The Beta-Binomial Distribution for Estimating the Number of False Rejections in Microarray Gene Expression Studies.

In differential expression analysis of microarray data, it is common to assume independence among null hypotheses (and thus gene expression levels). The independence assumption implies that the number of false rejections V follows a binomial distribution and leads to an estimator of the empirical false discovery rate (eFDR). The number of false rejections V is modeled with the beta-binomial distribution. An estimator of the beta-binomial false discovery rate (bbFDR) is then derived. This approach accounts for how the correlation among non-differentially expressed genes influences the distribution of V. Permutations are used to generate the observed values for V under the null hypotheses and a beta-binomial distribution is fit to the values of V. The bbFDR estimator is compared to the eFDR estimator in simulation studies of correlated non-differentially expressed genes and is found to outperform the eFDR for certain scenarios. As an example, this method is also used to perform an analysis that compares the gene expression of soft tissue sarcoma samples to normal tissue samples.