本研究建立一個可處理長期追蹤資料及多重事件的半母數聯合模型，以Cox比例風險模型或加速失敗模型的無特定分布準線風險配適各事件時間，事件間的相關性以共享脆弱模型描述，其脆弱因子服從廣義伽瑪分布。使用最大概似估計法估計參數時，會將線性混合效應模型及脆弱模型中的隨機效應當作遺失值處理，所以最大期望演算法將被用於尋找最大概似估計量。在E步驟中將使用蒙地卡羅積分法求得複雜積分的近似值，在M步驟中使用Nelder-Mead單純形法尋找最大概似估計量。最後用愛滋病資料驗證此方法的有效性。;In this study, we establish a more general semi-parametric joint model, which can deal with not only the single event but also the multiple events. We use the unspecified baseline hazard with Cox proportional hazards model or accelerated failure time model to fit the multiple event times with correlation between the events described by shared frailty model. We assume that frailty factor is from the generalized gamma distribution. When estimating the parameters, we treat the random effects from linear mixed effect model and shared frailty model as missing values, thus expectation-maximization algorithm can be implemented to find the maximum likelihood estimates. In E-step, Monte Carlo integration method is used to approximate complex integrals. In M-step, we adopt Nelder-Mead simplex method to find the maximum likelihood estimates. AIDS data is used to demonstrate the usefulness of the proposed method.
