Hi Everyone,

I am using Limma to analyze 8x60K Agilent Single Colour microarray data, however I’m confused about the interpretation of the interaction term

The design of the  experiment is as follows:

I have 15 samples, with 3 strains of mice(WT, 4d, 4e), each strain has uninfected samples(PBS) and infected samples, (KPn) and 2-3 biological replicates for each sample

I’ve corrected for background and normalized between arrays, using the quantile method, filtered control probes and low expressing probes, and averaged replicate probes:  

targets<-readTargets("Targets.txt")
RawData<-read.maimages(targets,source="agilent",green.only=T)
DataBG<-backgroundCorrect(RawData,method="normexp",offset=16)
DataNorm<-normalizeBetweenArrays(DataBG,method="quantile")

##filtering low expressing probes
neg95<-apply(DataNorm$E[DataNorm$genes$ControlType==-1,],2, function(x) quantile(x, p=0.95))
cutoff<-matrix(1.1*neg95,nrow(DataNorm),ncol(DataNorm),byrow=T)
isexpr<-rowSums(DataNorm$E > cutoff)>=2
table(isexpr)

DataNorm0<-DataNorm[DataNorm$genes$ControlType==0 & isexpr,]

##setting up Linear model
DataAvg<-avereps(DataNorm0,DataNorm0$genes$ProbeName)#averages log intensities of replicate probes
Condition<factor(targets$Condition,levels=c("WT.PBS","WT.KPn","mu4d.PBS","mu4d.KPn","mu4e.PBS","mu4e.KPn"))
design<-model.matrix(~0+Condition)
colnames(design)<-levels(Condition)
Fit<-lmFit(DataAvg,design)
ContMatrix<-makeContrasts(WT=WT.KPn-WT.PBS,
                          Mu.4d=mu4d.KPn-mu4d.PBS,
                          Mu.4e=mu4e.KPn-mu4e.PBS,
                          DvsWT=(mu4d.KPn-mu4d.PBS)-(WT.KPn-WT.PBS),
                          EvsWT=(mu4e.KPn-mu4e.PBS)-(WT.KPn-WT.PBS),
                          levels=design)

fit2<-contrasts.fit(Fit,ContMatrix)
fit2<-eBayes(fit2,trend=T)
results<-decideTests(fit2)
summary(results)

      WT Mu.4d Mu.4e DvsWT EvsWT
-1    11    89   210     0     0
0  55031 54752 54596 55254 55254
1    212   413   448     0     0

according to the summary of the results, there are no DE genes/probes between the 4d mutant and WT, and 4e mutant and WT. Yet mutant 4d had 502 DE probes, and mutant 4e had 658 DE probes compared to 223 DE probes in WT.  How can there be no DE probes between the mutants and the wild-type? Have I set up my contrasts incorrectly?

Thanks in advance,

There is no contradiction in the results. Just because you can detect KPn effects in the mutants, it doesn't mean that these effects are significantly different from the KPn effect for wild-type. It can easily be that the KPn effect in wild-type for many genes is intermediate between zero and the KPn effect in mutant and yet not significantly different from either. There is always less statistical power to detect interactions than simple comparisons.

This is an inevitable ambiguity of hypothesis tests. If you want limma to try to resolve the ambiguities somewhat, try decideTests with method="nestedF". That won't be a complete solution, but it will make the counts for the different contrasts more consistent with one another.

You could also try

genas(fit2, coef=c(1,2), plot=TRUE)
genas(fit2, coef=c(1,3), plot=TRUE)

to explore whether the WT KPn effects tend to be correlated with but smaller than the mutant KPn effects.