模擬發現控制FDR檢定過程之表現特質

Simulated Discoveries by Adaptive FDR-adjusted Procedures in Large-Scale Multiple Testing

黃義筌(Yi-Chuan Huang)

指導教授 ： 汪群超

國立臺北大學/商學院/統計學系/碩士(2009年)

摘要

Benjamini 及 Hochberg (1995) 根據拒絕總個數中錯誤拒絕之期望比例 (FDR,錯誤發現率)為準則提出一次同時大量檢定過程，本文簡記作 BH。利用模擬研究發現，此檢定過程的真實FDR表現會隨著虛無假設為真的比例下降和資料間存在高度內相依的影響而趨於保守。隨後，Benjamini 及 Hochberg (2000) 提出調整FDR誤差水準後執行BH檢定過程的方法，可以改善虛無假設為真比例下降所所造成FDR過於保守的問題；再者，模擬研究所設計的組合實驗則可以有效改善資料內相依結構所造成的問題，並使得檢定結果更加可靠。本文模擬展示4種對虛無假設為真之比例進行估計的調整BH檢定過程，企圖暸解當資料來自不同程度高低的相依結構在不同實驗控制虛無假設的比例之下，各種組合下產生多種不同結果的表現型態，期望可以提供後續研究探討的指引或參考依據。

關鍵字

錯誤發現率 ； BH 檢定過程 ； 調整 BH 檢定過程

並列摘要

The FDR (False Discovery Rate) is the expectation of proportion of the rejected true null hypotheses among all rejected hypotheses. In large-scale multiple testing problems, Benjamini and Hochberg (1995) developed the multiple testing procedure (BH procedure) based on the p values of the individual tests and FDR-controlling. In this paper, the main goal is to separate the alternative cases from the null cases. When the number of true alternative hypotheses increases, these controlling procedures become too conservative. Benjamini and Hochberg (2000) proposed an adaptive BH procedure that can improve the decline in the proportion of true null hypotheses of the problem, but ignores the increased expected number of type I errors. Furthermore, a design of data-reformed is proposed and is shown to effectively alleviate the problem caused by data dependencies within the structure. Four different adaptive BH procedures under various scenarios are simulated. The results can serve as a reference for further study.

並列關鍵字

FDR ； BH Procedure ； Adaptive BH Procedure

參考文獻

Benjamini, Y., Hochberg, Y. (2000). On the adaptive control of the false discovery rate in multiple testing with independent statistics. Journal of Educational and Behavioral Statistics. 25(1), 60-83.

Benjamini, Y., Yekutieli, D. (2001). The Control of the False Discovery Rate in Multiple Testing Under Dependency. The Annals of Statistics, 29(4), 1165-1188.

Benjamini, Y., Yekutieli, D. (2005). Quantitative Trait Loci Analysis Using the False Discovery Rate. Genetics. 171, 783-790.

Benjamini, Y., Yekutieli, D. (2005). False discovery rate - adjusted multiple confidence intervals for selected parameters (with Discussion). Journal of the American Statistical Association. 100, 71-80.

Benjamini, Y., Krieger, A. M., Yekutieli, D. (2006). Adaptive Linear Step-up False Discovery Rate controlling procedures, Biometrika. 93(3), 491-507.