Model-base Time dependent AUC and Predictive Accuracy

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林園馨(Yuan-Hsin Lin) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

(Model-base Time dependent AUC and Predictive Accuracy)

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摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 時間相依接受者作業特徵曲線下面積
★ 附帶型敏感度
★ 動態型特異度
★ 部分概似函數
★ 加速失敗時間模型
★ 比例風險模型
★ 聯合模型

關鍵字(英)

★ Prediction
★ time-dependent AUC
★ Cox regression
★ Accelerated failure time model
★ Hazard smoothing
★ Joint modeling
★ Measurement error

論文目次

Contents
1 Introduction 1
1.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Joint Modelling of Cox Proportional and Longitudinal Data . . . . . . 3
1.3 Joint Modelling of Accelerated Failure Time and Longitudinal Data . . 4
2 ROC with Censored Survival 5
2.1 Traditional ROC Curve Analysis . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Construction of ROC . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Construction of Area Under the ROC Curve . . . . . . . . . . . 10
2.2 Extensions of ROC Curves . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Time-Dependent ROC Curves . . . . . . . . . . . . . . . . . . . 13
2.2.2 Time-Dependent AUC and Concordance . . . . . . . . . . . . . 15
3 Estimation 17
3.1 Time Invariant Covariates . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.1 Cox Regression Model . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.2 AFT Regression Model . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Longitudinal Covariates and a Failure Time Process . . . . . . . . . . . 22
3.2.1 Cox Regression Model . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.2 AFT Regression Model . . . . . . . . . . . . . . . . . . . . . . . 23
4 Simulation 24
4.1 Time Invariant Covariates . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.1.1 Bivariate Normal to Biomarker and Log Survival Time . . . . . 24
4.1.2 Survival Time and Covariates Generated from Cox Model . . . . 34
4.1.3 Survival Time and Covariates Generated from AFT Model . . . 38
4.2 Longitudinal Covariates . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.1 With or Without Imputation of Cox Model . . . . . . . . . . . . 42
4.2.2 With or Without Imputation of AFT Model . . . . . . . . . . . 47
5 Data Analysis 52
5.1 Time Invariant Covariates . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.2 Time-Dependent Covariates . . . . . . . . . . . . . . . . . . . . . . . . 64
6 Discussion 72
REFERENCES 73
Appendix 78
A1. AFT Model with Fixed Covariates . . . . . . . . . . . . . . . . . . . . . 78
A2. Cox Model with Longitudinal Covariates . . . . . . . . . . . . . . . . . 79
A3. AFT Model with Longitudinal Covariates . . . . . . . . . . . . . . . . . 81
A4. Derivation of Section 4.1.1 . . . . . . . . . . . . . . . . . . . . . . . . . 82
A5. Derivation of Section 4.1.2 . . . . . . . . . . . . . . . . . . . . . . . . . 83
A6. Derivation of Section 4.1.3 . . . . . . . . . . . . . . . . . . . . . . . . . 85
A7. Derivation of survival time in Section 4.2.1 . . . . . . . . . . . . . . . . 87
A8. Derivation of survival time in Section 4.2.2 . . . . . . . . . . . . . . . . 87

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 compar-
ing timedependent areas under receiver operating characteristic curves for censored
event times with competing risks. Statistics in medicine 32, 5381-5397.
Blanche, P. and packaging by Paul Blanche (2015). timeROC: Time-Dependent
ROC Curve and AUC for Censored Survival Data. R package version 0.3. URL
http://CRAN.R-project.org/package=timeROC.
Cai, T., Pepe, M. S., Lumley, T., Zheng, Y., and Jenny, N. S. (2003). The sensitivity
and specificity of markers for event times. University of Washington Technical Report
188, 1-30.
Cai, Z. and Sun, Y. (2003). Local linear estimation for timedependent coefficients in
Cox’s regression models. Scandinavian Journal of Statistics 30, 93-111.
Chiou, S. H., Kang, S., 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). Incorporat-
ing 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 Survival Anal-
ysis. New York: John Wiley & Sons.
Grambsch, P. M. and Therneau, T. M. (1994). Proportional Hazards Tests and Diag-
nostics 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 time-dependent
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. & packaging by 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.
Kalbfleisch, 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 hazards 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 Classification 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 biomark-
ers of disease onset. Statistics in Medicine 19, 617-637.
Song, X., Davidian, M. and Tsiatis, A. A. (2002). A semiparametric likelihood ap-
proach to joint modelling of longitudinal and time-to-event data. Biometrics 58,
742-753.
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 Propor-
tional Hazards Model with Longitudinal Covariates Measured with Error. Biometrika
88, 447-458.

指導教授

曾議寬(Yi-Kuan Tseng)

審核日期

2017-7-24

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