P-values, q-values and posterior probabilities for equivalence in genomics studies

TL;DR

This paper explores the use of P-values, q-values, and posterior probabilities in equivalence testing within genomics, revealing limitations of P-values and proposing posterior-based measures for credible evidence of gene equivalence.

Contribution

It introduces a formal framework for equivalence testing in genomics and proposes a posterior probability-based approach to measure evidence of gene equivalence, addressing limitations of traditional P-values.

Findings

Equivalence P-values do not meet consistency requirements for evidence measurement.

Q-values cannot be directly applied to equivalence testing.

Posterior probabilities provide a credible measure of gene equivalence.

Abstract

Equivalence testing is of emerging importance in genomics studies but has hitherto been little studied in this content. In this paper, we define the notion of equivalence of gene expression and determine a `strength of evidence' measure for gene equivalence. It is common practice in genome-wide studies to rank genes according to observed gene-specific P-values or adjusted P-values, which are assumed to measure the strength of evidence against the null hypothesis of no differential gene expression. We show here, both empirically and formally, that the equivalence P-value does not satisfy the basic consistency requirements for a valid strength of evidence measure for equivalence. This means that the widely-used q-value (Storey, 2002) defined for each gene to be the minimum positive false discovery rate that would result in the inclusion of the corresponding P-value in the discovery set, cannot be translated to the equivalence testing framework. However, when represented as a posterior probability, we find that the q-value does satisfy some basic consistency requirements needed to be a credible measure of evidence for equivalence. We propose a simple estimate for the q-value from posterior probabilities of equivalence, and analyse data from a mouse stem cell microarray experiment which demonstrate the theory and methods presented here.