Estimation of the proportion of true null hypotheses in high-dimensional data under dependence

In multiple testing, a challenging issue is to provide an accurate estimation of the proportion π0π0 of true null hypotheses among the whole set of tests. Besides a biological interpretation, this parameter is involved in the control of error rates such as the False Discovery Rate. Improving its estimation can result in more powerful/less conservative methods of differential analysis. Various methods for π0π0 estimation have been previously developed. Most of them rely on the assumption of independent pp-values distributed according to a two-component mixture model, with a uniform distribution for null pp-values. In a general factor analytic framework, the impact of dependence on the properties of the estimation procedures is first investigated and exact expressions of bias and variance are provided in case of dependent data. A more accurate factor-adjusted estimator of π0π0 is finally presented, which shows large improvements with respect to the standard procedures.