藥物反應研究中，為了探討某一種藥物的效果，經常進行數個不同的治療方式當作處理組和一個對照組來做比較。醫學上所蒐集到的資料經常出現右設限資料，導致分析的困難，針對右設限存活資料，當兩組存活函數呈現交叉時，通常不會檢定兩組的存活函數有無差異，而是針對特定的時間點下兩組存活函數是否有差異。此外，藥物的藥效可能隨時間而改變，具相同條件的病人，其療效也不見得相同。這是因為病人本身的異質性所造成，而引起變異的因素不見得觀察的到。因此，本文考慮推廣Jeong et al. (2003)方法，在伽瑪脆弱(frailty)模型下，建立多組存活函數差異的聯合信賴區間。藉用模擬的方法來說明在特定時間點的多組存活函數差異聯合信賴區間的覆蓋機率以及面積的表現。最後將所提的方法應用於一筆實際資料做說明。 Medical studies for drug development are frequently conducted to evaluate the treatment effects of a drug, where subjects or patients are randomly allocated to receive different treatment groups of the drug and a control. For right-censored survival data, it is usually interested in comparing the difference between two survival functions at a fixed time point rather than comparing the entire survival curves, when the survival functions are crossing. Moreover, in practice, a treatment effect may fades as time progresses. Even for the patients with the same covariates, not only might their survival times be different, but their individual survival functions could also be different. To account for variability due to unobserved individual-level factors, therefore, in this thesis, we extend the method of Jeong et al. (2003) and consider construct the simultaneous confidence interval for the difference of several survival functions under a gamma frailty model for randomly right-censored survival data. The associated coverage probability and the interval will be investigated via a simulation study. The implementation of the confidence interval will be illustrated using a real data set.
