The Annals of Applied Statistics

FDR control with adaptive procedures and FDR monotonicity

Amit Zeisel, Or Zuk, and Eytan Domany

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The steep rise in availability and usage of high-throughput technologies in biology brought with it a clear need for methods to control the False Discovery Rate (FDR) in multiple tests. Benjamini and Hochberg (BH) introduced in 1995 a simple procedure and proved that it provided a bound on the expected value, FDRq. Since then, many authors tried to improve the BH bound, with one approach being designing adaptive procedures, which aim at estimating the number of true null hypothesis in order to get a better FDR bound. Our two main rigorous results are the following: (i) a theorem that provides a bound on the FDR for adaptive procedures that use any estimator for the number of true hypotheses (m0), (ii) a theorem that proves a monotonicity property of general BH-like procedures, both for the case where the hypotheses are independent. We also propose two improved procedures for which we prove FDR control for the independent case, and demonstrate their advantages over several available bounds, on simulated data and on a large number of gene expression data sets. Both applications are simple and involve a similar amount of computation as the original BH procedure. We compare the performance of our proposed procedures with BH and other procedures and find that in most cases we get more power for the same level of statistical significance.

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Ann. Appl. Stat., Volume 5, Number 2A (2011), 943-968.

First available in Project Euclid: 13 July 2011

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False Discovery Rate improved BH monotonicity gene expression analysis


Zeisel, Amit; Zuk, Or; Domany, Eytan. FDR control with adaptive procedures and FDR monotonicity. Ann. Appl. Stat. 5 (2011), no. 2A, 943--968. doi:10.1214/10-AOAS399.

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Supplemental materials

  • Supplementary material: Supplementary material for: FDR control with adaptive procedures and FDR monotonicity. In this supplementary file we provide proofs of the claims and theorem presented in the paper, together with technical details regarding the proposed estimator and of the simulations performed. The document includes the following sections: Supplement A: Proof of Theorem 2.3. Supplement B: Designing the IBHsum estimator. Supplement C: Proof of Claim 3.1. Supplement D: Proof of the monotonicity theorem. Supplement E: Details of the simulations.