Modeling Survival Data by Using Cox Regression Model

Medhat Mohamed Ahmed Abdelaal; Sally Hossam Eldin Ahmed Zakria

doi:doi:10.11648/j.ajtas.20150406.21

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Modeling Survival Data by Using Cox Regression Model

Medhat Mohamed Ahmed Abdelaal, Sally Hossam Eldin Ahmed Zakria

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 6)

Received: 10 September 2015 Accepted: 30 September 2015 Published: 30 October 2015

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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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 4, Issue 6)
DOI	10.11648/j.ajtas.20150406.21
Page(s)	504-512
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Survival Analysis, Censoring, Cox Proportional Hazard Regression Model, Cox- Snell Residual, Stratified Cox Regression Model

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.

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APA Style

Medhat Mohamed Ahmed Abdelaal, Sally Hossam Eldin Ahmed Zakria. (2015). Modeling Survival Data by Using Cox Regression Model. American Journal of Theoretical and Applied Statistics, 4(6), 504-512. https://doi.org/10.11648/j.ajtas.20150406.21

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Medhat Mohamed Ahmed Abdelaal; Sally Hossam Eldin Ahmed Zakria. Modeling Survival Data by Using Cox Regression Model. Am. J. Theor. Appl. Stat. 2015, 4(6), 504-512. doi: 10.11648/j.ajtas.20150406.21

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AMA Style

Medhat Mohamed Ahmed Abdelaal, Sally Hossam Eldin Ahmed Zakria. Modeling Survival Data by Using Cox Regression Model. Am J Theor Appl Stat. 2015;4(6):504-512. doi: 10.11648/j.ajtas.20150406.21

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@article{10.11648/j.ajtas.20150406.21,
  author = {Medhat Mohamed Ahmed Abdelaal and Sally Hossam Eldin Ahmed Zakria},
  title = {Modeling Survival Data by Using Cox Regression Model},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {6},
  pages = {504-512},
  doi = {10.11648/j.ajtas.20150406.21},
  url = {https://doi.org/10.11648/j.ajtas.20150406.21},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150406.21},
  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.},
 year = {2015}
}

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TY  - JOUR
T1  - Modeling Survival Data by Using Cox Regression Model
AU  - Medhat Mohamed Ahmed Abdelaal
AU  - Sally Hossam Eldin Ahmed Zakria
Y1  - 2015/10/30
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150406.21
DO  - 10.11648/j.ajtas.20150406.21
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 504
EP  - 512
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150406.21
AB  - 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.
VL  - 4
IS  - 6
ER  -

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Author Information

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

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APA Style

Medhat Mohamed Ahmed Abdelaal, Sally Hossam Eldin Ahmed Zakria. (2015). Modeling Survival Data by Using Cox Regression Model. American Journal of Theoretical and Applied Statistics, 4(6), 504-512. https://doi.org/10.11648/j.ajtas.20150406.21

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ACS Style

Medhat Mohamed Ahmed Abdelaal; Sally Hossam Eldin Ahmed Zakria. Modeling Survival Data by Using Cox Regression Model. Am. J. Theor. Appl. Stat. 2015, 4(6), 504-512. doi: 10.11648/j.ajtas.20150406.21

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AMA Style

Medhat Mohamed Ahmed Abdelaal, Sally Hossam Eldin Ahmed Zakria. Modeling Survival Data by Using Cox Regression Model. Am J Theor Appl Stat. 2015;4(6):504-512. doi: 10.11648/j.ajtas.20150406.21

Copy | Download

@article{10.11648/j.ajtas.20150406.21,
  author = {Medhat Mohamed Ahmed Abdelaal and Sally Hossam Eldin Ahmed Zakria},
  title = {Modeling Survival Data by Using Cox Regression Model},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {6},
  pages = {504-512},
  doi = {10.11648/j.ajtas.20150406.21},
  url = {https://doi.org/10.11648/j.ajtas.20150406.21},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150406.21},
  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.},
 year = {2015}
}

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TY  - JOUR
T1  - Modeling Survival Data by Using Cox Regression Model
AU  - Medhat Mohamed Ahmed Abdelaal
AU  - Sally Hossam Eldin Ahmed Zakria
Y1  - 2015/10/30
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150406.21
DO  - 10.11648/j.ajtas.20150406.21
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 504
EP  - 512
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150406.21
AB  - 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.
VL  - 4
IS  - 6
ER  -

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