CD4淋巴細胞是判斷愛滋病的重要指標，本篇針對愛滋病來研究，主要是觀察CD4百分比與存活時間之間的關係，並探討雞尾酒療法對愛滋病病患的療效，病患在不同時間重複測量CD4百分比作為有興趣的長期追蹤資料，傳統方法是使用部份概似法來分析，但是使用部分概似法必須要知道每一個病患的共變數歷史、不能有測量誤差與測量次數要夠多等要求，但臨床上常會因為個體本身差異與測量誤差等因素導致偏誤的產生。因此我們將使用能同時配適存活時間與長期追蹤資料的聯合模型來解決此種問題。在此我們將針對廣義的擴充風險模型來探討，因為Cox比例風險模型與加速失敗模型就是擴充風險的特例，而且在有時間相依共變數下 (CD4百分比就是時間相依共變數)，並沒有一個簡單的方法來檢測加速失敗模型是否能合理配適資料，為解決此問題我們會透過對迴歸參數作華特 (Wald)信賴區間、百分比信賴區間與偏誤修正百分比信賴區間來作模型選擇。

The CD4 lymphocytes is an important indicator of diagnosis of AIDS, this paper mainly studied of AIDS, and investigates the association between the percentage of CD4 and the survival time, and explores the efficacy of HAART to AIDS patients. The patients repeated measurements the percentile of CD4 at different times as an interesting longitudinal data. The traditional approach have been employs the partial likelihood method to analyze the above data, but the partial likelihood method has to recognize the covariate history for each subject, and satisfy the requirements that the measurement error can not exist and the number of measurements should be enough for each subject. However, in the clinical trial, the individual differences, measurement error, and the other factors have usually result in bias. Therefore, we use the jointing model, fitting the survival time and longitudinal data simultaneously, to solve this problem. Here we focus on the generalized extended hazard model because Cox proportional hazards model and accelerated failure model are two special cases of the extended hazard model. Under a time-dependent covariates assumptions, there is no simple method to detect that the accelerated failure model is suitable for data fitting. To solve this problem, we use the regression parameters to do model selection through the Wald confidence interval, the percentile confidence interval and the bias-correction percentile confidence interval.

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