存活時間與長期追蹤的生物指標之間的關聯，在許多醫學研究中時常被探討，在過去的文獻中，使用聯合模型同時分析存活時間與長期追蹤資料，是前述研究較為有效率的統計方法之一。此方法的存活模型最常使用Cox 比例風險模型，但Cox比例風險模型是一種乘法模型，且需要滿足比例風險條件，可是當共變量不符合比例風險又或著是共變量並非乘法效應時，便不適合使用Cox比例風險模型。本篇使用較為廣義的Cox-Aalen加乘法模型，將不符合比例風險的部分放置加法部分解決以上的問題，並結合聯合模型探討長期追蹤資料與存活時間之間的關聯，為了增加解釋能力，我們利用Weibull、Lognormal、Log-logistic和Gamma 等四種參數模型估計基底風險。參數估計由聯合概似函數及EM 演算法求得。Cox 模型和Aalen 模型為Cox-Aalen 模型的特殊案例，故可以使用概似比檢定進行模型選擇，判斷資料使用何種模型較為合適，針對各種不同的情況進行模擬研究，並以台灣愛滋病世代研究資料為例進一步進行實例分析。;The association between survival time and longitudinal data has been explored in manymedical studies frequently. In the literature, a joint model approach is one of efficient way to analyze survival data with longitudinal covariate at the same time. The most commonly used survival model is the Cox proportional hazards model. However the Cox proportional hazards model is a multiplicative model which needs to satisfy the proportional hazards assumption. Either the proportional hazards assumption may fail or covariate effect is not suitable in a multiplicative form. Consequently, we propose a generalized Cox-Aalen model, which includes addition and multiplicative component in the hazard function. In order to increase the explanatory capacity, we use four parameter models such as Weibull, lognormal, log-logistic, and gamma distribution to estimated baseline hazard. Cox model, Aalen model are special case from Cox-Aalen model, so we can make the model choice by likelihood ratio test, and then decide model is more appropriate. Hence, this paper uses the joint model and estimates the unknown parameters through the Monte Carlo EM Algorithm. Via simulation research to validate the effectiveness of the multiplication model and the case analysis was further conducted based on Taiwan HIV/AIDS cohort study data.
