Hello everyone. I have a little question about how to design a matrix taking into account covariables.

Subject : I have got agilent microarray data from 12 samples (6 mild malaria sample noted "MM" and 6 cerebral malaria noted "CM"). Data relative to age, sexe, ethnie and leucocytes count are also proven for each sample. These later parameters (age, sex and leucocytes counts) are in categorical form using some thresholds that we have chosen to classify them.

Objective : I want get differentially expressed genes (DEGs) comparing "MM" and "CM" samples whils taking into account the effect of age, sexe and leucocytes count.

What i did

1. Creating a data frame (called "targets") containing all informations that i need. Columns SEXE, AGE and LEUC are factors with "0" and "1" for levels and column "PHENO" is factor with levels "MM" and "CM"

 FileName      PHENO SEXE AGE LEUC
 NP15014.txt     CM    1   1    1
 NP15016.txt     CM    0   1    0
 TA15052.txt     CM    1   0    1
 HPIKNP01.txt    CM    1   0    0
 NP15013.txt     CM    1   1    1
 NP15015.txt     CM    0   1    0
 TA16037.txt     MM    1   0    1
 TA16036.txt     MM    1   0    1
 TA16035.txt     MM    0   0    1
 TA16031.txt     MM    0   1    1
 TA16006.txt     MM    1   0    0
 HPIKPS01.txt    MM    0   0    0

2. Creating desing by this commands

>  design <- model.matrix(~PHENO*AGE*SEXE*LEUC, data = targets)

>  Fit_design <- lmfit (my_ExpressionSet, design)     

## i got this errror message

Coefficients not estimable: SEXE1:AGE1 AGE1:LEUC1 PHENOMM:SEXE1:AGE1 PHENOMM:SEXE1:LEUC1 PHENOMM:AGE1:LEUC1 SEXE1:AGE1:LEUC1 PHENOMM:SEXE1:AGE1:LEUC1  ##

As you can see, the fiting results are wrong for almost of the design matrix coefficients. So topTable results is also wrong.

My question

Using the "targets" table above, how i can create a design matrix with model.matrix which allow me to get DEGs between "CM" and "MM" (my  real goal) but taking into account age, sexe and leuc as covariables (confounders).

Any help will be really appreciable.

Dieureudieuf in advance.

Hi ! Short answer: you are trying to estimate nearly as many parameters as samples. The * in the formula means that you are looking for interactions between the factors as well as well the factors independently. In order to estimate the factors without interactions, replace * by +. Long answer: I guess Aaron or Gordon will perform than me.

You have two options. The first (and recommended) approach is to follow SamGG's suggestion, and replace the * with + in your model.matrix call. This assumes that the effects of the confounders on log-expression are additive. You can then test for the effect of PHENO by selecting the appropriate coefficient in topTable (probably coef=2). Your original post mentions that you want the MM vs CM comparison, so I don't understand what you mean in your second post when you say that it's not what you're looking for.

The second option is to concatenate some or all of the factors into a single grouping variable. In the most extreme case, let's say we concatenate all of the factors:

group <- with(targets, paste(PHENO, AGE, SEXE, LEUC, sep="."))
design <- model.matrix(~0 + group)

You can then perform comparisons between MM and CM at each combination of the confounding factors, using makeContrasts. This avoids the additivity assumption for all of the factors that were concatenated together. However, for this to work, you need many samples, and 12 probably isn't enough for the 4 factors that you want to model in your design.

P.S. Please respond to answers with the "Add comment" button, not "Add answer" unless you are answering your own question.