Inference for Regression Coefficients and a Baseline Hazard Function under Proportional Hazards Models—Comparison between Cox Regression, Weibull Regression, Poisson Regression, and Spline Regression Methods—

Abstract

The partial likelihood method for the Cox proportional hazards model is a successful method for estimating regression coefficients without considering the baseline hazard function. On the other hand, if one is interested in estimating both the regression coefficients and the baseline hazard function, parametric methods such as Weibull regression, piecewise exponential hazard regression, and spline hazard regression are useful. The purpose of this paper is to explain these regression methods and compare their statistical performance. We provide a detailed explanation of Poisson regression under piecewise exponential models and penalized maximum likelihood under spline hazard models, and discuss important considerations when analyzing medical data. Simulations are performed under various baseline hazard functions for the population, and a numerical comparison of the estimation accuracy of Cox regression (partial likelihood), Weibull regression, Poisson regression, and spline regression is conducted. Finally, we compare the results of these regression methods through a data example.