I'm developing a Genome-Wide Selection Screening using a statistic called D’2IS or Dvalue. I have an experimental distribution of 70,411,837 Dvalues and a null empirical distribution of the same size. To account for the multiple testing problem I calculated the false discovery rate (FDR) for every experimental Dvalue (Dexp) as
FDR(Dexp) = Snull/Sexp
where Snull is the number of values ≥ Dexp in the null distribution and Sexp is the number of values ≥ Dexp in the experimental distribution (Noble, 2009).
I did not use methods to estimate FDR from p-values such as the Benjamini-Hochberg procedure since I found at bibliography that are only suitable if an analytical null model is available. With only an empirical null model, it will be necessary the estimation of p-values in an intermediate step. This could provide too pessimistic or too optimistic p-values, and in turn, lead to biased FDR values (Strimmer, 2008). Instead, obtaining the FDR directly from both experimental and null distributions (as specified above) seems a faster and more reliable procedure on this situation (Noble, 2009).
For my study three FDR threshold levels were set as FDR <= 0.15, 0.1 and 0.05. The problem comes for the most strict level, since the non-monotone behaviour of the FDR arises around this FDR level:
I know there are methods to achieve monotone FDR values. However, the processing of p-values and/or other parameters subtracted from the data is mandatory in most of them. Therefore:
How I interpret the FDR?
Should I take the minimum Dvalue to achieve FDR <= 0.05 as a threshold? I know that Storey defined the q-value as the minimum FDR attained at or above a given statistic value, but the algorithm proposed by Storey to obtain q-values needs intermediate steps to obtain p-values (Storey, 2003).
Does anyone know a method to achieve monotone FDR values without a theoretical null distribution?