# 臺灣博碩士論文加值系統

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 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.
 摘要 iAbstract ii致謝 iii第一章緒論 1第二章研究方法 72.1 Cox 比例風險模型(Cox Proportional Hazards Model) 92.2 加速失敗時間模型(Accelerated Failure Time Model) 102.3 共享脆弱模型(Shared Frailty Model) 112.4 聯合模型(Joint Model) 122.5 聯合概似函數(Likelihood Function) 142.6 最大期望演算法(Expectation-Maximization algorithm) 182.6.1 E 步驟(E-step) 182.6.2 M 步驟(M-step) 212.7 數值方法(Numerical Methods) 242.7.1 蒙地卡羅法(Monte Carlo method) 242.7.2 Nelder-Mead 單純形法(Nelder-Mead Simplex method) 25第三章模擬研究 30第四章實例分析 35第五章結論與討論 39參考文獻 42
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