探討以真實虛無假設個數估計量修正控制 FDR 之多重比較法

Evaluations the performance of the modified controlled FDR procedures based on the estimated number of the true null hypotheses.

蔡明哲(Ming-Che Tsai)

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

在多重問題比較中，早期方法是以相同的顯著水準作為檢定準則，其結果將造成整體檢定的型一誤差率過於膨脹。 Bonferroni (1936) 以至少發生一次錯誤拒絕假設的機率當作型一誤差率的控制準則， 稱 FWER (Family-Wise Error Rate)。由於依據此控制準則之檢定的結果造成檢定力過低，Benjamini 與 Hochberg (1995) 提出在檢定已拒絕的虛無假設中真實虛無假設占的比例之期望值 (稱 FDR， False Discovery Rate)， 改善 FWER 準則的缺點。 文獻中所提之檢定方式皆假設在弱控制的情況下， 但在對立假設為真的個數增加時， 檢定方法之控制型一誤的能力下降，因而導致檢定力下降很多。 Benjamini 與 Hochberg (2000) 建議利用真實虛無假設的個數 (m0) 來建構檢定準則，使得檢定方法有控制型一誤的能力， 但實驗中 m0 值是未知的， 過去文獻中許多學者陸續提出估計 m0 的方法， 本論文將以電腦模擬來評估不同環境下各估計 m0 方法的表現， 再將估計結果運用在控制 FDR 之檢定準則中，並以敏感度、 專一性、 偽陰性、 偽陽性及族錯誤率來衡量方法之好壞。

關鍵字

真實虛無假設個數 ； 多重檢定 ； FDR ； FWER ； 敏感度 ； 專一性 ； 偽陰率

並列摘要

In the multiple comparisons problem, using the same significant level for each hypothesis is a common practice but in turn, it will inflate the overall type I error rate.
Bonferroni (1936) suggested using the probability of rejecting at least one true null hypothesis as the Type I error rate, which is so called FWER (Family-Wise Error Rate). However, the power of the testing procedures based on FWER is very low. Benjamini and Hochberg (1995) thus proposed using the expected proportion of errors among the rejected hypotheses (FDR, False Discovery Rate). Nevertheless, most of the testing procedures proposed in the literatures assume under the weak-control. As a result, as the number of the true alternative hypotheses increases, the power of these testing methods will be decreasing dramatically. Benjamini and Hochberg (2000) used the number of the true null hypotheses (m0) to establish the testing criterion which can preserve the Type I error and in turn improve power. However, the value of m0 in experiment is often unknown; many estimators m0 have been proposed. This thesis will use Monte Carlo simulations to evaluate of the performance of the estimators under various settings. In addition, these estimators are used to form the adaptive testing procedures. We further investigate how the performance of the adaptive testing procedures based on five criteria, specificity, sensitivity, FDR, FNDR, FWER, is.

並列關鍵字

The number of True Null Hypotheses ； Multiplicity Testing ； FDR ； FWER ； Sensitivity ； Specificity ； FNDR

參考文獻

Controlling the false discovery rate: a practical and powerful approach to multiple testing.

Bonferroni, C. E.(1936)

Teoria statistica delle classi e calcolo delle probabilita,

Benjamini, Y., Liu, W. (1999).

A distribution-free multiple hypotheses testing produce that controls the false discovery rate.