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A Nonparametric Approach for Estimating the Number of True Null Hypotheses in Multiple Testing



The problem is important for the classical multiple comparison procedures to control the probability of type I error in families of comparisons. The solved method is to control the familywise error rate (FWER) or the false discovery rate (FDR) in testing a large number of hypotheses. When some hypotheses are not true, the classical FWER-controlling procedures and FDR-controlling procedures tend to have less power and less error rate than the significance level. To improve the power, Benjamini & Hochberg(2000) proposed an approach is to replace the number of null hypotheses by the number of true null hypotheses in FWER and FDR. Therefore, it is important to correctly estimate the number of true null hypotheses in multiple testing. A nonparametric approach based on the McNemar test is presented. The proposed estimate has the advantage of direct computation. It is not like the other estimation methods that need to compute iteratively. Furthermore, the statistical properties are also explored. The appropriateness of criterion is illustrated with an example from a microarray data set. Finally, a simulation study is conducted to evaluate the performance of proposed procedure and the methods proposed by reviewed literatures. The simulation results show that the proposed procedure has smaller mean square error than the other methods.

Parallel abstracts

在同時檢定多個假設的問題上,控制整體的型一誤差一直是進行多重比較檢定時很重要的議題。解決的方法是控制整體的錯誤率(the familywise error rate;FWER)或錯誤拒絕率(the false discovery rate;FDR)。當某些假設不為真時,控制FWER 和FDR 的方法都會檢定力較小而且趨於保守,欲改進多個統計檢定的檢定力,Benjamini & Hochberg(2000)提出在使用FWER 和FDR 時,利用虛無假設為真的個數來取代所有假設檢定的個數,因此正確的計算虛無假設為真的個數,是非常重要的問題。本文利用McNemar 檢定方法提出一無母數方法,優點是可以直接計算,不像其他方法須透過疊代計算而得。再者,此方法的統計性質也被探討,我們將以基因表現值的資料來舉例說明。最後,使用模擬研究來評估所提方法和過去文獻上方法的表現。模擬結果顯示所提方法比其他方法有較小的均方誤。