聯合長期追蹤與存活資料分析-愛滋病病患之實例分析

Joint modeling of longitudinal and survival data - A case study in AIDS data

廖哲瑋(Che-wei Liao)

指導教授 ： 曾議寬

國立中央大學/理學院/統計研究所/碩士(2012年)

摘要

在本篇文章中主要利用CD4 細胞數用來評估愛滋病的嚴重程度, 並探討DDI 與DDC 藥物對愛滋病病患的療效。此種包含存活與時間相依共變數的資料, 最常使用Cox 比例風險模型來描述長期追蹤共變數與存活時間的關係。然而,當我們使用部分概似法時必須要知道每位病患的共變數歷史、並且不能有測量誤差的存在,但在實務上常會因為病患本身差異與測量誤差因素造成偏誤,因此,本篇文章當中我們使用能同時配適長期追蹤資料與存活時間的聯合模型來解決此問題。在長期追蹤資料方面使用線性隨機效應模型來配適,而存活模型使用Cox 比例風險模型來描述共變數與存活時間之關係,在參數估計方面,結合前面兩個部份建立聯合函數利用EM 演算法做參數估計,並透過華特信賴區間、百分比信賴區間與偏誤修正百分比信賴區間來對參數做檢定。另外,分別使用MATLAB 軟體與R 軟體針對估計值、標準差以及運算時間等來做軟體比較,並且,透過長期追蹤資料模型,可以計算出接受者作業特徵曲面下體積,了解隨著時間的改變接受者作業特徵曲面的變化以及預測能力。

關鍵字

聯合模型 ； 長期追蹤資料 ； Cox 比例風險模型 ； 期望值- 最大化演算法 ； 接受者作業特徵曲線

並列摘要

We used the CD4 cell counts appraise AIDS progression, and explored the efficacy of DDI and DDC to AIDS patients. In survival analysis, the Cox model with partial likelihood
is the most popular model to describe the relationship between longitudinal covariates and the survival time. However, when using partial likelihood, we have to recognize the complete covariate history for each patient, and the measurement error can not exist. In clinical trials, such situations can not hold due to the individual differences, measurement error of medical machines. Consequently, in this study, we applied the joint model to overcome these
difficulties. We propose a linear random effects model for longitudinal process. The Cox proportion hazards model is used to link the covariates and event time, and EM algorithm is implemented to search for the maximum likelihood estimates. Interval estimation of parameters is derived by the Wald confidence interval, the percentile confidence interval and the
bias-correction percentile confidence interval. In addition, we compare the estimate, standard deviation and operating time between Matlab software and R software. Moreover, revised VUS (volume under the ROC surface) of ROC surface is used to identify the prediction of longitudinal biomaker which suggests that the CD4 has well prediction capacity.

並列關鍵字

Joint model ； Longitudinal data ； Cox proportional hazard model ； EM algo- rithm ； ROC curve

參考文獻

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