在醫學應用上，常見的問題為，針對兩組相依的右設限資料(或成對右設限資料)，檢定兩組的存活函數是否有差異。當兩組存活函數呈交叉現象時，通常不會檢定兩組的存活函數的差異，而是在固定一些感興趣的時間點上比較兩組的存活機率之差異。針對兩組獨立資料， Klein et al. (2007)提出在固定時間上比較兩組的存活機率的檢定統計量。然而，這些檢定統計量無法適用在兩組相依資料上。因此，本論文針對兩組相依資料，推廣Klein et al. (2007)所建議的檢定統計量，在固定時間上比較兩組的存活機率之差異。接著以模擬方式探討所推廣的檢定統計量，其漸近分布的準確性，和比較這些檢定統計量的檢定力。最後，將這些檢定統計量應用於比較糖尿病患者接受二種治療方法後的五年失明機率。

A common problem arises in many medical applications is testing equality of survival functions based on paired right-censored data. Rather than comparison of entire survival curves, interest is often focused on the comparison at a fixed point in time when the survival curves of the treatments are known to cross. Klein et al. (2007) had studied a number of methods for comparing two survival functions at a fixed point in time based on some transformations of the survival function for two independent samples of right-censored data. However, these test statistics are not appropriate for paired right-censored data since the intra-pair correlation are ignored. Therefore, in this paper, Klein’s methods are extended to compare the equality of two survival functions at a fixed point in time for paired right-censored data and the standard error of test statistics should be modified to accommodate the possible dependence between matched subjects. Finally, simulation studies are conducted to assess finite sample properties, and the methods are illustrated with an application to a diabetes data in Diabetic Retinopathy Study.

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