Adapting to one- and two-way classified structures of hypotheses while controlling the false discovery rate

Abstract

There is ample research on false discovery rate (FDR) control for testing hypotheses classified according to one criterion. However, scenarios of hypotheses partitioned via two different criteria are often encountered in practice. Such two-way classification encodes more structural information in the associated multiple testing of the hypotheses than its one-way or un-classified counterparts. Unfortunately, there seems to be very little research tailored for multiple testing under that classification setting. This article proposes weighted versions of the Benjamini–Hochberg (BH) method, both in their oracle and data-adaptive forms, efficiently capturing one- or two-way classified structure of hypotheses through appropriately chosen weights. The proposed methods control FDR non-asymptotically in their oracle forms under positive regression dependence on subset (PRDS) of null p-values and in their data-adaptive forms for independent p-values. The one-way data-adaptive methods are asymptotically conservative under weak dependence. Simulations demonstrate these methods’ superior power performances over some contemporary procedures and provide evidence of their non-asymptotic conservativeness under certain dependence scenarios. The proposed two-way adaptive procedure is effectively applied to a data set from microbial abundance study.