Signal Identification for Rare and Weak Features: Higher Criticism or False Discovery Rates?

TL;DR

This paper explores the relationship between higher criticism and false discovery rate methods for signal detection in high-dimensional biostatistics, showing their practical equivalence in certain settings through analysis and data applications.

Contribution

It demonstrates that higher criticism thresholding is effectively equivalent to FDR thresholding in rare-weak signal scenarios, connecting two prominent methods analytically and empirically.

Findings

HC threshold approximates the FDR threshold in certain regimes.

HC and CB thresholds are practically indistinguishable in the phase space of interest.

Application to gene expression data supports the theoretical findings.

Abstract

Signal identification in large-dimensional settings is a challenging problem in biostatistics. Recently, the method of higher criticism (HC) was shown to be an effective means for determining appropriate decision thresholds. Here, we study HC from a false discovery rate (FDR) perspective. We show that the HC threshold may be viewed as an approximation to a natural class boundary (CB) in two-class discriminant analysis which in turn is expressible as FDR threshold. We demonstrate that in a rare-weak setting in the region of the phase space where signal identification is possible both thresholds are practicably indistinguishable, and thus HC thresholding is identical to using a simple local FDR cutoff. The relationship of the HC and CB thresholds and their properties are investigated both analytically and by simulations, and are further compared by application to four cancer gene expression data sets.