本文在病例對照研究之下，建立兩種醫學診斷方法的相等性檢定。此一研究中的每一個受試者皆接受兩種不同的診斷方法，所得到的是具有相關性的成對診斷值。本文考慮將成對資料利用冪轉換，轉換成近似二元常態分布的資料，然後進行現有文獻中的有母數相等性檢定。另一方面，本文應用不同的廣義伽瑪分布描述右偏分布的二個診斷資料，並且使用適當的關聯結構函數(Copula)聯結上述的兩個邊際分布，用以描述成對資料的聯合分布。然後，在此一聯合分布之下，建構兩條受試者操作特徵(Receiver Operating Characteristic; ROC)曲線，並且根據二條估計的曲線下面積之差異進行相等性檢定，驗證這兩種醫學診斷方法的受試者操作特徵曲線下面積的真正差異是否在可容忍的範圍內。本文進一步在不同的關聯結構函數、邊際分布、相關係數等條件下，藉由模擬研究探討本文所提到檢定方法的型I 誤差率和檢定力表現。最後藉由分析一個實例說明上述檢定方法的應用。 In this paper, we consider testing the equivalence of two medical diagnostic methods in a case-control study where each subject receiving the two different diagnostics produces correlated paired measurements. Note that it occurs often in practice that the marginal distributions of the measurements are right-skewed. Therefore, we first apply the power transformation to the paired data so that they would behave like the bivariate normal data. One parametric equivalent test is then implemented based on the transformed data. On the other hand, we suggest and employ appropriate copula function which links two generalized gamma distributions to describe the joint distribution of the paired measurements. Under the joint distribution, an approximate test based on the difference between the areas under the two estimated Receiver Operating Characteristic (ROC) curves is then constructed. In this paper, we would like to test if the difference between the true areas is within an allowable region. The results of a simulation investigation of the level and power performances of the approximate test for different degrees of correlation in several possible copula functions with a variety of marginal distributions are reported. Finally, a real data set is illustrated by using the approximate test.
