Note: this was in answer to: Limma design: paired samples, batch effect

Dear John,

You can't expect to be able to estimate more things than your experiment contains information about.  In this case, your batches are entirely confounded with patients+treatment, and hence you can't estimate coefficients for them. That is what the message from limma is telling you.

BTW, you got a diagnostic message and a warning, not an "error" message.

Best wishes
Gordon

> Date: Thu, 2 Apr 2009 15:22:36 +0300
> From: John Burger <clinicalgenomics at="" gmail.com="">
> Subject: [BioC] Limma design: paired samples, batch effect
> To: bioconductor at stat.math.ethz.ch
> Content-Type: text/plain
>
> Hello,
>
> This is yet again a question about limma design matrices. I would like to
> perform analysis on single channel arrays (Affy). The experimental design
> is: paired samples before and after treatment, and I would also like to take
> into account batch effect.
>
> I am having problems with the batch effect, by reading through mails in this
> mailing list, I've gotten the impression that you can include batch to your
> design matrix, but when I try to do that, I get an error message. Here is a
> simulated example of what I am trying to do:
>
> Create example date, patient (5 patients, 2 samples), treatment (A or B),
> and batch (three batches, 1-3)
>
>> patient <- factor(rep(1:5,2))
>> patient
> [1] 1 2 3 4 5 1 2 3 4 5
> Levels: 1 2 3 4 5
>> treatment <- factor(c(rep("A",5), rep("B",5)))
>> treatment
> [1] A A A A A B B B B B
> Levels: A B
>> batch <- factor(c(rep(1,3), rep(2,3), rep(3,4)))
>> batch
> [1] 1 1 1 2 2 2 3 3 3 3
> Levels: 1 2 3
>
> If I would like to perform a basic analysis between the paired samples and
> not taking into account batch effect, I could just do:
>
>> design <- model.matrix(~patient+treatment)
>> design
>   (Intercept) patient2 patient3 patient4 patient5 treatmentB
> 1            1        0        0        0        0          0
> 2            1        1        0        0        0          0
> 3            1        0        1        0        0          0
> 4            1        0        0        1        0          0
> 5            1        0        0        0        1          0
> 6            1        0        0        0        0          1
> 7            1        1        0        0        0          1
> 8            1        0        1        0        0          1
> 9            1        0        0        1        0          1
> 10           1        0        0        0        1          1
>
> And then use treatmentB to obtain the differences between treatments A and
> B.
>
> But, how could I include batch effect to the model? My inital thought was:
>
>> design <- model.matrix(~patient+treatment+batch)
>> design
>   (Intercept) patient2 patient3 patient4 patient5 treatmentB batch2 batch3
> 1            1        0        0        0        0          0      0      0
> 2            1        1        0        0        0          0      0      0
> 3            1        0        1        0        0          0      0      0
> 4            1        0        0        1        0          0      1      0
> 5            1        0        0        0        1          0      1      0
> 6            1        0        0        0        0          1      1      0
> 7            1        1        0        0        0          1      0      1
> 8            1        0        1        0        0          1      0      1
> 9            1        0        0        1        0          1      0      1
> 10           1        0        0        0        1          1      0     1
>
> But when I do that with actual data, I get the following error message:
>
> Coefficients not estimable: batch2 batch3
> Warning message:
> Partial NA coefficients for 10163 probe(s)
>
> Any ideas what I am doing wrong, and more importantly, what I should do to
> take that batch effect into account?
>
> Thanks,
> John