[BioC] limma multiple groups comparison produces different pvalue comparing with two group comparsion

[Shao, Chunxuan]

Hi everyone:

I am trying limma for multiple group comparison, and found that the pvalue of pairwise comparison is different from the two group comparsion.

A simple example:

## multiple groups
sd <- 0.3*sqrt(4/rchisq(100,df=4))
y2 <- matrix(rnorm(100*9,sd=sd),100,9)
rownames(y2) <- paste("Gene",1:100)
y2[1:2,4:6] <- y2[1:2,4:6] + 2
y2[1:2,7:9] <- y2[1:2,7:9] + 2
f <- factor(c(rep("A",3),rep("B",3),rep("C",3)),levels=c("A","B","C"))
design <- model.matrix(~0+f)
colnames(design) <- c("A","B","C")
fit2 <- lmFit(y2,design)
contrast.matrix <- makeContrasts("B-A", "C-A", "C-B", levels=design)
fit2 <- contrasts.fit(fit2, contrast.matrix)
fit2 <- eBayes(fit2)
topTable(fit2, adjust="BH",coef=1)

        ID      logFC         t      P.Value   adj.P.Val          B
1   Gene 1  1.8961975  8.697056 1.038672e-05 0.001038672  3.9011567
2   Gene 2  2.3140816  6.104506 1.690945e-04 0.008454727  0.9859443
96 Gene 96 -0.8959120 -4.039216 2.855951e-03 0.095198377 -1.9787088
49 Gene 49 -0.4983110 -2.776108 2.128499e-02 0.462011867 -4.0378662
86 Gene 86  0.7288518  2.726366 2.310059e-02 0.462011867 -4.1198456
74 Gene 74 -0.8456774 -2.367919 4.171492e-02 0.695248750 -4.7045985
50 Gene 50 -1.5597167 -2.107329 6.396187e-02 0.783183079 -5.1177738
46 Gene 46 -0.6530683 -2.028684 7.269084e-02 0.783183079 -5.2394326
8   Gene 8 -0.3348446 -1.986208 7.786841e-02 0.783183079 -5.3044289
89 Gene 89 -0.4574447 -1.942438 8.356956e-02 0.783183079 -5.3708387

## two groups
y <- y2[,1:6]
design <- cbind(Grp1=1,Grp2vs1=c(0,0,0,1,1,1))
options(digit=3)
fit <- lmFit(y,design)
fit <- eBayes(fit)
topTable(fit, adjust="BH",coef= "Grp2vs1")

        ID      logFC         t      P.Value  adj.P.Val          B
1   Gene 1  1.8961975  7.962269 0.0001316933 0.01316933  1.6748248
2   Gene 2  2.3140816  6.190071 0.0005783671 0.02891836  0.1114107
96 Gene 96 -0.8959120 -4.124112 0.0050946000 0.16982000 -2.2231052
64 Gene 64 -0.6611682 -3.824833 0.0073401109 0.18350277 -2.6140362
86 Gene 86  0.7288518  3.503703 0.0110265957 0.22053191 -3.0478852
49 Gene 49 -0.4983110 -2.922543 0.0239288895 0.39881483 -3.8654279
74 Gene 74 -0.8456774 -2.411705 0.0489411131 0.69915876 -4.6045844
89 Gene 89 -0.4574447 -2.282469 0.0588626872 0.73578359 -4.7916531
50 Gene 50 -1.5597167 -2.064728 0.0804679751 0.79599004 -5.1040241
46 Gene 46 -0.6530683 -2.020227 0.0857867706 0.79599004 -5.1671760


In this case,  in the multiple group p_value is much smaller than the two group.
Any suggestion to this ? Which is the appropriate way to do if I want to do the pairwise comparison among three groups?

Thanks in advance.

--
Chunxuan