The Distribution of the Number of False Discoveries in DNA Microarray Data

In drawing inferences from differential analysis of DNA microarray data, it is important to have a reliable estimate of the number of falsely rejected null hypotheses, also known as false discoveries. When hypothesis tests are assumed to be independent, estimation of the number of false discoveries (NoFD) is straightforward; however, due to strong causal relationships among genes, proper analysis requires a model of highly correlated tests. Correlation greatly complicates the inference of the NoFD, and understanding and correcting its effects have proven to be a challenging problem. A novel method for inferring the complete distribution of the NoFD in a general correlation setting is presented. The method is based on estimating the moments of test statistics histogram counts and then constructing their joint distribution via entropy maximization. Results on widely-studied BRCA data are reported.