在傳統基因與疾病的研究中，通常僅討論一個基因座的影響，但是基因與疾病的關聯性相當複雜，往往致病的因子並不僅止於單一個基因座；因此許多的學者將基因的主效用與交互作用影響一起討論，而且此模式大幅提升了檢定方法的偵測效率。在現有的許多檢定方法中，很難找出一個穩健且檢定力最佳的方法，故本文中我們針對此問題提出一個更穩健且檢定力更佳的方法；先討論兩基因座之模式，再延伸至三基因座以上使得我們的方法的應用更廣泛。事實上，在直接模式(direct model)下統計量是屬於Cochran-Mantel-Haenszel的統計量且在虛無假設下為自由度1的卡方分配；在間接模式(indirect model)下則須要靠排列的方法(permutation procedure)來幫助計算檢定的p值。此處我們並討論population stratification所帶來的影響，並修正我們的統計量使其保有穩定的型I誤差並且有很好的檢定力。利用模擬研究將所提之新檢定統計量與其他方法比較，在直接模式下各有所長，而在間接模式時則是以新檢定統計量較佳。我們並應用此統計量來檢測台灣人的糖尿病視網膜病變(diabetic retinopathy)實際資料。最後，我們提出了一個界限(bound)來幫助我們了解population stratification所帶來的影響大小，進一步了解在檢定時所得到的結果是否適合並正確。

The research in detecting the association of gene and disease often starts at one gene, but it may not be the only one reason which the disease happened since the complication relationship of gene and disease. Complex models which contain more genes, environmental factors and their interactions are discussed, and this kind of models increases detecting efficiency in statistical method. The most important goal is to find a robust and powerful method, so that we want to propose a new method to solve this problem. First, we construct a two factor model for detecting the association of gene and disease. To make our method more general, we further construct a multi-factor model. In fact, the idea of our statistic under direct model is from Cochran-Mantel-Haenszel statistic, and is a Chi-square distribution with degree of freedom one. Under indirect model, we use permutation argument to calculate p-value. We also discuss the effect of population stratification and modify the method to maintain reasonable type I error rate. The statistic is competitive to other methods under direct or indirect model. The use of the proposed method is illustrated with the diabetic retinopathy data in Taiwan. Finally, we propose a specific vision “bound” which help us to understand the bias from population stratification, and also help to detect the correctness of the association tests.

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