A COMPARISON OF COX AND FRAILTY MODELS IN PRESENCE OF UNKNOWN RISK FACTORS
Abstract
One of the most popular models for survival analysis is the Cox proportional hazard model. In this model, the hazard function may depend on unknowon risk factors which are impossible to include them in the model. This will lead to an increase in the variability of responses, which implies biased and misleading estimates of the- parameters of the Cox model. This problem can be overcome by inclusion of a random effect in the Cox model. The modified model is known as frailty model.
In this paper, we compare parameter estimates of Cox and frailty models with a simulation study. The results show that in the univariate survival data, as the number of unknown risk factors incrase so do the magnitude of the bias and the mean square error (MSE) of estimators in the Cox model compared to the frailty model. In bivariate survival data, magnitude of the biased and the mean square error of estimator of the Cox model depends on the magnitude of the correlation of survival times. In comparison, the frailty models remove the disadvantage of the Cox model by considering the correlation of the survival times.
In this paper, we compare parameter estimates of Cox and frailty models with a simulation study. The results show that in the univariate survival data, as the number of unknown risk factors incrase so do the magnitude of the bias and the mean square error (MSE) of estimators in the Cox model compared to the frailty model. In bivariate survival data, magnitude of the biased and the mean square error of estimator of the Cox model depends on the magnitude of the correlation of survival times. In comparison, the frailty models remove the disadvantage of the Cox model by considering the correlation of the survival times.
Keywords
Survival Analysis, Unknown Risk Factors, Multivariate Survival Data, Cox Proportional Hazard Model, Frailty ModeL