A semiparametric Bayesian approach for estimating the gene expression distribution

Gene expression microarrays are powerful tools for global comparison and estimation of gene expression. Many microarray studies have demonstrated biologically plausible results with only a few arrays, leading to a misperception that a handful of hybridized arrays can always find something meaningful. From a statistical point of view, it is important to prospectively estimate required sample sizes prior to undertaking a microarray experiment. However, all sample size calculations need to directly or indirectly estimate the unknown distribution of the effect sizes of gene expression intensities. A parametric mixture model has been developed for relating the sample size directly to the false discovery rate (FDR), the most popular multiple-comparison control criteria. In this paper, we extend the parametric mixture model and propose a robust semiparametric Dirichlet process mixture model, where the parametric distribution of gene expressions is no longer specified. This analysis is performed in a Bayesian inference framework using Markov-chain Monte Carlo steps. The usefulness of the method is illustrated by simulations and a real murine lung study.