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姓名	林威廷(Wei-Ting Lin)  查詢紙本館藏	畢業系所	統計研究所
論文名稱	風險回歸模型下時間相依 ROC 曲線 (Hazard Regression Model-base Time-dependent ROC Curve)
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摘要(中)	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。
摘要(英)	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.
關鍵字(中)	★ 比例風險模型 ★ 加速失敗模型 ★ 比例勝算模型 ★ 聯合模型 ★ 時間相依接受者作業特徵曲線下面積	關鍵字(英)	★ Cox model ★ AFT model ★ PO model ★ Joint model ★ Time-dependent AUC
論文目次	目錄 摘要i Abstract ii 致謝iii 目錄iv 圖目錄vi 表目錄vii 第一章緒論1 1.1 ROC 曲線介紹2 1.2 時間相依ROC 曲線推廣7 1.3 PH 模型-預測精準度13 1.4 AFT 模型-預測精準度15 1.5 Semiparametric transformation 半參數轉換模型17 1.6 聯合模型18 第二章統計方法20 2.1 PO 模型-預測精準度21 2.2 修正AFT 模型- 預測精準度23 2.3 AUC 與一致性指標信賴區間25 第三章模擬研究30 3.1 PO 模型31 3.2 模型錯誤配適38 3.3 AUC 與一致性指標信賴區間45 3.4 時間相依共變數58 第四章資料分析65 4.1 愛滋病資料介紹65 4.2 時間獨立共變數存活模型66 4.3 時間相依共變數存活模型68 4.4 資料分析結論71 第五章結論72 參考文獻73 附錄A.1 I/D 定義下之AUC 與一致性指標推導77 附錄A.2 Weibull PO 模型推導80 附錄A.3 Lognormal PO 模型推導82 附錄A.4 Loglogistic PO 模型推導84 附錄A.5 PH 模型AUC 與一致性指標大樣本性質推導86 附錄A.6 PO 模型AUC 與一致性指標大樣本性質推導89 附錄A.7 AFT 模型AUC 與一致性指標大樣本性質推導92 附錄A.8 R code - AUC 與一致性指標估計95 附錄A.9 R code - 真實值計算110
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指導教授	曾議寬(Yi-Kuan Tseng)	審核日期	2021-7-21
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