Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models

TL;DR

This paper develops new global and simultaneous testing methods for high-dimensional logistic regression, providing asymptotic optimality, FDR control, and demonstrating superior performance through simulations and real data analysis.

Contribution

It introduces a bias-corrected test statistic for global null hypothesis testing and multiple testing procedures that control FDR and FDV in high-dimensional logistic models.

Findings

Proposed tests are asymptotically minimax optimal.

Methods control FDR and FDV asymptotically.

Simulation and real data show improved performance.

Abstract

High-dimensional logistic regression is widely used in analyzing data with binary outcomes. In this paper, global testing and large-scale multiple testing for the regression coefficients are considered in both single- and two-regression settings. A test statistic for testing the global null hypothesis is constructed using a generalized low-dimensional projection for bias correction and its asymptotic null distribution is derived. A lower bound for the global testing is established, which shows that the proposed test is asymptotically minimax optimal over some sparsity range. For testing the individual coefficients simultaneously, multiple testing procedures are proposed and shown to control the false discovery rate (FDR) and falsely discovered variables (FDV) asymptotically. Simulation studies are carried out to examine the numerical performance of the proposed tests and their superiority over existing methods. The testing procedures are also illustrated by analyzing a data set of a metabolomics study that investigates the association between fecal metabolites and pediatric Crohn's disease and the effects of treatment on such associations.