Modeling Survival Data by Using Cox Regression Model

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.