190-31: Estimate the False Discovery Rate Using SAS®

This paper gives an exposition of recently developed methods of estimating the false discovery rate (FDR) under multiple comparisons and discusses their implementation using SAS. For example, microarray experiments typically involve tests of significance for hundreds or thousands of genes. For biologists confronted by this problem of multiplicity, the FDR is an appealing quantification of error. Recent literature establishes theoretical properties of an estimator for FDR associated with any chosen critical region. SAS code using the SAS/MACRO, SAS/STAT, and SAS/IML facilities is presented to compute this estimate, and appears in the appendix. Q-values, which are to FDR as p-values are to the type I error rate, are also obtained and used to reproduce plots generated by the R package “qvalue” that may be helpful for conducting multiple tests. Two approaches to estimating the proportion of true null hypotheses are considered. The first arises by choosing several values of a tuning parameter and fitting a smoothing spline (e.g. using PROC TPSPLINE ) to the resulting estimates. The second is to fit a two-component mixture to the sample of observed p-values via maximum likelihood (using PROC NLMIXED). A microarray example using p-values from tests on 384 genes is given.