A study of the slope of cox proportional hazard and Weibull models: simulated and real life data approach

Abstract

Parametric models require that the distribution of survival time is known and the hazard function is completely specified except for the values of the unknown parameters. These include the Weibull model, the exponential model, and the log-normal model. In this research work, Weibull Model is used for modelling survival time situations because it is flexible and also allows the inclusion of covariates. However, when the distributional assumptions for Weibull Model is not satisfied, Cox Proportional Hazard Model will be used, although semi-parametric, because it possessed a similar characteristic of covariates inclusion. The main objective of this research work is to determine if the cox proportional hazard model depend on the shape parameter of the Weibull model. And to investigate if there exist an advantage of using a parametric form of the survival distribution (Weibull distribution) instead of the semi parametric cox proportional hazard model when the parametric form of the model is known. This has two phases, the simulated and the real life data approach. We observed that the shape parameter of the Weibull model does not depend or have effect on the performance of the Cox Proportional Hazard model. And as the sample size increases the Mean Squared errors of the Maximum likelihood estimates of proportional hazard function of both the Weibull and Cox Proportional Hazard Models approximately the same.

Keywords: Cox Proportional Hazard Model, Weibull Model, Slope, Shape parameters, Scale parameter, Survival time