[BioC] Testing for no change in RNA-seq data?

Ryan C. Thompson rct at thompsonclan.org
Fri Mar 22 00:11:18 CET 2013

Ok, after poking around a bit, I'm not sure how to do this. Could you 
provide an example of computing p-values for the case where

H0 = abs(coefficient) > epsilon
H1 = abs(coefficient) <= epsilon

I got as far as computing the z-scores, but I'm not sure how to go from 
there to p-values for a test of equivalence.



On 03/21/2013 06:42 AM, Simon Anders wrote:
> Hi Ryan
> On 21/03/13 01:05, Ryan C. Thompson wrote:
>> So, we have several great packages for testing for evidence of
>> differential expression using RNA-seq counts, and I am happily using
>> those. However, I would like to know if there is any method for testing
>> for evidence of equivalent expression. That is, I would like to show
>> with some level of confidence that treatment X has no (or negligible)
>> effect on gene Y. Is there any way to conduct such a test?
> One of the new features of DESeq2 is that it provides a 
> empirical-Bayes style shrinkage estimates of coefficients (i.e., log 
> fold changes) and also estimates standard errors for these 
> coefficients (taken from the the reciprocal curvature of the 
> posterior). Your task is one of the application we had in mind for this.
> You want to know whether the fold change is zero or nearly zero, and 
> you also want to be ascertained that this estimate of a nearly-zero 
> fold change is a precise one. So, to find genes whose absolute log 
> fold change is _reliably_ smaller than some threshold, take all those 
> genes for which the estimated abs log fold change is below the 
> threshold and the standard error is well below the threshold, too.
> The reason, why I write "below a threshold" rather than "equal to 
> zero" is that it's biologically unreasonable to assume that a 
> treatment has exactly zero effect on a gene's expression. Gene 
> regulation is such an interconnected network that, at least in my 
> view, every gene will react ever so slightly to every perturbance, but 
> often, this reaction is too small to be measurable. This is why you 
> should define a threshold for "biologically unlikely to be relevant". 
> Let's say, we don't believe that an expression change of less than 15% 
> (0.2 on a log2 scale) is worth bothering. So, if you might take all 
> genes with abs log2 fold change below 0.2, and furthermore require 
> that the standard error of this log2 fold change estimate is below, 
> say, 0.05, than you will get gene with true values well below at least 
> 0.3 or so.
> In the end, the thresholds won't matter too much but if you want real 
> p values, this is possible, too: Simply divide the log2 fold change 
> estimates by their standard errors to get z scores (this works because 
> the sampling distribution of our fold change estimates is reasonably 
> close to normal), and do two one-sided tests (TOST) as suggested by 
> Ryan above.
> Actually, as this may come up more often, we should maybe explain the 
> details of using this approach in the vignette. Ask again if you want 
> to see some code.
>  Simon
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