在本篇文章中，我們利用免疫球蛋白抗體Igm值以及注射疫苗的不同(IFN+GMK和GMK)來評估術後黑色素細胞瘤病患的復發狀況。主要是利用聯合模型(joint model)的概念來對資料做分析，聯合模型包含了兩種訊息，其一為長期追蹤資料，其二為存活資訊。以聯合模型所求得的參數估計值具有一致性(consistency)、有效性(efficiency)以及漸進常態(asymptotic normality)的性質。在第一部分我們使用線性隨機效應模型(linear random effect model)對長期追蹤資料做配適，並利用概似比檢定診斷長期追蹤模型的適合度。而在第二部分則是使用Cox比例風險模型描述變數與存活時間。結合這兩部分建構出聯合概似模型且利用EM演算法(expectation maximize algorithm)對參數做估計。接著利用Wald type 拔靴法、Percentile拔靴法及BC percentile 法檢視參數的顯著與否。In this study, we want to investigate the relationship between recurrent time of patients with resected melanoma and their immunoglobulin M serologic. In addition, we are interested in the influence of different types of vaccines. Since the data includes both information of survival and longitudinal processes, joint model approach is applied to analyze the data. The longitudinal data is described by a linear random effects model, and the survival time is fitted by the Cox model. To derive the estimates of all parameters, Monte Carlo EM algorithm is used by taking random effects as missing. The standard error estimates are obtained through bootstrap re-sampling and corrected by both Percentile bootstrap and BC percentile method.
