在本論文中，利用CD4 細胞數以及病毒承載量來預測愛滋病患的發病時間，並探討使用雞尾酒療法與沒有使用雞尾酒療法對愛滋病患的療效。此種包含長期追蹤共變數與存活時間的資料，常會因為長期追蹤資料的測量誤差或生物體本身的差異，以及共變數觀測值測量與存活有關時，導致推論產生偏差，因此，本研究利用聯合模型來解決此問題，在生物指標方面，使用線性隨機效應模型對長期追蹤資料做配適，並利用概似比檢定診斷長期追蹤模型的適合度；在事件時間方面，使用Cox比例風險模型描述共變數與存活時間之關係。結合這兩部分建構出多重長期追蹤資料的聯合概似模型且利用EM演算法對參數做估計。 In this thesis, we use AIDS patients’ CD4 counts and viral loads to predict their onset times and explore the curative effect whether patients were treated with HAART. Usually, the study data include longitudinal and survival time information, and, in general, result in inference bias due to the measurement errors on the longitudinal part, the differences among patients themselves, or the time-dependent covariates. Thus, we use the joint model to solve this problem. The approach uses a linear random effects model to characterize the longitudinal part and conducts the likelihood test to select a suitable longitudinal model, and utilizes the Cox proportional hazard model to describe the relationship between covariates and survival time information. Incorporated these two parts to build a multiple longitudinal data joint likelihood function of which EM algorithm is implemented to search for the maximum likelihood estimate.
