在本篇文章中，我們利用免疫球蛋白抗體Igg值來評估術後黑色素細胞瘤的復發狀況，並且探討疫苗干擾素α-2b (IFNα-2b) 的加入是否會影響免疫治療劑GMK對於抗體的反應以及混合後疫苗的治療效果。主要利用聯合模型 (joint model) 的概念來對資料做分析，聯合模型同時包含了長期追蹤資料與存活資訊，
使得估計量具有一致性 (consistency)、有效性 (efficiency)、以及漸近常態 (asymptotic normality) 的良好性質。在第一部分我們使用線性隨機效應模型 (linear random effect model) 來對長期追蹤資料做配適，並利用概似比檢定來診斷長期追蹤模型的適合度；在第二部分使用擴充風險模型 (extended hazard model) 描述變數與存活時間的關係，結合這兩部分建構出聯合概似函數且利用EM演算法 (expectation maximization algorithm) 對參數做估計。由於Cox比例風險模型 (Cox proportional hazards model) 和加速失敗時間模型 (accelerated failure time model) 皆為擴充風險模型的特例，因此可利用Wald type拔靴法、Percentile拔靴法以及BC percentile法建構參數信賴區間來對模型做選擇。

We utilize immunoglobulin G serologic responses to the vaccine to appraise the
progression of patients with resected melanoma, and determine whether there are any
adverse response to GMK and evaluate therapeutic efficacy of the combined-modality
therapy. The joint model approach has been used to analyze the data, which includes
both longitudinal and survival data. It makes estimators contains nice properties, such
as consistency, efficiency and asymptotic normality. In the first part, we fit the longit-
udinal data with the linear random effects model, and use the likelihood ratio test to
choose a proper longitudinal model. In the second part, the relationship between the
longitudinal covariates and the failure time can be assessed by means of the extended
hazard model, and then use the EM algorithm to obtain the maximum likelihood esti-
mates. Since the extended hazard model includes two popular survival models, the
Cox proportional hazards model and the accelerated failure time model, we use Wald
type bootstrap, Percentile bootstrap and BC percentile method to select the appropriate
one.

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