Adaptive methods for testing hypotheses with group structure while simultaneously controlling several error rates
In many statistical applications a large set of hypotheses is tested, and the hypotheses can be naturally classified into groups based on different criteria, defined by the characteristics of the problem. Examples of such applications include brain imaging, microbiome, and genome-wide association studies. In such settings, it may be of interest to identify groups containing signals, for each partition into groups, with control over false discoveries. This goal was addressed by Barber and Ramdas (2016) and Ramdas, Barber, Wainwright, and Jordan (2019) who developed the p-filter method for controlling the group-level false discovery rate (FDR), simultaneously for all partitions.
We address the same goal, and aim to improve the power of the p-filter method by capturing the group structure of the hypotheses using adaptive weights. We prove that the modified method controls the group-level FDR for each partition into groups under independence, and show by simulations that it seems to retain the control under certain forms of positive dependence. Our simulation study shows that the proposed modification improves the power of the method significantly in the settings where the signals are concentrated within groups, and does not result in a power loss in less favorable settings. We compare the performance of the modified method to that of the original p-filter on real brain imaging data, where the hypotheses are grouped with respect to two criteria.