本文在病例對照研究之下，探求相對於一種既存標準的醫學診斷方法，另一種嫌究中的醫學診斷方法是否具備非劣性。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非劣性檢定。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曲線，並且根據二條估計的曲線下的部分面積之差異進行非劣性檢定。本文進一步在不同的關聯結構函數、廣義伽瑪分邊際分布、相關係數等條件下，藉由模擬研究探討本文所提檢定方法的型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 non-inferiority of two medicaldiagnostic methods in a case-control study where each subject receiving the twodifferent diagnostics produces correlated paired measurements. Note that itoccurs often in practice that the marginal distributions of the measurements areright-skewed. Therefore, we first apply the power transformation to thepaired data so that they would behave like the bivariate normal data. Oneparametric non-inferiority test is then implemented based on the transformeddata. On the other hand, we suggest and employ appropriate copula functionwhich links two generalized gamma distributions to describe the jointdistribution of the paired measurements. Under the joint distribution, anapproximate test based on the difference between the partial areas under the twoestimated Receiver Operating Characteristic (ROC) curves is then constructed.In this paper, we would like to test if the difference between the true areas iswithin an allowable region. The results of a simulation investigation of thelevel and power performances of the approximate test for different degrees ofcorrelation in several possible copula functions with a variety of marginaldistributions are reported. Finally, a real data set is illustrated by using theapproximate test.
