本篇論文利用CD4細胞數和病毒乘載量來預測愛滋病患的發病時間，並探討愛滋病患接受雞尾酒療法是否有療效。有重複測量的長期追蹤資料常常因為機器、人為測量誤差或生物體本身的差異，造成觀測上的誤差，因此本研究利用聯合模型來解決這樣的問題。在生物指標的部分，使用線性混合效應模型對長期追蹤資料軌跡做配適；在事件時間的部分，使用加速失敗時間風險模型描述共變數與存活時間的關係，再結合這兩個部分建構出聯合模型，並使用EM演算法對參數做估計，其中使用拔靴法來估算參數估計值的標準差。

關鍵字：聯合模型、長期追蹤資料、線性混合效應模型、加速失敗時間風險模型 、EM演算法、拔靴法。

In this thesis, we use CD4 and viral load to predict AIDS patients’ time to death and explore whether HAART works or not when patients were treated with it. The study which contains longitudinal covariates and survival time information is usually subject to measurement errors. Thus, we use joint model to solve this problem instead of partial likelihood approach. The approach uses linear mixed effects models to fit the longitudinal part and conducts the likelihood ratio test to select the suitable longitudinal model, and utilizes the accelerated failure time model to describe the relationship between covariates and survival time information. We combine these two parts to build a joint likelihood function and estimate the maximum likelihood estimators of all parameters by EM algorithm. The estimates of standard errors are derived by bootstrap method.

Keywords: join model, longitudinal data, linear mixed effects model, accelerated failure time model, EM algorithm, bootstrap method.

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