MOTIVATION: A typical approach for the interpretation of high-throughput experiments, such as gene expression microarrays, is to produce groups of genes based on certain criteria (e.g. genes that are differentially expressed). To gain more mechanistic insights into the underlying biology, overrepresentation analysis (ORA) is often conducted to investigate whether gene sets associated with particular biological functions, for example, as represented by Gene Ontology (GO) annotations, are statistically overrepresented in the identified gene groups. However, the standard ORA, which is based on the hypergeometric test, analyzes each GO term in isolation and does not take into account the dependence structure of the GO-term hierarchy. RESULTS: We have developed a Bayesian approach (GO-Bayes) to measure overrepresentation of GO terms that incorporates the GO dependence structure by taking into account evidence not only from individual GO terms, but also from their related terms (i.e. parents, children, siblings, etc.). The Bayesian framework borrows information across related GO terms to strengthen the detection of overrepresentation signals. As a result, this method tends to identify sets of closely related GO terms rather than individual isolated GO terms. The advantage of the GO-Bayes approach is demonstrated with a simulation study and an application example.

BACKGROUND: In high throughput screening, such as differential gene expression screening, drug sensitivity screening, and genome-wide RNAi screening, tens of thousands of tests need to be conducted simultaneously. However, the number of replicate measurements per test is extremely small, rarely exceeding 3. Several current approaches demonstrate that test statistics with shrinking variance estimates have more power over the traditional t statistic. RESULTS: We propose a Bayesian hierarchical model to incorporate the shrinkage concept by introducing a mixture structure on variance components. The estimates from the Bayesian model are utilized in the optimal discovery procedure (ODP) proposed by Storey in 2007, which was shown to have optimal performance in multiple significance tests. We compared the performance of the Bayesian ODP with several competing test statistics. CONCLUSION: We have conducted simulation studies with 2 to 6 replicates per gene. We have also included test results from two real datasets. The Bayesian ODP outperforms the other methods in our study, including the original ODP. The advantage of the Bayesian ODP becomes more significant when there are few replicates per test. The improvement over the original ODP is based on the fact that Bayesian model borrows strength across genes in estimating unknown parameters. The proposed approach is efficient in computation due to the conjugate structure of the Bayesian model. The R code (see Additional file 1) to calculate the Bayesian ODP is provided.

BACKGROUND: Many researchers use the double filtering procedure with fold change and t test to identify differentially expressed genes, in the hope that the double filtering will provide extra confidence in the results. Due to its simplicity, the double filtering procedure has been popular with applied researchers despite the development of more sophisticated methods. RESULTS: This paper, for the first time to our knowledge, provides theoretical insight on the drawback of the double filtering procedure. We show that fold change assumes all genes to have a common variance while t statistic assumes gene-specific variances. The two statistics are based on contradicting assumptions. Under the assumption that gene variances arise from a mixture of a common variance and gene-specific variances, we develop the theoretically most powerful likelihood ratio test statistic. We further demonstrate that the posterior inference based on a Bayesian mixture model and the widely used significance analysis of microarrays (SAM) statistic are better approximations to the likelihood ratio test than the double filtering procedure. CONCLUSION: We demonstrate through hypothesis testing theory, simulation studies and real data examples, that well constructed shrinkage testing methods, which can be united under the mixture gene variance assumption, can considerably outperform the double filtering procedure.