二階段多重檢定之設計

Abstract

多重檢定問題的產生，是由於同時進行多個檢定的推論。主要的考量在於避免犯型一錯誤與型二錯誤，也就是控制偽陽率及提升檢定力。隨著檢定的個數變大，犯型一錯誤的機會也增加。傳統的Bonferroni方法雖然可以有效的控制型一錯誤，但是嚴格的顯著水準卻造成了型二錯誤的增加。在利用SNP作為相關性研究的材料，以尋找可能的基因位置時，提升檢定力是較為重要的考量，以利於找出有可能的基因位置。本論文針對多重檢定的二階段設計進行研究，在給定的條件之下，藉著演算的方式求出檢定力與偽陽率，並且透過模擬研究，來分析影響檢定表現的因素。本論文主要目的在提出二階段設計方式的建議，包括第一階段顯著水準建議設為0.05，以及整合性的樣本數估計方法等。

Multiple testing problem occurs when the simultaneous inference of multiple statistical tests is of interest. Two major concerns when design with multiple testing are type I error and power. In other words, a large power under limited false positive rate is the focus. However, as the number of tests increases, the overall false positive rate increases. Traditional Bonferroni’s method is conservative and controls overall false positve rate well. Consequently, its overall power is usually small. In association studies using SNP’s as genetic markers, it is common that the statistical power becomes more important than the type I error. This thesis focuses on a two stage design for multiple hypothesis testing. I will present the exact calculation of power and false positive rate under given conditions. An efficient algorithm for computation will also be presented. Analysis of possible influential factors will be investigated through simulation studies. Recommendations for the two stage design will be suggested, including choice of the sample size and using 0.05 as the first stage significance level.