How accurately can we control the FDR in analyzing microarray data?

We want to evaluate the performance of two FDR-based multiple testing procedures by Benjamini and Hochberg (1995, J. R. Stat. Soc. Ser. B, 57, 289-300) and Storey (2002, J. R. Stat. Soc. Ser. B, 64, 479-498) in analyzing real microarray data. These procedures commonly require independence or weak dependence of the test statistics. However, expression levels of different genes from each array are usually correlated due to coexpressing genes and various sources of errors from experiment-specific and subject-specific conditions that are not adjusted for in data analysis. Because of high dimensionality of microarray data, it is usually impossible to check whether the weak dependence condition is met for a given dataset or not. We propose to generate a large number of test statistics from a simulation model which has asymptotically (in terms of the number of arrays) the same correlation structure as the test statistics that will be calculated from the given data and to investigate how accurately the FDR-based testing procedures control the FDR on the simulated data. Our approach is to directly check the performance of these procedures for a given dataset, rather than to check the weak dependency requirement. We illustrate the proposed method with real microarray datasets, one where the clinical endpoint is disease group and another where it is survival.