Comparison of Methods for Estimating the Proportion of Null Hypotheses π0 in High Dimensional Data When the Test Statistics is Continuous

Abstract

Advances in Genomics have re-energized interest in multiple hypothesis testing procedures but have simultaneously created new methodological and computational challenges. In Genomics for instance, it is now commonplace for experiments to measure expression levels in thousands of genes creating large multiplicity problems when thousands of hypotheses are to be tested simultaneously. Within this context we seek to identify differentially expressed genes, that is, genes whose expression levels are associated with a particular response or covariate of interest. The False Discovery Rate (FDR) is the preferred measure since the Family Wise Error Rates (FWERs) are usually overly restrictive. In the FDR methods, estimation of the proportion of null hypotheses (π0) is an important parameter that needs to be estimated.In this paper, we compare the effectiveness of 12 methods for estimating π0 when the test statistics are continuous using simulated data with independent, weak dependence, and moderate dependence structures.