許多存活分析研究中，Cox比例風險模型(記做Cox模型)時常被廣泛討論以及應用。然而，當使用Cox模型時，所有共變量均需滿足比例風險此條件，一旦有任一共變量違背，Cox模型即無法使用。在此種情況下加速失效時間模型(記做AFT模型)可以做為替代模型，而Cox模型和AFT模型兩者皆為乘法模型。在實際情況有一些研究資料，其共變量以加法效應描述較合適，例如Aalen加法模型。為了處理較複雜的資料，本研究建議一個較廣義的Aalen-Cox加乘法模型，將無法滿足Cox比例風險假設的共變量放置於Aalen-Cox模型中加法部分。此外我們可以進一步用AFT模型取代Cox模型，Aalen-AFT的模型也能被建立。為了處理事件時間結合長期追蹤共變量，我們使用聯合模型方法，結合EM-演算法、馬可夫鏈蒙地卡羅法以及牛頓迭代法做參數估計，以模擬研究來評估本論文所提出之估計方法，最後用愛滋病資料來驗證本論文新方法之實用性。;In many survival studies, Cox PH model is widely discussed and applied in lots of situations. However, when we use Cox model, all the covariates have to satisfy proportional hazard assumption. Once any one of covariates violates the assumption, Cox model cannot be used. In such case, The AFT model may be an alternative model. Both Cox model and AFT model are multiplicative model. There are some research data in practice that are more appropriate to describe the covariate effects as additive, such as the Aalen additive model. To handle complicated data, we propose a more general addictive-multiplicative model, Aalen-Cox model, by putting those covariates which violate proportional hazard assumption into the addictive part in the Aalen-Cox model. In addition, we may further replace the Cox model by AFT model, thus the so-called Aalen-AFT model is constructed. In particular, to handle event time data with longitudinal covariates, we uses the joint model method, incorporating the EM-algorithm、MCMC and Newton-Raphson to do parameter estimation. The estimation method is evaluated via simulation. The Taiwan AIDS cohort data is used to verify the practicability of the new method.
