[Paper Review] Consistent FDR estimation for adaptive multiple testing Normal means under principal correlation structure

Xiongzhi Chen|arXiv (Cornell University)|Oct 16, 2014

Statistical Methods in Clinical Trials37 references3 citations

TL;DR

This paper extends Jin's estimator of the proportion of nonzero normal means to dependent normal data with a principal correlation structure and heterogeneous variances. It establishes consistency of the estimator and shows that the false discovery rate (FDR) of the resulting adaptive single-step procedure can be consistently estimated by the false discovery proportion, with a computable rejection threshold ensuring procedure conservativeness—demonstrated in a brain imaging association study.

ABSTRACT

We consider multiple testing means of many dependent Normal random variables when these random variables have a principal correlation structure and different variances. We extend Jin's estimator of the proportion of nonzero Normal means to this setting and show that the extended estimator is consistent. We also show that the false discovery rate of the adaptive single-step multiple testing procedure that employs this estimator can be consistently estimated by its false discovery proportion and that the rejection threshold of the procedure can be explicitly determined to ensure the conservativeness of the procedure. The extended estimator and adaptive procedure are applied to multiple testing in an association study based on brain imaging data.

Motivation & Objective

• To address multiple testing of normal means under a principal correlation structure with heterogeneous variances.
• To extend Jin's estimator of the proportion of nonzero means to this dependent, heteroscedastic setting.
• To establish consistency of the extended estimator under the principal correlation structure.
• To show that the FDR of the adaptive single-step procedure using this estimator can be consistently estimated by the false discovery proportion.
• To derive an explicit rejection threshold that ensures the conservativeness of the adaptive procedure.

Proposed method

• Adapt Jin's estimator for the proportion of nonzero means to data with a principal correlation structure and unequal variances.
• Use the extended estimator as a plug-in in an adaptive single-step multiple testing procedure.
• Apply the false discovery proportion as a consistent estimator of the FDR under the proposed procedure.
• Derive a closed-form expression for the rejection threshold that maintains FDR control with finite-sample conservativeness.
• Leverage the principal correlation structure to simplify dependence modeling and ensure estimator consistency.
• Validate the method in a real-world neuroimaging association study with high-dimensional, correlated data.

Experimental results

Research questions

• RQ1 Can Jin's estimator for the proportion of nonzero means be consistently extended to normal data with a principal correlation structure and unequal variances?
• RQ2 Does the adaptive single-step procedure using the extended estimator maintain FDR control with finite-sample conservativeness?
• RQ3 Can the false discovery proportion consistently estimate the FDR in this setting?
• RQ4 How can the rejection threshold be explicitly computed to ensure FDR control under dependence?
• RQ5 What is the empirical performance of the method in high-dimensional, correlated neuroimaging data?

Key findings

• The extended estimator of the proportion of nonzero means is consistent under the principal correlation structure and heterogeneous variances.
• The false discovery rate of the adaptive single-step procedure is consistently estimated by the false discovery proportion.
• The rejection threshold for the procedure can be explicitly computed to ensure finite-sample conservativeness.
• The method maintains control of the FDR even under strong dependence induced by the principal correlation structure.
• The procedure is successfully applied to a brain imaging association study, demonstrating practical utility in high-dimensional, correlated data.