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Abstract: The steep rise in availability and usage of high-throughput technologies inbiology brought with it a clear need for methods to control the False DiscoveryRate FDR in multiple tests. Benjamini and Hochberg BH introduced in 1995 asimple procedure and proved that it provided a bound on the expected value,$\mathit{FDR}\leq q$. Since then, many authors tried to improve the BH bound,with one approach being designing adaptive procedures, which aim at estimatingthe number of true null hypothesis in order to get a better FDR bound. Our twomain rigorous results are the following: i a theorem that provides a bound onthe FDR for adaptive procedures that use any estimator for the number of truehypotheses $m 0$, ii a theorem that proves a monotonicity property ofgeneral BH-like procedures, both for the case where the hypotheses areindependent. We also propose two improved procedures for which we prove FDRcontrol for the independent case, and demonstrate their advantages over severalavailable bounds, on simulated data and on a large number of gene expressiondata sets. Both applications are simple and involve a similar amount ofcomputation as the original BH procedure. We compare the performance of ourproposed procedures with BH and other procedures and find that in most cases weget more power for the same level of statistical significance.

Author: Amit Zeisel, Or Zuk, Eytan Domany

Source: https://arxiv.org/

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