Statistical Inference in High-dimensional Poisson Regression with Applications to Mediation Analysis

TL;DR

This paper develops bias-corrected estimators for high-dimensional Poisson regression, enabling valid inference and hypothesis testing in applications like mediation analysis with count data.

Contribution

It introduces bias correction techniques and asymptotic theory for inference in high-dimensional Poisson models, including mediation analysis with count outcomes.

Findings

Estimators are asymptotically normal.

Constructed confidence intervals are valid.

Method performs well in simulations and real data.

Abstract

Large-scale datasets with count outcome variables are widely present in various applications, and the Poisson regression model is among the most popular models for handling count outcomes. This paper considers the high-dimensional sparse Poisson regression model and proposes bias-corrected estimators for both linear and quadratic transformations of high-dimensional regression vectors. We establish the asymptotic normality of the estimators, construct asymptotically valid confidence intervals, and conduct related hypothesis testing. We apply the devised methodology to high-dimensional mediation analysis with count outcome, with particular application of testing for the existence of interaction between the treatment variable and high-dimensional mediators. We demonstrate the proposed methods through extensive simulation studies and application to real-world epigenetic data.