Estimation of false discovery proportion in multiple testing: From normal to chi-squared test statistics

Abstract

Multiple testing based on chi-squared test statistics is common in many scientific fields such as genomics research and brain imaging studies. However, the challenges of designing a formal testing procedure when there exists a general dependence structure across the chi-squared test statistics have not been well addressed. To address this gap, we first adopt a latent factor structure ([14]) to construct a testing framework for approximating the false discovery proportion ($\mathrm{FDP}$) for a large number of highly correlated chi-squared test statistics with a finite number of degrees of freedom $k$. The testing framework is then used to simultaneously test $k$ linear constraints in a large dimensional linear factor model with some observable and unobservable common factors; the result is a consistent estimator of the $\mathrm{FDP}$ based on the associated factor-adjusted $p$-values. The practical utility of the method is investigated through extensive simulation studies and an analysis of batch effects in a gene expression study.