Empirical Bayes estimation of posterior probabilities of enrichment

TL;DR

This paper compares different estimators for the local false discovery rate in gene enrichment analysis, recommending specific methods based on the number of categories to improve biological interpretation.

Contribution

It introduces and evaluates three estimators (SPE, NMLE, MLE) for LFDR, providing practical guidance for their use in gene enrichment studies.

Findings

MLE performs well with about 100 categories

SPE is more reliable with around 10 categories

NMLE is suitable for very few categories (~1)

Abstract

To interpret differentially expressed genes or other discovered features, researchers conduct hypothesis tests to determine which biological categories such as those of the Gene Ontology (GO) are enriched in the sense of having differential representation among the discovered features. We study application of better estimators of the local false discovery rate (LFDR), a probability that the biological category has equivalent representation among the preselected features. We identified three promising estimators of the LFDR for detecting differential representation: a semiparametric estimator (SPE), a normalized maximum likelihood estimator (NMLE), and a maximum likelihood estimator (MLE). We found that the MLE performs at least as well as the SPE for on the order of 100 of GO categories even when the ideal number of components in its underlying mixture model is unknown. However, the MLE is unreliable when the number of GO categories is small compared to the number of PMM components. Thus, if the number of categories is on the order of 10, the SPE is a more reliable LFDR estimator. The NMLE depends not only on the data but also on a specified value of the prior probability of differential representation. It is therefore an appropriate LFDR estimator only when the number of GO categories is too small for application of the other methods. For enrichment detection, we recommend estimating the LFDR by the MLE given at least a medium number (~100) of GO categories, by the SPE given a small number of GO categories (~10), and by the NMLE given a very small number (~1) of GO categories.