Bayesian Analysis of an Additive Survival Model with Frailty

Abstract

There has been some interest in survival models with additive hazard function (e.g., the Aalen's linear model), which is considered an alternative or supplementary model to the most common Cox model in analysis of censored data. One advantage of the Aalen's model is to allow the influence of each covariate to vary separately over time. In this article, an additive survival model, based on counting processes, is presented introducing additive frailties into the intensity in order to account for the heterogeneity of the data due to unobserved risk factors or dependence among individuals in study. The additive frailty model is analyzed under a Bayesian point of view and illustrated by two well-known data sets.

Key Words:

• Additive frailty model
• Aalen's linear model
• