存活資料具有二元設限狀態以及連續追蹤時間兩種性質，所以只要經過適當的修正，即可定義時間相依敏感度和特異度。使用此定義，時間相依接受者作業特徵曲線以及曲面下面積將能有效運用在存活資料。目前文獻上已使用比例風險模型結合時間相依接受者作業特徵曲線，在固定變量下做存活模型的預測。然而醫學研究上，所蒐集的資料時常違反比例風險的假設，故本篇論文將使用加速失敗模型取代比例風險模型建構出時間相依特異度與敏感度。同時，現在的醫學觀測值通常有重複測量值，本篇論文也發展出在長期追蹤資料下結合加速失敗模型或比例風險模型的接受者作業特徵曲線下面積。而當長期追蹤資料有測量誤差或是沒有完整共變異數資料時，我們將使用文獻上的聯合模型來進行補值，進而修補偏誤的問題。本篇論文透過模擬研究來也驗證此方法在存活模型預測上的表現。在實例分析上，我們使用退伍軍人肺癌資料與台灣愛滋病世代資料，探討時間相依接受者作業特徵曲線下面積的實用性。;Survival data is the combination of binary censoring status and continuous length of follow-up time. Under suitable revised definition of sensitivity and specificity, the framework of receiver operating characteristic curves can be applied to survival data. Previous studies developed predictive accuracy summaries based on time-dependent sensitivity and specificity derived from the Cox model with fixed covariates. However, the Cox regression model needs a proportional hazard assumption which may fail in some of the medical studies. In such situation, we develop an approach to replace the Cox model by the accelerated failure time (AFT) model to derive time-dependent sensitivity and specificity. Moreover, we further extended the develop approach to the Cox model or the AFT model with longitudinal covariates. When the longitudinal covariates are subject to measurement errors or do not have complete covariate history, an imputation method through joint model is used to correct the bias of estimates. Simulation studies were conducted to evaluate the performance of proposed approach. Two case studies, Veteran′s Administration lung cancer data and Taiwanese HIV cohort data were used to illustrate the usefulness of the proposed model-base time-dependent AUC and predictive accuracy.
