Robust semiparametric mixing for detecting differentially expressed genes in microarray experiments

An important goal of microarray studies is the detection of genes that show significant changes in observed expressions when two or more classes of bio- logical samples such as treatment and control are compared. Using the c-fold rule, a gene is declared to be differentially expressed if its average expression level varies by more than a constant factor c between treatment and control (typically c = 2). While often used, however, this simple rule is not completely convincing. We pro- pose to model this filter and define a binary variable at the genečexperiment level, allowing for a more powerful treatment of the corresponding information. We in- troduce a gene-specific random term controlling for both dependence among genes and variability with respect to the c-fold threshold. We make inference via a two- level finite mixture model under a likelihood approach. Then, using the counting distribution we show how parameter estimates can be usefully derived also under a Bayesian nonparametric approach which allows to keep under control some er- ror rate of erroneous discoveries. We illustrate the effectiveness of both proposed approaches through a large- scale simulation study and an real-data application based on the well known dataset introduced by Alon et al. (1999). Key words and phrases: Microarray Data, Up-regulated genes, Mixture Models, Counting Distribution, False Discovery Rate. Rapporto Tecnico #4, Dipartimento di Satistica, Probabilità e Statistiche Applicate, Università "La Sapienza" - Roma