An Empirical Bayes Adjustment to Multiple p-values for the Detection of Differentially Expressed Genes in Microarray Experiments

In recent microarray experiments thousands of gene expressions are simultaneously tested in comparing samples (e.g., tissue types or experimental conditions). Application of a statistical test, such as the t-test, would lead to a p-value for each gene that reflects the amount of statistical evidence present in the data that the given gene is indeed differentially expressed. We show how to use these p-values across the genes using the method of empirical Bayes estimation so that each gene in turn borrows evidence of differential expression (or nondifferential expression, whatever the case may be) from all other genes on the microarray. A new set of accept/reject decisions are reached for the differential expressions using the empirical Bayes adjusted p-values through a resampling based step-down p-value calculation that protects the analyst against the overall (familywise) type 1 error rate. The utility of incorporating the empirical Bayes adjustment is illustrated via a number of simulation experiments where we compute various performance measures such as sensitivity, specificity, false discovery rate and false non-discovery rate of the overall testing mechanism with and without the empirical Bayes adjustment.