Modeling Survival Data by Using Cox Regression Model
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 6, November 2015, Pages: 504-512
Received: Sep. 10, 2015; Accepted: Sep. 30, 2015; Published: Oct. 30, 2015
Views 5025      Downloads 234
Authors
Medhat Mohamed Ahmed Abdelaal, Statistics and Mathematics Department, Faculty of Commerce, Ain Shams University, Cairo, Egypt
Sally Hossam Eldin Ahmed Zakria, Statistics and Mathematics Department, Faculty of Commerce, Ain Shams University, Cairo, Egypt
Article Tools
Follow on us
Abstract
Survival analysis refers to the general set of statistical methods developed specifically to model the timing of events. A popular regression model for the analysis of survival data is the Cox proportional hazards regression model. The Cox regression model is a semi parametric model, making fewer assumptions than typical parametric methods but more assumptions than those nonparametric methods. The main objective of this paper is to construct Cox proportional hazards regression model for examining the covariate effects on the hazard function and to determine the risk factors affecting the outcome of liver transplantation operation for end-stage liver disease. This article will focus on a review of (a) the Cox model and interpretation of its results, (b) assessment of the validity of the PH assumption, and (c) accommodating non-proportional hazards using covariate stratification. Cox PH model showed that the variables: Recipient age, 〖MELD〗_3 Score, Ln_Creatinine, and GRWR are statistically significant and selected as significant factors for risk of death after liver transplantation operation. Also the scaled Schoenfeld residual displayed non-proportionality for variable Recipient Age and this variable needed to be stratified. And the Cox-Snell residual showed the Cox PH model does not fit these data adequately. So the stratified Cox model could be more appropriate to the current study. The stratified Cox model with interaction and with no interaction were applied and showed that the no-interaction model is acceptable at 0.05 level of significance and the variables〖MELD〗_3 Score, Ln_Creatinine are statistically significant and selected as significant factors for risk of death after liver transplantation operation at 0.05 level of significance.
Keywords
Survival Analysis, Censoring, Cox Proportional Hazard Regression Model, Cox- Snell Residual, Stratified Cox Regression Model
To cite this article
Medhat Mohamed Ahmed Abdelaal, Sally Hossam Eldin Ahmed Zakria, Modeling Survival Data by Using Cox Regression Model, American Journal of Theoretical and Applied Statistics. Vol. 4, No. 6, 2015, pp. 504-512. doi: 10.11648/j.ajtas.20150406.21
References
[1]
Therneau, T. M., Grambsch, P. M. (2000). Modeling Survival Data, Extending the Cox Model. Springer, New York.
[2]
Gill, Richard D. (1984). Understanding Cox's Regression Model: A Martingale Approach. Journal of American Statistical Association, 79: 441-447.
[3]
David W. Hosmer, Jr., and Stanley Lemeshow (1999). Applied survival analysis: regression modeling of time to event data. Wiley, New York.
[4]
Lawless, J. F. (2003). Statistical Models and Methods for Lifetime Data. Second Edition, Wiley, New York.
[5]
Kalbfleisch, J.D. & Prentice, R.L. (2002). The Statistical Analysis of Failure Time Data. Wiley, New York.
[6]
Klein, J. P. and Moeschberger, M. L. (1997). Survival Analysis Techniques for Censored and Truncated Data. Springer, New York.
[7]
Cox, D.R. and Oakes, D., (1984) Analysis of Survival Data. Chapman and Hall, London.
[8]
Collett D. (1994). Modeling survival data in Medical research. Chapman & Hall, London.
[9]
Klembaum, D. G. (1996). Survival Analysis: A Self learning text. Springer, New York.
[10]
Grambsch, P. and Therneau, T. M. (1994). Proportional Hazards Tests and Diagnostics Based on Weighted Residuals. Biometrrika, 81: 515–526.
[11]
Lee, E. T., and Wang, J. W. (2003). Statistical Methods for Survival Data Analysis. Third Edition, Wiley, New York.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186