Sample size calculations for controlling the distribution of false discovery proportion in microarray experiments

The false discovery proportion (FDP), the proportion of false rejections among all rejections, provides useful criteria for controlling false positives in multiple testing to detect differential genes in microarray experiments. Owing to a substantial variability in FDP for correlated genes, some authors considered controlling actual FDP, instead of its expectation, that is false discovery rate, in multiple testing. However, there has been no attempt to do this in the design of microarray experiments. In this article, we develop a procedure for sample size calculation to control the distributions of FDP and true positives simultaneously under blockwise correlation structures among genes. The sizes of gene blocks, correlation coefficients, and effect sizes within gene blocks can vary across gene blocks. Gene clustering is proposed to identify gene blocks using historical data sets. The adequacy of the procedure is demonstrated using simulated data sets. An application to a clinical study for lymphoma is also provided.