跳到主要內容

簡易檢索 / 詳目顯示

研究生: 張雯婷
Wen-Ting Chang
論文名稱: 加速失效模型與Cox風險迴歸模型之模型選擇以時間相依AUC及預測精準度為指標
指導教授: 曾議寬
口試委員:
學位類別: 碩士
Master
系所名稱: 理學院 - 統計研究所
Graduate Institute of Statistics
論文出版年: 2018
畢業學年度: 106
語文別: 中文
論文頁數: 85
中文關鍵詞: 接受者作業特徵曲線下面積時間相依接受者作業特徵曲線下面積事件型敏感度動態型特異度預測一致性指標Cox風險迴歸模型加速失效模型
相關次數: 點閱:14下載:0
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 傳統上接受者作業特徵曲線(ROC)是針對二元的分類結果進行預測,然而存活資料為結合二元設限狀態及連續存活時間的資料型態,因此若將敏感度與特異度的定義經過適當的修改後,即可將接受者作業特徵曲線應用於存活資料上。在過去文獻中,已有學者將其推廣到時間獨立共變數下配適Cox比例風險模型,並結合時間相依敏感度與特異度預測精準度。然而在部分的醫學研究中,常有資料不符合比例風險假設,因此我們建議以參數化加速失效模型取代Cox比例風險模型,結合時間相依敏感度與特異度,並以接受者作業特徵曲線下面積(AUC)及一致性指標Concordance判斷生物指標對疾病的區別能力,亦進一步擴展此方法到含有長期追蹤共變數的資料上。


    Traditionally, the receiver operating characteristic curve (ROC) are used to predict the binary classification results. However, survival data are data types that combine the binary censored status and continuous survival time. Therefore, if the definition of sensitivity and specificity have been slightly modified, the ROC curve can be applied to the survival data. In the past literature, some scholars have extended it when conditioned at time-independent covariate to fit Cox proportional hazard model, and combined with time-dependent sensitivity and specificity to predict model accuracy. However, in some medical studies, there are often data that violate the proportional hazard assumption. Therefore, we recommend to replace the Cox proportional hazard model as the parametric accelerated failure time model with combining time-dependent sensitivity, specificity, and AUC. And finally use AUC and Concordance to evaluate the ability of biomarkers to discriminate diseases and further extended this method to longitudinal covariates.

    第一章 序論 1 1.1 傳統的ROC曲線分析……………………………………….2 1.1.1 敏感度與特異度………………………………………..2 1.1.2 ROC曲線……………………………………………….3 1.1.3 建構ROC……………………………………………….4 1.1.4 建構AUC……………………………………………….6 1.2 推廣的ROC曲線分析………………………………………..9 1.2.1 時間相依的ROC曲線…………………………………9 1.2.2 時間相依的AUC和一致性(Concordance)…………..11 1.3 Cox比例風險與長期追蹤資料之聯合建模………………..16 1.4 參數化AFT模型與長期追蹤資料之聯合建模……………17 第二章 統計方法 18 2.1 Cox迴歸模型………………………………………………..19 2.2 AFT迴歸模型……………………………………………….22 2.2.1 Weibull迴歸模型……………………………………..24 2.2.2 Loglogistic迴歸模型…………………………………25 2.2.3 Lognormal迴歸模型…………………………………26 第三章 模擬研究 28 3.1 時間固定共變數…………………………………………….28 3.1.1 資料生成來自Weibull Cox模型…………..................28 3.1.2 資料生成來自 Weibull AFT模型……………………32 3.1.3 資料生成來自 Loglogistic Cox模型……...................36 3.1.4 資料生成來自 Loglogistic AFT模型……..................40 3.1.5 資料生成來自 Lognormal Cox模型….......................44 3.1.6 資料生成來自 Lognormal AFT模型……..................48 第四章 資料分析 52 4.1 資料背景與分析…………………………………………..52 4.2 分析結果…………………………………………………..54 第五章 總結與討論 65 參考文獻 67

    參考文獻
    Bamber, D. (1975). The area above ordinal dominance graph and the area
    below the receiver operating characteristic graph. Journal of Mathematical
    Psychology 12, 387-415.
    Blanche, P., Dartigues, J. F. and Jacqmin-Gadda, H. (2013). Estimating
    and comparing timedependent areas under receiver operating characteristic
    curves for censored event times with competing risks. Statistics in
    medicine 32, 5381-5397.
    Blanche, P. (2015). timeROC: Time-Dependent ROC Curve and AUC for
    Censored Survival Data. R package version 0.3. URL http://CRAN.Rproject.
    org/package=timeROC.
    Cai, T., Pepe, M. S., Lumley, T., Zheng, Y., and Jenny, N. S. (2003). The
    sensitivity and speci city of markers for event times. University of Wash-
    ington Technical Report 188, 1-30.
    Cai, Z. and Sun, Y. (2003). Local linear estimation for timedependent
    coecients in Cox's regression models. Scandinavian Journal of Statistics
    30, 93-111.

