A multivariate version of the Benjamini-Hochberg method

Jose A. Ferreira, Free University of Amsterdam
Stephen O. Nyangoma, Amsterdam Medical Centre, University of Amsterdam


We propose a multivariate method for combining results from independent studies about the same `large scale' multiple testing problem. The method works asymptotically in the number of hypotheses and consists of applying the Benjamini-Hochberg procedure to the p-values of each study separately by determining the `individual false discovery rates' which maximize power subject to a restriction on the (global) false discovery rate. We show how to obtain solutions to the associated optimization problem, provide both theoretical and numerical examples, and compare the method with a simpler, univariate one.