- 學位論文
真實虛無假設個數估計方法與修正控制FDR檢定之探討
Evaluations of estimators of the number of true null hypotheses and adaptive FDR controlling procedures under multiplicity testing
摘要
在實驗中若需同時檢定多個假設時,檢定時設定每個假設都有相同的顯著水準,將會造成整體的型一誤差過於膨脹。一般常見的型一誤差為族誤差率(Family-Wise Error Rate; FWER)或是偽陽率(False Discovery Rate; FDR)。現有許多可以控制FDR或FWER的控制準則,但在真實對立假設的個數不少時,這些檢定通常會過份保守。為改善此缺點,Benjamini 和 Hochberg(2000)提出利用估計真實虛無假設的個數(m0)來調整控制 FDR 的檢定準則。許多研究學者陸續提出估計m0的方法,例如: Hsueh 等(2003)及 Hwang(2007)。本篇文章將介紹幾個文獻中估計m0的方法,另外提出幾種估計m0的方法的修正方法。再者,利用蒙地卡羅模擬來評估估計方法的精確性及準確性會,此些估計方法會套用在Benjamini及Hochberg(2000)所提的檢定準則中來衡量m0估計方法的實用性。
並列摘要
The overall Type I error may be inflated if many hypotheses are compared simultaneously. The Family-Wise Error Rate(FWER) and the False Discovery Rate(FDR) are some of commonly used methods to define the overall Type I error. Many controlling FWER and FDR procedures are proposed and have good ability in controlling the overall Type I error under certain scenarios. However, when the number of true alternative hypotheses increases, these controlling procedures become too conservative. To overcome this problem, Adapting the information of the number of true null hypotheses(m0), Benjamini and Hochberg(2000) proposed an adaptive FDR controlling procedure. Many estimators of m0 have been proposed, for example, Hsueh et al.(2003) and Hwang(2007). This thesis proposes new estimators for m0, which are used to implement in the adaptive procedures. Monte Carlo simulations are used to evaluate accuracy and precision of new estimators. Moreover, the feasibility of these new adaptive procedures is evaluated under various simulation settings.