Hi! While re-analyzing GSE65106 from GEO, I have constructed a table containing a subset of samples, as follows:

> a # see below for dput(a)
         accession   cond donor batch pair
A1.r1   GSM1587362    ASD   AA1    1a    1
A1.r2   GSM1587363    ASD   AA1    2a    1
A2.r1   GSM1587364    ASD   AA2    1a    2
A2.r2   GSM1587365    ASD   AA2    2a    2
A3.r1   GSM1587366    ASD   AA3    1a    3
A3.r2   GSM1587367    ASD   AA3    2a    3
SC1.r1  GSM1587368 Normal   AN1    3a    1
SC1.r2  GSM1587369 Normal   AN1    3a    1
SC2.r1  GSM1587370 Normal   AN2    3a    2
SC2.r2  GSM1587371 Normal   AN2    3b    2
SC3.r1  GSM1587372 Normal   AN3    3a    3
SC3.r2  GSM1587373 Normal   AN3    3b    3
ASC1.r1 GSM1587374 Normal   NN1    4a    1
ASC1.r2 GSM1587375 Normal   NN1    4a    1
ASC2.r1 GSM1587376 Normal   NN2    4a    2
ASC2.r2 GSM1587377 Normal   NN3    4a    2

Here, r1/r2 are the replications of experiment on the same subject,

Rows named A1\A2 are autistic (diseased) subjects

Rows named SC1\SC2 are sibling controls; the number denoting to which A(diseased subject) they are paired,

Rows named ASC1\2 are age- and sex-matched controls to ADF.

I want to calculate DEGs between ASD & Normal conditions:

    a=structure(list(accession = structure(1:16, .Names = c("ADF.AA1.1", 
"ADF.AA1.2", "ADF.AA2.1", "ADF.AA2.2", "ADF.AA3.1", "ADF.AA3.2", 
"USCf.AN1.1", "USCf.AN1.2", "USCf.AN2.1", "USCf.AN2.2", "USCf.AN3.1", 
"USCf.AN3.2", "ASCF.NN1.1", "ASCF.NN1.2", "ASCF.NN2.1", "ASCF.NN2.2"
), .Label = c("GSM1587362", "GSM1587363", "GSM1587364", "GSM1587365", 
"GSM1587366", "GSM1587367", "GSM1587368", "GSM1587369", "GSM1587370", 
"GSM1587371", "GSM1587372", "GSM1587373", "GSM1587374", "GSM1587375", 
"GSM1587376", "GSM1587377"), class = "factor"), cond = structure(c(ADF.AA1.1 = 1L, 
ADF.AA1.2 = 1L, ADF.AA2.1 = 1L, ADF.AA2.2 = 1L, ADF.AA3.1 = 1L, 
ADF.AA3.2 = 1L, USCf.AN1.1 = 2L, USCf.AN1.2 = 2L, USCf.AN2.1 = 2L, 
USCf.AN2.2 = 2L, USCf.AN3.1 = 2L, USCf.AN3.2 = 2L, ASCF.NN1.1 = 2L, 
ASCF.NN1.2 = 2L, ASCF.NN2.1 = 2L, ASCF.NN2.2 = 2L), .Label = c("ASD", 
"Normal"), class = "factor"), donor = structure(c(ADF.AA1.1 = 1L, 
ADF.AA1.2 = 1L, ADF.AA2.1 = 2L, ADF.AA2.2 = 2L, ADF.AA3.1 = 3L, 
ADF.AA3.2 = 3L, USCf.AN1.1 = 4L, USCf.AN1.2 = 4L, USCf.AN2.1 = 5L, 
USCf.AN2.2 = 5L, USCf.AN3.1 = 6L, USCf.AN3.2 = 6L, ASCF.NN1.1 = 7L, 
ASCF.NN1.2 = 7L, ASCF.NN2.1 = 8L, ASCF.NN2.2 = 9L), .Label = c("AA1", 
"AA2", "AA3", "AN1", "AN2", "AN3", "NN1", "NN2", "NN3"), class = "factor"), 
    batch = structure(c(ADF.AA1.1 = 1L, ADF.AA1.2 = 2L, ADF.AA2.1 = 1L, 
    ADF.AA2.2 = 2L, ADF.AA3.1 = 1L, ADF.AA3.2 = 2L, USCf.AN1.1 = 3L, 
    USCf.AN1.2 = 3L, USCf.AN2.1 = 3L, USCf.AN2.2 = 4L, USCf.AN3.1 = 3L, 
    USCf.AN3.2 = 4L, ASCF.NN1.1 = 5L, ASCF.NN1.2 = 5L, ASCF.NN2.1 = 5L, 
    ASCF.NN2.2 = 5L), .Label = c("1a", "2a", "3a", "3b", "4a"
    ), class = "factor"), pair = structure(c(1L, 1L, 2L, 2L, 
    3L, 3L, 1L, 1L, 2L, 2L, 3L, 3L, 1L, 1L, 2L, 2L), .Label = c("1", 
    "2", "3"), class = "factor")), class = "data.frame", row.names = c("A1.r1", 
"A1.r2", "A2.r1", "A2.r2", "A3.r1", "A3.r2", "SC1.r1", "SC1.r2", 
"SC2.r1", "SC2.r2", "SC3.r1", "SC3.r2", "ASC1.r1", "ASC1.r2", 
"ASC2.r1", "ASC2.r2"))


eset= matrix (rnorm(80),5)*10# test dataset
    library (limma)
    mm = model.matrix (~0+cond+donor+batch+pair,a)
    mc= makeContrasts ('condASD-condNormal', levels=mm) 
    lf= lmFit (eset, mm )
    cf=contrasts.fit (lf, mc)
    eb=eBayes (cf)
    tt=topTable(eb)
    tt

I wondered: 0) Is it a (biologically) common/accepted practice to treat unaffected siblings and age-and sex-matched controls equally?

1) Whether what I coded correctly answer the problem?

2) What is the "practical" meaning of following warning: (I am very uncomfortable with "pair2 pair3" being part of the message! )

Coefficients not estimable: donorNN3 batch3b batch4a pair2 pair3

Warning message:

Partial NA coefficients for 5 probe(s)

3) Is it passable to neglect certain factors - here, pair for example- and proceed with the "less accurate" analysis?

You are correct to be concerned about the results. The model you have fitted is heavily over-parametrized and will not give meaningful results.

It is not meaningful to put factors into a linear model that are confounded with each other. Here cond is completely confounded with both donor and batch. On top of that, pair is founded with donor and donor is almost completely confounded with batch.

In your case it is not just "passable" to remove factors but compulsory. The issue is not accuracy but rather the need to estimate quantities that have a meaning.

One simple way to analyse the data would be to use design <- model.matrix(~cond) in conjunction with duplicateCorrelation to estimate the within-donor correlation. That doesn't model all the complexity of the data, in particular it doesn't allow for which normals are siblings of which affected, but at least it gives an overall comparison between ASD and Normal and it does allow for the fact that the replicate samples from the same donor are correlated.

Note that you can't adjust for batch because it is completely confounded.

You ask whether it is biologically acceptable to treat age-sex-matched controls the same as sibling controls. I would think not, but it is up to you. The matched controls couldn't be expected to be as similar to the corresponding affected as the siblings are, but there might be some pairing. You are the biologist and this is your analysis, so it is your job to make biological judgements rather than mine.