[BioC] confusing P-value of one gene

[Wolfgang Huber]

Dear Xinwei

as far as I can see, this is a case where transformation of the count data (e.g. regularized log, or variance-stabilizing) and ANOVA with a normal linear model should give useful results. Since these transformations are like the logarithm for higher counts but avoid the singularity around zero.

One place to start with that is chapter 2 of the DESeq2 vignette, functions rlogTransformation and varianceStabilizingTransformation. Doing the testing in this way is also not entirely without pitfalls (e.g. it tends to have less statistical power esp. in the small sample and low-counts regime, and may be susceptible to library-size related biases). I'd be interested to hear how it turns out in your case.

	Best wishes
	Wolfgang





On Aug 29, 2013, at 4:15 am, Gordon K Smyth <smyth at wehi.edu.au> wrote:

> Dear Xinwei,
> 
> This is a correct result.  The reason that the interaction is not statistically significant is inherent in the log-linear model, and hence in the definition of interaction for this sort of model.
> 
> You are probably thinking that the cpm values are much higher for the joint condition CX&RGF than for the other conditions, hence there should be a positive interaction, and this should be statistically significant.
> 
> Indeed, had you tested the joint condition vs the other three conditions it would certainly be significantly higher.
> 
> However the interaction is different.  The problem is that there are zero counts for the controls.  Hence the fold change from control to CX is infinity, and the fold change from control to RGF is infinity.  Hence the counts in the joint condition can be indefinitely large even the absence of any positive interaction.  Hence there is no evidence for any positive interaction.  In fact, you could make the counts for the CX&RGF libraries as large as you like, and the interaction would never become significant. To make this clear, the counts could have been:
> 
>  0 0 0 0 0 1 0 0 1 1e10 1e10 1e10
> 
> and this would not give a significant interaction. So long as there are zero counts for the controls, and least one count for the single treatments CX and RGF, the interaction will never become significant.
> 
> You should ignore the logFC in this case, because the interaction logFC is not defined in any meaningful way for this data.
> 
> On the other hand, if you had any positive counts for the controls, then the interaction would suddenly become significant, because the fold changes from control to CX and control to RGF would now be finite.
> 
> I suspect that you might find it more meaningful to test for
> 
>  CX&RGF - (control+CX+RGF)/3
> 
> This will certainly be significant.  Or else test for CX&RGF vs each of the other three individually.
> 
> As I've said before, I am not a fan of factorial interaction models for genomic data, and this is yet another example of why this is so.
> 
> Best wishes
> Gordon
> 
> 
> On Wed, 28 Aug 2013, Xinwei Han wrote:
> 
>> Hi,
>> 
>> I manually checked p-values from edgeR and found the p-value of this particular gene, AT1G04500, difficult to understand. The CPM of this gene is like this:
>> 
>> control replicate1: 0
>> control replicate2: 0
>> control replicate3: 0
>> CX replicate1: 0
>> CX replicate2: 0.24
>> CX replicate3: 0
>> RGF replicate1: 0
>> RGF replicate2: 0.14
>> RGF replicate3: 0.19
>> CX&RGF replicate1: 25.14
>> CX&RGF replicate2: 44.36
>> CX&RGF replicate3: 34.62
>> 
>> I fitted GLM with model.matrix(~RGF + CX + RGF:CX).  To find out genes under significant interaction effect, lrt <- glmLRT(fit, coef=4) gives the following results to this gene:
>> 
>> logFC: 5.43
>> logCPM: 3.19
>> LR: 0.012
>> PValue: 0.91
>> 
>> I do not understand why such dramatic change and such large logFC have p-value of 0.91. I attached the data and R script I used. Could you take a look to see whether I did something wrong in the script? Or there are some other reasons for that?
>> 
>> I used the latest version of R and edgeR. "ms" in the data and script is
>> the control.
>> 
>> Thanks
>> Xinwei
>> 
> 
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