Maximum likelihood estimation in the additive hazards model

arXiv (Cornell University)

Abstract

The additive hazards model specifies the effect of covariates on the hazard in an additive way, in contrast to the popular Cox model, in which it is multiplicative. As non-parametric model, it offers a very flexible way of modeling time-varying covariate effects. It is most commonly estimated by ordinary least squares. In this paper we consider the case where covariates are bounded, and derive the maximum likelihood estimator under the constraint that the hazard is non-negative for all covariate values in their domain. We describe an efficient algorithm to find the maximum likelihood estimator. The method is contrasted with the ordinary least squares approach in a simulation study, and the method is illustrated on a realistic data set.

Authors 3

1. Chengyuan Lu Aachen Department of Biomedical Data Sciences

   Leiden University Medical Center

   Affiliation as printed

   Department of Biomedical Data Sciences , Leiden University Medical Center , Leiden , The Netherlands

   LEIDEN UNIVERSITY (MEDICAL CENTER)

2. Jelle J. Goeman Aachen Department of Biomedical Data Sciences

   Leiden University Medical Center

   Affiliation as printed

   Department of Biomedical Data Sciences , Leiden University Medical Center , Leiden , The Netherlands

3. Hein Putter