[BioC] Limma design matrix for time course experiment

[Gordon K Smyth]

Dear Uthra Suresh,

There is no single shrink-wrapped analysis which is standard and correct 
for a time course experiment, or for any experiment really.  Rather the 
appropriate analysis depends on what questions are of interest to you and 
relevant to the biology of the experiment.  Each analysis is the answer to 
a particular question.  The section of the Limma User's Guide that you 
refer to tries to emphasise this point by posing each contrast matrix in 
terms of a question.

Both of the contrast matrices that you give are corrrect, they just answer 
different questions.  See below.

> Date: Fri, 2 Apr 2010 15:15:30 -0500
> From: "Suresh, Uthra" <suresh at uthscsa.edu>
> To: "bioconductor at stat.math.ethz.ch" <bioconductor at stat.math.ethz.ch>
> Subject: [BioC] Limma design matrix for time course experiment
> Content-Type: text/plain
>
> Hello List,
>
> I am currently working on Affy arrays for a time course experiment. I have two groups (Control and Treated) with samples taken at 1hr, 24hrs and 48hrs.
>
> The following is how my targets file looks like:
> FileName      Targets
> Files 1-4       control.0hr
> Files 5-8       control.1hr
> Files 9-12      treatment.1hr
> Files 13-16     control.24hr
> Files 17-20     treatment.24hr
> Files 21-24     control.48hr
> Files 25-28     treatment.48hr
>
> I followed the limma user guide (pg48 and 49) to set up the design matrix for the lmFit test.  A part of the design matrix is given below.
>
> Design:
>   fcon.0hr fcon.1hr fmms.1hr fcon.24hr fmms.24hr fcon.48hr fmms.48hr
> 1         1        0        0         0         0         0         0
> 2         1        0        0         0         0         0         0
> 3         1        0        0         0         0         0         0
> 4         1        0        0         0         0         0         0
> 5         0        1        0         0         0         0         0
> 6         0        1        0         0         0         0         0
> 7         0        1        0         0         0         0         0
> 8         0        1        0         0         0         0         0
>
> I have 7 columns and 28 rows in my design matrix.
> I am now interested to look at the differentially expressed genes between the control and treated samples across different time points.
>
> I have the following questions:
>
>
> 1.  Should my contrast matrix be,
> cont.dif<-makeContrasts(Dif1hr=(fmms.1hr-fcon.0hr)-(fcon.1hr-fcon.0hr),
>                        Dif24hr=(fmms.24hr-fmms.1hr)-(fcon.24hr-fcon.1hr),
>                        Dif48hr=(fmms.48hr-fmms.24hr)-(fcon.48hr-fcon.24hr),
>                        levels=design)?
>
>
> 2.  If yes, does Dif24hr give those genes that are differentially expressed between the treated and control samples from time 1hr to 24hrs and similarly for Dif48hr?
>
>
>
> 3.  Can the following contrast matrix also be used?
>
>
>
> cont.dif1<-makeContrasts(Dif1hr=(fmms.1hr- fcon.1hr),
>                    Dif24hr=(fmms.24hr-fcon.24hr),
>                     Dif48hr=(fmms.48hr- fcon.48hr),
>
>                    levels=design)? (this contrast matrix completely ignores the files for the control samples at time 0hr? can this be correct?)

The second contrast matrix is correct if you want to find genes which are 
differentially expressed between the treatment and control at each time 
point.

The first contrast matrix is correct if you want to find genes which 
change over time differently between the treatment and the control.

With the second design matrix you are looking for straight differences in 
expression.  With the first design you are looking for differences between 
time-specific responses, i.e., differences between changes in expression. 
(Statisticians call this an interaction effect.) Results from the second 
matrix will include genes which are different between control and 
treatment regardless of time.  The first matrix instaed focuses on 
time-course changes, mostly subtracting out any baseline differences.

What question do you want to ask?  Only you can decide.

Best wishes
Gordon


> I would really appreciate if someone can suggest an appropriate method 
> to deal with this kind of experimental design.
>
> Thank you,
> Regards,
> Uthra Suresh
> UTHSCSA

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