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I am reading paper by Benjamini and Yekutieli (2001) on controlling FDR under dependence. My question is to figure out, in practical applications, whether the PRDS property is fulfilled in a given application, or not. Specifically:

  1. for example, I am running a series of t-tests on a number of variables. When do I run into the danger of violating the PRDS property?
  2. What happens to the FDR when I do?

I get the maths in the paper, technically, but I don't get a feeling for it.

Intuitively, I understand the PRDS property as not having a negative interaction between the p-values; if one test gives a p value rejecting the given hypothesis, then another test is not less likely to reject the hypothesis.

As a practical example, I imagine the following situation violates PRDS: two genes react to a treatment; however, if gene A is expressed, it prevents regulation of gene B, and vice versa. That is, it is unlikely that $H_A$ (gene A is not regulated) wis rejected and at the same time $H_B$ (gene B is not regulated) is rejected. $Pr(p_a \le q | p_b \le q) < Pr(p_a \le q | p_b > q)$.

Does this have any connection to reality?

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    $\begingroup$ +1. Related: stats.stackexchange.com/questions/111756 (there was a high bounty on that Q until a day or two ago). See my answer and also user43849's answer. $\endgroup$
    – amoeba
    Commented Mar 31, 2017 at 9:45
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    $\begingroup$ Thanks, that is a great thread. Should have mentioned it in my question, and actually, my question was prompted by me being still quite dim on the two specific (hopefully specific) points after reading the responses. $\endgroup$
    – January
    Commented Mar 31, 2017 at 9:54
  • $\begingroup$ @amoeba I was never satisfied with my answer in that thread and i think that yours should be marked as the accepted one, since I am still quite foggy on the details myself. Last summer I was working on a mathematical extension to FDR and still got quite confused, so I think the "big picture" approach is the most useful for those who are applying it. $\endgroup$
    – Chris C
    Commented Apr 1, 2017 at 23:36

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