Optimal two-stage testing of multiple mediators

TL;DR

This paper investigates the finite sample error control and power optimization of a two-stage mediation testing procedure called ScreenMin, which screens variables before testing to identify mediators in high-dimensional data.

Contribution

It derives a power-maximizing selection threshold for ScreenMin and demonstrates its approximation by an adaptive threshold, improving finite sample error control.

Findings

The proposed threshold improves finite sample FWER control.

Simulation results show enhanced power with the new threshold.

Application to a case-control study illustrates practical utility.

Abstract

Mediation analysis in high-dimensional settings often involves identifying potential mediators among a large number of measured variables. For this purpose, a two step familywise error rate (FWER) procedure called ScreenMin has been recently proposed (Djordjilovi\'c et al. 2019). In ScreenMin, variables are first screened and only those that pass the screening are tested. The proposed threshold for selection has been shown to guarantee asymptotic FWER. In this work, we investigate the impact of the selection threshold on the finite sample FWER. We derive power maximizing selection threshold and show that it is well approximated by an adaptive threshold of Wang et al. (2016). We study the performance of the proposed procedures in a simulation study, and apply them to a case-control study examining the effect of fish intake on the risk of colorectal adenoma.