Data-driven hypothesis weighting increases detection power in multiple testing

Hypothesis weighting is a powerful approach for improving the power of data analyses that employ multiple testing. However, in general it is not evident how to choose the weights in a data-dependent manner. We describe independent hypothesis weighting (IHW), a method for making use of informative covariates that are independent of the test statistic under the null, but informative of each test’s power or prior probability of the null hypothesis. Covariates can be continuous or categorical and need not fulfill any particular assumptions. The method increases statistical power in applications while controlling the false discovery rate (FDR) and produces additional insight by revealing the covariate-weight relationship. Independent hypothesis weighting is a practical approach to discovery of associations in large datasets.