Estimating the proportion of true null hypotheses in multiple testing problems (Q1658053)

Summary: The problem of estimating the proportion, \(\pi_0\), of the true null hypotheses in a multiple testing problem is important in cases where large scale parallel hypotheses tests are performed independently. While the problem is a quantity of interest in its own right in applications, the estimate of \(\pi_0\) can be used for assessing or controlling an overall false discovery rate. In this article, we develop an innovative nonparametric maximum likelihood approach to estimate \(\pi_0\). The nonparametric likelihood is proposed to be restricted to multinomial models and an EM algorithm is also developed to approximate the estimate of \(\pi_0\). Simulation studies show that the proposed method outperforms other existing methods. Using experimental microarray datasets, we demonstrate that the new method provides satisfactory estimate in practice.