title: Unscaled Bayes factors for multiple hypothesis testing in microarray experiments.
abstract: Multiple hypothesis testing collects a series of techniques usually based on p-values as a summary of the available evidence from many statistical tests. In hypothesis testing, under a Bayesian perspective, the evidence for a specified hypothesis against an alternative, conditionally on data, is given by the Bayes factor. In this study, we approach multiple hypothesis testing based on both Bayes factors and p-values, regarding multiple hypothesis testing as a multiple model selection problem. To obtain the Bayes factors we assume default priors that are typically improper. In this case, the Bayes factor is usually undetermined due to the ratio of prior pseudo-constants. We show that ignoring prior pseudo-constants leads to unscaled Bayes factor which do not invalidate the inferential procedure in multiple hypothesis testing, because they are used within a comparative scheme. In fact, using partial information from the p-values, we are able to approximate the sampling null distribution of the unscaled Bayes factor and use it within Efron's multiple testing procedure. The simulation study suggests that under normal sampling model and even with small sample sizes, our approach provides false positive and false negative proportions that are less than other common multiple hypothesis testing approaches based only on p-values. The proposed procedure is illustrated in two simulation studies, and the advantages of its use are showed in the analysis of two microarray experiments.
authors.affiliation: Department of Mathematics and Informatics, University of Cagliari, via Ospedale 72, Cagliari, Italy.
authors.forename: Francesco
authors.initials: F
authors.lastname: Bertolino
authors.affiliation: Department of Mathematics and Informatics, University of Cagliari, via Ospedale 72, Cagliari, Italy s.cabras@unica.it.
authors.forename: Stefano
authors.initials: S
authors.lastname: Cabras
authors.affiliation: Department of Statistics and Operations Research, Rey Juan Carlos University, c/Tulipan sn, Mostoles, Spain.
authors.forename: Maria Eugenia
authors.initials: ME
authors.lastname: Castellanos
authors.affiliation: Department of Mathematics and Informatics, University of Cagliari, via Ospedale 72, Cagliari, Italy.
authors.forename: Walter
authors.initials: W
authors.lastname: Racugno
mesh_terms: D001499:Bayes Theorem; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D020411:Oligonucleotide Array Sequence Analysis / Q000379:methods*; D013223:Statistics as Topic