醫學研究中，受試者特徵曲線(Receiver Operating Characteristic curve，簡稱ROC曲線)常被用於評估生物指標對疾病預測能力。目前文獻研究在於建構時間相依 ROC 曲線，提高預測效率且可評估生物指標動態(Dynamic)預測能力。過去已導出具有固定共變數的比例風險模型(Proportional hazard model,簡稱 PH)時間相依 ROC 曲線，本研究將其延伸至時間相依共變數。此外，基於時間相依 ROC 曲線可得到時間相依曲線下面積 (the area under the ROC curves,簡稱 AUC)，並對各時間下的 AUC 加權平均後取得一致性指標(Concordance)，此指標被已被證明對預測精準度有一致性。我們將時間相依 AUC 與一致性指標推導為風險回歸的函數，透過不同風險迴歸模型得到對應模型的時間相依 AUC 與一致性指標。PH 模型為最常用的風險回歸模型，但若資料不符合比例風險假設，則考慮使用 AFT 模型為替代，本研究提出修正 AFT 模型風險的估計並以比例勝算模型(Proportional Odds model，簡稱 PO)建構風險回歸模型，當資料來自不同風險回歸模型下，比較三種模型在錯誤配適時的 AUC 與一致性指標。目前仍未有文獻討論時間相依 AUC 與一致性指標的信賴區間，我們更進一步利用大樣本理論推導出對應風險回歸模型下時間相依 AUC 與一致性指標的信賴區間，並以模擬驗證其覆蓋機率的準確性，最後以實際愛滋病資料來展示三種模型分析的結果。;The ROC (receiver operating characteristic) curve methodology is currently a well-developed statistical tool to evaluate the ability of biomarkers to discriminate the case (disease) and control (non-disease) of patients. Recent research has been focused on incorporating time-dependency to ROC framework to gain efficiency and to do dynamic prediction. In the literature, the time-dependent ROC curves for the Proportional hazards (PH) model with fixed covariates has been derived. We further extends it to time-dependent covariates. Moreover, we prove that the time-dependent AUC and concordance are actually functions of hazard regression models. Those hazards regression models studies in this thesis include the PH model, the accelerated failure time (AFT) model and the Proportional Odds (PO) model. The PH model is the most commonly used hazard regression model. However, if the data does not follow the proportional hazard assumption, the AFT model is an attractive alternative model. We propose a kernel-smooth approach to derive hazard estimation for the AFT model. In addition, we investigate the PO model through transformation model setting. We further use large sample theory to derive the confidence interval of time-dependent AUC and concordance under the corresponding hazard regression model, and verify its coverage probability in the simulation chapter , and uses AIDS data to show the results based on three hazard regression models.
