Estimating the Proportion of True Null Hypotheses in Multiple Testing Problems

Abstract EN

The problem of estimating the proportion, π 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 π 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 π 0 .

The nonparametric likelihood is proposed to be restricted to multinomial models and an EM algorithm is also developed to approximate the estimate of π 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.