在存活分析當中, 病患們於不同時間點時重複測量感興趣的長期追蹤共變數是非常普遍的。在這種情況下, 常會因測量誤差或生物體本身的差異, 以及共變數觀測值是否測量得到與存活有關時, 使得推論產生偏差。為了修正偏差,我們使用可以同時配適存活與長期追蹤共變數的聯合模型來解決此問題。聯合模型可以被應用來分析原發性膽汁性肝硬化疾病之病患資料, 主要是探討D-青黴胺治療藥物與年齡層不同以及Mayo 風險評分測量值之變化對存活的影響。最後得到結果為: D-青黴胺對原發性膽汁性肝硬化病情並無顯著的效、 年齡層對存活無顯著差異、以及病患的Mayo 風險評分與風險成正相關, 評分越高其死亡風險越高。而且, 從接受者作業特徵曲線下面積得到, 對於原發性膽汁性肝硬化疾病而言, Mayo 風險評分比生物指標膽紅素有較高的預測準確性能力, 其值越高代表病患有較高的風險會死亡, 其值越低代表病患之病情較輕緩。 In survival analysis, it’s very common that the interesting covariates were measured intermittently at different measurment times for different patients. In this scenario, the repeated measurments could include measurment errors and measurments can not be observed after the survival time. Those situations could result in biased inferences for study when using Cox partial likelihood. To corret the bias, we use a joint model approach which models survival time and the longitudinal covariates simultaneously. This approach was applied to analyze Primary Biliary Cirrhosis patients data with the main interest of exploring the relationship between longitudinal Mayo risk score and survival. The results suggested that the drug D-penicillamine and age groups have no significant effect on survival and the longitudinal covariate Mayo risk score can be well described through a cubic random coefficient model and has a significant impact on patients’ lifetime. Moreover, from AUC (area under the ROC curve) of ROC curve (Receiver Operating Characteristic curve) which suggests that the Mayo risk score has better prediction capacity than the biomarker, bilirubin.
