Multiple testing procedures under confounding

TL;DR

This paper reviews existing multiple testing methods under confounding, introduces two novel approaches combining sensitivity analysis and shrinkage estimators, and demonstrates their application in prostate cancer gene expression data.

Contribution

It proposes two new multiple testing procedures that address confounding, integrating sensitivity analysis and mixture model-based shrinkage estimators.

Findings

New procedures effectively control false discovery rate under confounding

Application to prostate cancer data demonstrates practical utility

Enhanced detection of true signals in gene expression studies

Abstract

While multiple testing procedures have been the focus of much statistical research, an important facet of the problem is how to deal with possible confounding. Procedures have been developed by authors in genetics and statistics. In this chapter, we relate these proposals. We propose two new multiple testing approaches within this framework. The first combines sensitivity analysis methods with false discovery rate estimation procedures. The second involves construction of shrinkage estimators that utilize the mixture model for multiple testing. The procedures are illustrated with applications to a gene expression profiling experiment in prostate cancer.