Fdr control with adaptive procedures and FDR monotonicity

Amit Zeisel, Or Zuk, Eytan Domany*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


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, FDR ≤ q. 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.

Original languageAmerican English
Pages (from-to)943-968
Number of pages26
JournalAnnals of Applied Statistics
Issue number2 A
StatePublished - Jun 2011
Externally publishedYes


  • False discovery rate
  • Gene expression analysis
  • Improved BH
  • Monotonicity


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