利用混合模式之估計處理多重檢定

處理多重檢定問題時，必須注重有效性及正確性，因此如何應用所得到的資料，增加更多有效資訊以完成檢定，並且準確判別出各檢定的真實情況，是值得關注研究的課題。以往的多重檢定程序，多針對多重檢定中所有檢定的p值，並尋找一個合適臨界切點(Threshold)，本文提出一個與以往多重檢定程序不同的想法，先引入混合模式(Mixture Model)的概念，進行多重檢定中對立假設為真的比例之估計，再將估計後所得到的資訊，藉由排序後之p值或貝氏因子(Bayes Factor)，以判別各個檢定是否顯著地拒絕虛無假設。本文也利用模擬研究，探討本文所提出之多重檢定方式與其他的多重檢定程序，於判別對立假設為真比例的準確情形，以及整體型一誤差與整體檢定力的表現；而由分析結果顯示，本文提出之方法，能夠較準確的估計出所有檢定中對立假設為真的比例；且利用此方式，在一般條件下，能夠稍加改善Bonferroni法與Benjamini-Hochberg程序分別於整體檢定力與整體型一誤差較為不佳的情況，而提供一個較中和且適當的判別決策。

關鍵字

多重檢定；混合模式；最大概似估計值；後驗分配眾數值； p值；貝氏因子

並列摘要

Current research about multiple hypotheses testing has focused more on the development of strategies in order to increase the overall power. Most approaches try to identify a number when deciding the threshold for p values. If only a fixed proportion of the null hypotheses are true, then for each hypothesis, it may have a certain probability of being significant. Here I adopt the mixture model to account for the uncertainty. In other words, after considering the possibility of being true and false, the test statistic becomes a weighted average with the weight equals to the probability that the hypothesis is true. The value of the threshold is then determined based on the estimate of the proportion. This procedure can be applied to frequentisits’ approach using p values or Bayesians’ Bayes factors. Simulations studies are conducted to assess the performance of the proposed procedure and comparisons are made with the traditional Bonferroni’s procedure and Benjamini-Hochberg (BH) procedure. It appears that this proposal has a smaller overall type I error, and achieves almost the same power as BH procedure.

並列關鍵字

Multiple Testing ； Mixture Model ； Maximum Likelihood Estimator(MLE) ； Posterior Mode ； p-Value ； Bayes Factor

參考文獻

Benjamini, Y., and Hochberg, Y. (2000), “On the Adaptive Control of the False Discovery Rate in Multiple Testing With Independent Statistics”, Journal of Education and Behavioral Statistics, 25, 60-83.

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

Benjamini, Y., Yekutieli, D. (2005), “False Discovery Rate－Adjusted Multiple Confidence Intervals for Selected Parameters”, Journal of the American Statistical Association, 100, 71-81.

Casella, G., and Berger, R. L. (2001), Statistical Inference, CA: Duxbury.

Genovese, C., and Wasserman, L. (2002), ”Operating Characteristics and Extensions of The False Discovery Rate Procedure”, Journal of the Royal Statistical Society, Ser. B, 64, 499-517.

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利用混合模式之估計處理多重檢定

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