FDP control in multivariate linear models using the bootstrap

TL;DR

This paper introduces a bootstrap-based method for controlling the false discovery proportion in multivariate linear models, providing simultaneous asymptotic control and demonstrating improved power over existing methods through simulations and real data applications.

Contribution

It develops a novel bootstrap approach combined with post hoc bounds for FDP control in multivariate linear models, with a new proof of bootstrap consistency.

Findings

Provides asymptotic FDP control over all hypothesis subsets

Demonstrates higher power than existing parametric methods

Validates approach on neuroimaging and transcriptomic data

Abstract

In this article we develop a method for performing post hoc inference of the False Discovery Proportion (FDP) over multiple contrasts of interest in the multivariate linear model. To do so we use the bootstrap to simulate from the distribution of the null contrasts. We combine the bootstrap with the post hoc inference bounds of Blanchard (2020) and prove that doing so provides simultaneous asymptotic control of the FDP over all subsets of hypotheses. This requires us to demonstrate consistency of the multivariate bootstrap in the linear model, which we do via the Lindeberg Central Limit Theorem, providing a simpler proof of this result than that of Eck (2018). We demonstrate, via simulations, that our approach provides simultaneous control of the FDP over all subsets and is typically more powerful than existing, state of the art, parametric methods. We illustrate our approach on functional Magnetic Resonance Imaging data from the Human Connectome project and on a transcriptomic dataset of chronic obstructive pulmonary disease.