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

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 (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 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. © 2017, Institute of Mathematical Statistics. All rights reserved.