Genome-Wide Significance Levels and Weighted Hypothesis Testing

TL;DR

This paper reviews methods for weighted hypothesis testing in genetic studies, deriving optimal weights, and demonstrating robustness to misspecification, with practical approaches based on prior knowledge or data-driven estimates.

Contribution

It provides a comprehensive review, derivation of optimal weights, and analysis of robustness in weighted p-value methods for genetic hypothesis testing.

Findings

Optimal weights can significantly improve power.

Power is robust to weight misspecification.

External and estimated weighting methods are practical approaches.

Abstract

Genetic investigations often involve the testing of vast numbers of related hypotheses simultaneously. To control the overall error rate, a substantial penalty is required, making it difficult to detect signals of moderate strength. To improve the power in this setting, a number of authors have considered using weighted $p$-values, with the motivation often based upon the scientific plausibility of the hypotheses. We review this literature, derive optimal weights and show that the power is remarkably robust to misspecification of these weights. We consider two methods for choosing weights in practice. The first, external weighting, is based on prior information. The second, estimated weighting, uses the data to choose weights.