Abstract

The partial conjunction null hypothesis is tested in order to discover a signal that is present in multiple (sub-)studies. The standard approach of carrying out a multiple test procedure on the partial conjunction p-values can be extremely conservative. We suggest alleviating this conservativeness, by eliminating many of the conservative partial conjunction p-values prior to the application of a multiple test procedure.

This leads to the following two-step procedure: first, select the set with partial conjunction p-values below a selection threshold; second, within the selected set only, apply a family-wise error rate or false discovery rate controlling procedure on the conditional partial conjunction p-values, where conditioning is on the selection event. We discuss theoretical properties of the proposed procedure, and we demonstrate its performance on simulated and real data.

(joint work with Ruth Heller, Anh-Tuan Hoang, Yosef Rinott, and Anna Vesely)