利用混合模型估計多重比較中真實虛無假設個數

Using mixture models to estimate the number of true null hypotheses in the multiple comparison

許乾祐(Chian-You Hsu)

指導教授 ： 黃怡婷

國立臺北大學/商學院/統計學系/碩士(2008年)

摘要

控制整體的型一誤差一直是進行多個統計檢定時很重要的議題。對於型一誤差的定義有族型一誤 (familywise error rate) 或是偽陽率 (false discovery rate),有許多相對應的檢定準則可以控制FWER 或 FDR,但在錯誤虛無假設的個數增加時,控制FWER或 FDR的方法都會趨於保守。Benjamini 和 Hochberg (2000)提出以正確虛無假設的個數來調整原有的控制FWER或 FDR的方法,用以提高檢定的控制型一誤的能力及提高檢定力。為有效始用調整檢定的檢定方法,本論文套用Parker 及 Rothenberg (1988) 的混合模型,假設多重比較中每一個檢定所產生的檢定統計量的值,或每一個檢定所產生的P值會服從混合模型,利用混合模型中的參數估計來預測正確虛無假設的個數,而混合模型的參數估計利用EM演算法加以迭代求得。為正確知道配適混合模型的成分個數,用重抽方法及Cramer-von Mises檢定來選取最恰當的成分個數。文中以不同情況的資料型態加以模擬,最後再使用白血病(Leukemia)患者的基因表現資料對上述方法進行實證討論。

關鍵字

Cramer-von Mises 檢定 ； 混合模型 ； 多重比較 ； EM演算法 ； 概似比檢定 ； 白血病

並列摘要

Controlling the overall Type I error is an important issue in the multiple hypotheses. Familywise error rate (FWER)or false discovery rate (FDR) are commonly used definitions for Type I error and controlling procedures are proposed accordingly.
However, when the number of true alternative hypotheses
increases, the ability in controlling Type I error and the power of the controlling procedures reduce. Benjamini and Hochberg (2000) proposed a adaptive procedure that incorporates the number of true null hypotheses and is shown to have the ability in controlling the error and have higher power. To use this adaptive procedure, this thesis adapts the mixture model proposed by Parker and Rothenberg (1988) to model the test statistics or the corresponding $p$ values from the multiple hypotheses. The model parameter can be used to estimate the number of true null
hypotheses. Furthermore, the bootstrap type likelihood ratio test and Cramer-von Mises test are used to assess the number of components in the mixture model. Simulations are performed to evaluate the feasibility of this model. Gene expression data for leukemia patients are used to illustrate the method.

並列關鍵字

Bootstrap ； Cramer-von Mises test ； EM algorithm ； likelihood ratio test ； mixture model ； multiple comparison

參考文獻

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