System No. U0002-1807201317130500 使用優劣比-風險模型對現狀數據之迴歸診斷 Regression Diagnostics for Current Status Data using the Odds-Rate Model 淡江大學 數學學系碩士班 Department of Mathematics 101 2 102 洪筱涵 Hsiao-Han Hung 600190234 碩士 English 2013-06-26 24page advisor - Chi-Chung Wen co-chair - 黃逸輝 co-chair - 吳裕振 現狀數據 優劣比-風險模型 配適度指標 Goodness of fit index Current status data Odds-rate model `在進行迴歸分析之前，應先執行迴歸診斷，即對觀測數據評估迴歸模型的合適性。對於完整或右設限毀壞時間資料的迴歸診斷，許多的圖形法或量化法已被建立(如，Collett (1994), Klein and Moeschberger (2003), and Lawless (2003))。在本文中，對於現狀數據在優劣比-風險模型下，我們發展了評估比例風險假設和比例優劣比假設之診斷方法(Scharfstein, Tsiatis, and Gilbelt (1998))，同時對所提估計提供一穩定且快速計算法則。我們藉由模擬研究和三個實例分析來說明所提方法的表現。` `The regression diagnostics that assess the adequacy of a regression model for observed data should be conducted before the regression analysis. For complete or right censored failure time data, several graphical or quantitative methods have been established for regression diagnostics (e.g. Collett (1994), Klein and Moeschberger (2003), and Lawless (2003)). In the thesis, we develop a diagnostic method for assessing the proportional hazards and proportional odds assumptions with current status data under the odds-rate model (Scharfstein, Tsiatis, and Gilbelt (1998)) and provide a stable and efficient computation method for proposed estimators. We illustrate the performance of our method via simulation studies and three real data analysis.` ```Contents 1 Introduction　1 2 Odds-rate model　2 3 Some modeling checking methods　5 3.1 Log-log survival plots/ log odds plots　5 3.2 Observed versus expected survival plots　6 3.3 Cox-Snell residuals method　7 3.4 Brier-Score method　8 4 The proposed approach　9 4.1 Diagnostics based on OR model　9 4.2 Computation algorithm　11 5 Numerical studies and applications　13 5.1 Simulation studies　13 5.2 Applications　14 6 Concluding remarks　16 References　18``` ```References Brier, G. W. (1950). Verification of forecasts expressed in terms of probability. Monthly weather review 78, 1-3. Chang, Y. S. (張晏昇) (2013). Evaluating the Proportional Odds Assumption with Current Status Survival Data. Master Thesis, Tamkang University. Collett, W. E. (1994). Modelling survival data in medical research. Chapman and Hall, London. Cox, D. R. & Snell, E. J. (1968). A general definition of residuals (with discussion). 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