Hi Simon,

Thanks for the suggestions. I'll see about implementing them soon and 
let you know if I have any problems.

-Ryan

On Mar 21, 2013 6:44 AM, "Simon Anders" <anders@embl.de 
<mailto:anders@embl.de>> 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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