Fitting Semiparametric Additive Hazards Models using Standard Statistical Software

Abstract

The Cox proportional hazards model has become the standard in biomedical studies, particularly for settings in which the estimation covariate effects (as opposed to prediction) is the primary objective. In spite of the obvious flexibility of this approach and its wide applicability, the model is not usually chosen for its fit to the data, but by convention and for reasons of convenience. It is quite possible that the covariates add to, rather than multiply the baseline hazard, making an additive hazards model a more suitable choice. Typically, proportionality is assumed, with the potential for additive covariate effects not evaluated or even seriously considered. Contributing to this phenomenon is the fact that many popular software packages (e.g., SAS, S-PLUS/R) have standard procedures to fit the Cox model (e.g., proc phreg, coxph), but as of yet no analogous procedures to fit its additive analog, the Lin and Ying (1994) semiparametric additive hazards model. In this article, we establish the connections between the Lin and Ying (1994) model and both Cox and least squares regression. We demonstrate how SAS's phreg and reg procedures may be used to fit the additive hazards model, after some straightforward data manipulations. We then apply the additive hazards model to examine the relationship between Model for End-stage Liver Disease (MELD) score and mortality among patients wait-listed for liver transplantation. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)