在許多臨床醫學實驗中, 同時觀察多重的存活時間及長期追蹤共變數已變的非常常見. 在過去文獻的相關研究,聯合模型法經常用來分析存活時間與長期追蹤共變數並尋找兩者之間的關聯.早期的研究重心通常基於事先選定的單一存活模型而後發展有彈性適應不同情況的長期追蹤過程.而這事先選定的單一存活模型最常選擇Cox模型.基於聯合模型的架構之下,我們提出邊際模型法處理多重存活時間之情行.此邊際法是借用現行研究假設存活時間之間為獨立.此邊際法可導入多種常用的半母數存活模型於概似函數中.這些半母數存活模型除了包含Cox模型外也可導入AFT, 擴充風險等等模型.此邊際法使用蒙地卡羅EM演算法來求取最大概似估計並以拔靴法來計算參數估計的標準誤.此方法將藉由模擬研究來評估其好壞,並由實例分析來闡述其實用性. In clinical trials and other medical studies, it has become increasingly common to observe multiple event times of interest and longitudinal covariates simultaneously. In the literature, joint modeling approaches have been employed to analyze both survival and longitudinal processes and to investigate their association. Early attention has mostly been placed on developing adaptive and flexible longitudinal processes based on a prespecified univariate survival model, most commonly chosen as the Cox proportional model. We propose a marginal likelihood approach to handle multivariate survival time in joint model framework which implements the similar idea of marginal methods used in literature by ignoring the dependency among event times. The marginal likelihood could be easily incorporated various survival model in the likelihood function including two popular survival models, Cox and AFT models, or others such as extended hazard model. The maximization of the marginal likelihood is conducted through Monte Carlo EM and the standard error estimates are obtained via bootstrap method. The performance of the procedure is demonstrates through simulation study. A case study of cancer vaccine data from Eastern Cooperative Oncology Group (ECOG) further illustrates the usefulness of the proposed marginal approach. 研究期間：10008 ~ 10107
