Permutation-Based True Discovery Guarantee by Sum Tests

TL;DR

This paper introduces a permutation-based closed testing procedure for sum tests that provides simultaneous confidence bounds on the true discovery proportion across all hypothesis subsets, enabling exploratory analysis with controlled error rates.

Contribution

It develops a novel, general closed testing framework for sum tests that offers simultaneous TDP bounds without alpha adjustment, adaptable to various data types and global tests.

Findings

Method controls TDP even with post hoc subset selection

Iterative shortcut converges quickly to full results

Effective in high-dimensional brain imaging and genomics data

Abstract

Sum-based global tests are highly popular in multiple hypothesis testing. In this paper we propose a general closed testing procedure for sum tests, which provides lower confidence bounds for the proportion of true discoveries (TDP), simultaneously over all subsets of hypotheses. These simultaneous inferences come for free, i.e., without any adjustment of the alpha-level, whenever a global test is used. Our method allows for an exploratory approach, as simultaneity ensures control of the TDP even when the subset of interest is selected post hoc. It adapts to the unknown joint distribution of the data through permutation testing. Any sum test may be employed, depending on the desired power properties. We present an iterative shortcut for the closed testing procedure, based on the branch and bound algorithm, which converges to the full closed testing results, often after few iterations; even if it is stopped early, it controls the TDP. We compare the properties of different choices for the sum test through simulations, then we illustrate the feasibility of the method for high dimensional data on brain imaging and genomics data.