Computationally efficient permutation-based confidence interval estimation for tail-area FDR

Challenges of satisfying parametric assumptions in genomic settings with thousands or millions of tests have led investigators to combine powerful False Discovery Rate (FDR) approaches with computationally expensive but exact permutation testing. We describe a computationally efficient permutation-based approach that includes a tractable estimator of the proportion of true null hypotheses, the variance of the log of tail-area FDR, and a confidence interval (CI) estimator, which accounts for the number of permutations conducted and dependencies between tests. The CI estimator applies a binomial distribution and an overdispersion parameter to counts of positive tests. The approach is general with regards to the distribution of the test statistic, it performs favorably in comparison to other approaches, and reliable FDR estimates are demonstrated with as few as 10 permutations. An application of this approach to relate sleep patterns to gene expression patterns in mouse hypothalamus yielded a set of 11 transcripts associated with 24 h REM sleep [FDR = 0.15 (0.08, 0.26)]. Two of the corresponding genes, Sfrp1 and Sfrp4, are involved in wnt signaling and several others, Irf7, Ifit1, Iigp2, and Ifih1, have links to interferon signaling. These genes would have been overlooked had a typical a priori FDR threshold such as 0.05 or 0.1 been applied. The CI provides the flexibility for choosing a significance threshold based on tolerance for false discoveries and precision of the FDR estimate. That is, it frees the investigator to use a more data-driven approach to define significance, such as the minimum estimated FDR, an option that is especially useful for weak effects, often observed in studies of complex diseases.