Laplace Approximated EM Microarray Analysis: An Empirical Bayes Approach for Comparative Microarray Experiments

TL;DR

This paper introduces LEMMA, a scalable empirical Bayes method using Laplace approximations for microarray data analysis, improving gene-treatment interaction detection and FDR control.

Contribution

The paper presents a novel fast algorithm for fitting a two-groups mixed-effects model, unifying and extending existing methods for microarray data analysis.

Findings

LEMMA outperforms existing methods in simulation studies.

The approach effectively controls false discovery rates.

Application to real data demonstrates practical utility.

Abstract

A two-groups mixed-effects model for the comparison of (normalized) microarray data from two treatment groups is considered. Most competing parametric methods that have appeared in the literature are obtained as special cases or by minor modification of the proposed model. Approximate maximum likelihood fitting is accomplished via a fast and scalable algorithm, which we call LEMMA (Laplace approximated EM Microarray Analysis). The posterior odds of treatment $\times$ gene interactions, derived from the model, involve shrinkage estimates of both the interactions and of the gene specific error variances. Genes are classified as being associated with treatment based on the posterior odds and the local false discovery rate (f.d.r.) with a fixed cutoff. Our model-based approach also allows one to declare the non-null status of a gene by controlling the false discovery rate (FDR). It is shown in a detailed simulation study that the approach outperforms well-known competitors. We also apply the proposed methodology to two previously analyzed microarray examples. Extensions of the proposed method to paired treatments and multiple treatments are also discussed.