Survival distribution and Kaplan-Meier survival function are usually used as descriptive methods to estimate the distribution of survival times from a sample life table. There are also several regression models for estimating the relationship of continuous variables to survival times, of which the Weibull regression and the Cox regression models are widely used. Cox regression model is applicable to a wider class of distributions and it is a semi-parametric model while the Weibull regression model is fully a parametric model. If the Weibull regression model is applicable to a data set, then the Cox regression model could be used as an equivalent model to the same data set. When both models are applicable to a data set, then the Cox model estimates are less accurate and less efficient than the Weibull model estimates. It appears also that the tests are less powerful for the Cox model than that for the Weibull regression model. Besides, because of the nature of the model, the parametric models may offer advantages over the Cox model. In this study, we have examined the performances of the two models with simulated data sets that follow both the Weibull regression model and the Cox proportional regression model.

efficiency, Cox regression, survival distribution, Weibull regression.