27 36 45[10,] -50 -40 -30 -20 -10 0 10 20 30 40 50[11,] -55 -44 -33 -22 -11 0 11 22 33 44 55

Matrix outer product

Complex Math.

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A single element> c[3,2][1] -12

A column > c[,2] [1] -4 -8 -12 -16 -20 -24 -28 -32 -36 -40 -44

A row> c[3,] [1] -15 -12 -9 -6 -3 0 3 6 9 12 15

> image(c)

Both are vectors

Image of a matrix, color corresponds to matrix elements

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More complex graph…a<-c(-440:200)/200b<-c(-300:300)/200b<-complex(length(b),0,b)c<-outer(a,b,FUN="+")magnitude.c<-sqrt(Re(c)^2+Im(c)^2)z<-matrix(0,length(a),length(b))for (i in (1:20)){ z<-z^2+c }magnitude.z<-sqrt(Re(z)^2+Im(z)^2)magnitude.z[is.na(magnitude.z)]<-magnitude.c[is.na(magnitude.z)]^500

image(a,Im(b),-log(magnitude.z)*(magnitude.z>10),col=c(heat.colors(100),1))

Okay, this is a little advanced

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R object types, cont.

• Data frame:

– a set of data organized similarly to a matrix. However, each column of the data frame may contain its own type of data. Columns typically correspond to variables in a statistical study, while rows correspond to observations of these variables. A data frame may be handled similarly to a matrix, and individual columns of the data frame may be handled as vectors.

• List: – an arbitrary collection of other R objects (which may

include other lists).

Source: http://www.ma.hw.ac.uk/~stan/R/Rnotes.pdf

Powerful feature of R

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R object types, cont.

• function:

- Doesn’t have a data type. This is an object that takes other objects as arguments and does something with them.

We’ll cover data frames, lists, and functions more next time

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> help(regression)No documentation for 'regression' in specified packages and libraries:you could try 'help.search("regression")'> > help("regression")No documentation for 'regression' in specified packages and libraries:you could try 'help.search("regression")'> > help("lsfit")> help.search("regression")

Needs quotes

Wrong name anyway

Searching for information/functions

Now we’re getting somewhere (see popup)

Searches for anything with `regression’ in it

How to enter and read data

• To developing a database, you can enter into any available commercial software such as MS Excel, MS Access

• Easy way to upload into R for analysis is by converting either into .csv (comma-separated values) file or .dat (tab delimited file)

• Example data: Smoking, Alcohol and Esophageal Cancer data

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Data information

• Data from a case-control study of esophageal cancer in Ile-et-Vilaine, France

• A data frame with records for 88 age/alcohol/tobacco combinations.– Variables: Age group (agegp), Alcohol

consumption(alcgp), Tobacco consumption (tobgp), # of cases(ncases), # of controls (ncontrols)

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Reading data from.csv or .dat files

• > e.csv<-read.table("Esophageal.csv", header=T, sep=",")

• > e.dat<-read.table("Esophageal.dat", header=T, sep="\t")

• > summary(e.dat) agegp alcgp tobgp ncases ncontrols 25-34:15 0-39g/day:23 0-9g/day:24 Min. : 0.000 Min. : 1.00

35-44:15 120+ :21 10-19 :24 1st Qu.: 0.000 1st Qu.: 3.00

45-54:16 40-79 :23 20-29 :20 Median : 1.000 Median : 6.00

55-64:16 80-119 :21 30+ :20 Mean : 2.273 Mean :11.08

65-74:15 3rd Qu.: 4.000 3rd Qu.:14.00

75+ :11 Max. :17.000 Max. :60.00

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Some basic statistics commands

• >mean(e.dat$ncases)

• >sd(e.dat$ncases)

• >var(e.dat$ncases)

• >plot(e.dat$ncases)

• >hist(e.dat$ncases)

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