A robust method for large-scale multiple hypotheses testing.

When drawing large-scale simultaneous inference, such as in genomics and imaging problems, multiplicity adjustments should be made, since, otherwise, one would be faced with an inflated type I error. Numerous methods are available to estimate the proportion of true null hypotheses pi(0), among a large number of hypotheses tested. Many methods implicitly assume that the pi(0) is large, that is, close to 1. However, in practice, mid-range pi(0) values are frequently encountered and many of the widely used methods tend to produce highly variable or biased estimates of pi(0). As a remedy in such situations, we propose a hierarchical Bayesian model that produces an estimator of pi(0) that exhibits considerably less bias and is more stable. Simulation studies seem indicative of good method performance even when low-to-moderate correlation exists among test statistics. Method performance is assessed in simulated settings and its practical usefulness is illustrated in an application to a type II diabetes study.