[BioC] limma: coefficient not estimable when dataset reduced by a few samples

[Gordon K Smyth]

Dear Natasha,

The results limma has given you are completely correct.

As James MacDonald has explained, the reason for the warning is that you 
have put too many variables into the model.  There is no need to correct 
for the batch effect, because you are already correcting for baseline 
differences between the patients, and this includes the batch effect 
because the patients are different in the two batches.  You will have got 
exactly the same warning even with 42 patients, unless one or more of the 
patient appeared in both batches.

When you put the unnecessary batch term into model, limma automatically 
adjusts the model for you, removing the unnecessary terms, and gives you 
exactly the same paired t-test that you would have got had you not added 
the batch effect.  The warning is just to let you know that an adjustment 
was made.

In other words, limma gives you the correct test whether or not you put in 
extra unnecessary between-patient terms.  The fact that NA coefficients 
are produced has no effect at all on your tests for the treatment effect.

Best wishes
Gordon

----------- original message -------------
[BioC] limma: coefficient not estimable when dataset reduced by a few 
samples
Natasha Sahgal nsahgal at well.ox.ac.uk
Fri Aug 3 14:11:31 CEST 2012

Dear List,

I have array data for 42 tumorBT - tumorAT patients. Initial analysis
(adding patient and batch covariates to the model) I managed to obtain a
list of DE genes.

However now, I need to reduce this set of 42 to 33 patients pairs and
reanalyse the data. This time though it seems that it can't estimate the
coefficient of one patient, would this not affect my results as NA
coefficients are produced?

What I do not understand is what has changed for this to happen now? How
do I rectify it?

Code:
dim(tum.dat.red)
27555 66

## Overall Sample Descriptions
>batch = as.factor(t.info.red$Batch)
batch
  [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 2 2
[39] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
Levels: 1 2


>treat = droplevels(t.info.red$Status_Treatment)
>treat = as.factor(treat, levels=c("Tumour_BT", "Tumour_AT"))
treat
[1] Tumour_AT Tumour_BT Tumour_BT Tumour_AT Tumour_AT Tumour_BT Tumour_BT
  [8] Tumour_AT Tumour_BT Tumour_AT Tumour_AT Tumour_BT Tumour_BT Tumour_AT
[15] Tumour_BT Tumour_AT Tumour_AT Tumour_BT Tumour_BT Tumour_AT Tumour_BT
[22] Tumour_AT Tumour_AT Tumour_BT Tumour_BT Tumour_AT Tumour_BT Tumour_AT
[29] Tumour_BT Tumour_AT Tumour_AT Tumour_BT Tumour_BT Tumour_AT Tumour_AT
[36] Tumour_BT Tumour_BT Tumour_BT Tumour_BT Tumour_BT Tumour_BT Tumour_BT
[43] Tumour_BT Tumour_BT Tumour_AT Tumour_AT Tumour_AT Tumour_AT Tumour_AT
[50] Tumour_AT Tumour_AT Tumour_AT Tumour_BT Tumour_BT Tumour_BT Tumour_BT
[57] Tumour_BT Tumour_BT Tumour_BT Tumour_AT Tumour_AT Tumour_AT Tumour_AT
[64] Tumour_AT Tumour_AT Tumour_AT
Levels: Tumour_BT Tumour_AT


>patient = as.factor(t.info.red$Trial.number)
patient
  [1] 13 25 13 25 18 28 18 28 30 39 30 53 39 53 32 42 32 51 42 51 34 45 34
55 45
[26] 55 54 54 37 57 37 57 35 52 35 52 17 7  12 10 14 11 16 15 14 16 15 17
7  12
[51] 10 11 20 26 36 40 48 23 24 23 20 24 26 36 40 48
33 Levels: 7 10 11 12 13 14 15 16 17 18 20 23 24 25 26 28 30 32 34 35 36
... 57


## Deisgning model with BATCH effect
>design.tum = model.matrix(~treat+batch+patient)

## Fit model  & make contrasts
> fit.tum <- lmFit(tum.dat.red, design.tum)
Coefficients not estimable: patient57
Warning message:
Partial NA coefficients for 27555 probe(s)


sessionInfo()
R version 2.15.0 (2012-03-30)
Platform: x86_64-pc-linux-gnu (64-bit)

locale:
  [1] LC_CTYPE=en_GB.UTF-8       LC_NUMERIC=C
  [3] LC_TIME=en_GB.UTF-8        LC_COLLATE=en_GB.UTF-8
  [5] LC_MONETARY=en_GB.UTF-8    LC_MESSAGES=en_GB.UTF-8
  [7] LC_PAPER=C                 LC_NAME=C
  [9] LC_ADDRESS=C               LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

other attached packages:
[1] limma_3.12.0

loaded via a namespace (and not attached):
[1] tools_2.15.0


Many Thanks in advance,
Natasha

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