Estimating the proportion of true null hypotheses, with application to DNA microarray data

We consider the problem of estimating the proportion of true null hypotheses, pi(0), in a multiple-hypothesis set-up. The tests are based on observed p-values. We first review published estimators based on the estimator that was suggested by Schweder and Spjotvoll. Then we derive new estimators based on nonparametric maximum likelihood estimation of the p-value density, restricting to decreasing and convex decreasing densities. The estimators of pi(0) are all derived under the assumption of independent test statistics. Their performance under dependence is investigated in a simulation study. We find that the estimators are relatively robust with respect to the assumption of independence and work well also for test statistics with moderate dependence.