    Chiou, S. H., Kang, S., and Yan, J. (2014). Fitting Accelerated Failure
    Time Models in Routine Survival Analysis with R Package aftgee. Journal
    of Statistical Software 61(11), 1-23.
    Cox, D. R. (1972). Regression models and life tables. Journal of the Royal
    Statistical Society, Series B Methodological 34, 187-220.
    Etzioni, R., Pepe, M., Longton, G., Hu, C., and Goodman, G. (1999). Incorporating
    the time dimension in receiver operating characteristic curves:
    A case study of prostate cancer. Medical Decision Making 19, 242-251.
    Fleming, T. R. and Harrington, D. P. (1991). Counting Processes and Sur-
    vival Analysis. New York: John Wiley & Sons.
    Grambsch, P. M. and Therneau, T. M. (1994). Proportional Hazards Tests
    and Diagnostics Based on Weighted Residuals. Biometrics 81, 515-26.
    Hanley, J. A. and McNeil, B. J. (1982). The meaning and use of the area
    under a receiver operating characteristic (ROC) curve. Radiology 143, 29-
    36.

    Harrell, F. E., Lee, K. L., and Mark, D. B. (1996). Multivariable prognostic
    models: Issues in developing models, evaluating assumptions and
    adequacy, and measuring and reducing errors. Statistics in Medicine 15,
    361-387.
    Heagerty, P. J., Lumley, T., and Pepe, M. S. (2000). Time-dependent ROC
    curves for censored survival data and a diagnostic marker. Biometrics 56,
    337-344.
    Heagerty, P. J. and Zheng, Y. (2004). Semiparametric estimation of timedependent
    ROC curves for longitudinal marker data. Biometrics 5, 651-
    632.
    Heagerty, P. J. and Zheng, Y. (2005). Survival Model Predictive Accuracy
    and ROC Curves. Biometrics 61, 92-105.
    Heagerty, P. J. and Paramita Saha (2012). risksetROC: Riskset ROC curve
    estimation from censored survival data. R package version 1.0.4. URL
    http://CRAN .R-project.org/package=risksetROC.

    Hung, H., Chiang, C.T. (2010). Estimation methods for time-dependent
    AUC models with survival data. Canadian Journal of Statistics 38(1),
    8-26.
    Henderson, R. (1995). Problems and prediction in survival data analysis.
    Statistics in Medicine, 14, 161-184.
    Hess K. R., Serachitopol D. M. and Brown B. W. (1999). Hazard function
    estimators: A simulation study. Statistics in Medicine 18(22), 3075-3088.
    Kalb
    eisch, J. D. and Prentice, R. L. (2002). The Statistical Analysis of
    Failure Time Data. New York: John Wiley & Sons.
    Mueller, H. and Wang, J. (1994) Hazard Rate Estimation Under Random
    Censoring with Varying Kernels and Bandwidth. Biometrics 50, 61-76.
    O'Quigley, J. and Xu, R. (2000). Proportional hazards estimate of the conditional
    survival function. Journal of the Royal Statistical Society, Series
    B, Methodological 62, 667-680.
    O'Quigley, J. and Xu, R. (2001). Explained variation in proportional haz-

    ards regression. Handbook of Statistics in Clinical Oncology, J. Crowley
    (ed), 397-409. New York: Marcel Dekker.
    Pepe, M. S. (2003). The Statistical Evaluation of Medical Tests for Classi-
    cation and Prediction. Oxford: Oxford University Press.
    Schemper, M. and Henderson, R. (2000). Predictive accuracy and explained
    variation in Cox regression. Biometrics 56, 249-255.
    Slate, E. H. and Turnbull, B. W. (2000). Statistical models for longitudinal
    biomarkers of disease onset. Statistics in Medicine 19, 617-637.
    Song, X., Davidian, M. and Tsiatis, A. A. (2002). A semiparametric likelihood
    approach to joint modelling of longitudinal and time-to-event data.
    Biometrics 58, 742-753.
    Terry M. Therneau and Mayo Foundation(1999).A package for survival
    analysis in S.
    Tseng, Y. K., Wang, J. L. and Hsieh, F. (2005). Joint Modeling of Accelerated
    Failure Time and Longitudinal Data. Biometrika 92, 587-603.
    Tseng, Y. K., Wang, J. L., SU, Y. R. and Mao, M. (2015). An extended

    hazard model with longitudinal covariates. Biometrika 102, 135-150.
    Tsiatis, A. A. and Davidian, M. (2001). A Semiparametric Estimator for
    the Proportional Hazards Model with Longitudinal Covariates Measured
    with Error. Biometrika 88, 447-458.
    van Houwelingen, H. C. and Putter H. (2012). Dynamic Prediction in Clin-
    ical Survival Analysis Chapman & Hall
    Wang, Y. and Taylor, J. M. G. (2001). Jointly modeling longitudinal and
    event time data with application to acquired immunode ciency syndrome.
    Journal of the American Statistical Association 96, 895-905.
    Wulfsohn, M. S. and Tsiatis, A. A. (1997). A Joint Model for Survival and
    Longitudinal Data Measured with Error. Biometrics 53, 330-339.
    Zhou, X. H., McClish, D. K., and Obuchowski, N. A. (2002). Statistical
    Methods in Diagnostic Medicine. New York: John Wiley & Sons.

    中華民國衛生福利部疾病管制署(2018)。傳染病防治工作手冊。
    張雅玟(2015)。三種時間相依的接受者作業特徵曲線下面積估計方法之
    比較與修正。國立中央大學統計研究所碩士論文。
    林園馨(2016)。Model-base Time-dependent AUC and Predictive Accuracy.
    國立中央大學統計研究所碩士論文。

    QR CODE
    :::