Estimating the number of true null hypotheses in multiple hypothesis testing

摘要

The overall Type I error computed based on the traditional means may be inflated if many hypotheses are compared simultaneously. The family-wise error rate (FWER) and false discovery rate (FDR) are some of commonly used error rates to measure Type I error under the multiple hypothesis setting. Many controlling FWER and FDR procedures have been proposed and have the ability to control the desired FWER/FDR under certain scenarios. Nevertheless, these controlling procedures become too conservative when only some hypotheses are from the null. Ben-jamini and Hochberg (J. Educ. Behav. Stat. 25:60-83,2000) proposed an adaptive FDR-controlling procedure that adapts the information of the number of true null hypotheses (mo) to overcome this problem. Since m_0 is unknown, estimators of m_0 are needed. Benjamini and Hochberg (J. Educ. Behav. Stat. 25:60-83, 2000) suggested a graphical approach to construct an estimator of mo, which is shown to overestimate m_0 (see Hwang in J. Stat. Comput. Simul. 81:207-220, 2011). Following a similar construction, this paper proposes new estimators of m_0· Monte Carlo simulations are used to evaluate accuracy and precision of new estimators and the feasibility of these new adaptive procedures is evaluated under various simulation settings.