Learning false discovery rates by fitting sigmoidal threshold functions

TL;DR

This paper explores fitting sigmoidal threshold functions, specifically half-normal decay and beta-uniform mixture models, for estimating false discovery rates, highlighting their performance and limitations through simulations and real data analysis.

Contribution

It introduces a parametric approach to FDR estimation using sigmoidal threshold functions and compares its effectiveness with existing methods, emphasizing the importance of correct model specification.

Findings

Performance depends on correct model specification

Empirical null distribution impacts FDR accuracy

Method is sensitive to model misspecification

Abstract

False discovery rates (FDR) are typically estimated from a mixture of a null and an alternative distribution. Here, we study a complementary approach proposed by Rice and Spiegelhalter (2008) that uses as primary quantities the null model and a parametric family for the local false discovery rate. Specifically, we consider the half-normal decay and the beta-uniform mixture models as FDR threshold functions. Using simulations and analysis of real data we compare the performance of the Rice-Spiegelhalter approach with that of competing FDR estimation procedures. If the alternative model is misspecified and an empirical null distribution is employed the accuracy of FDR estimation degrades substantially. Hence, while being a very elegant formalism, the FDR threshold approach requires special care in actual application.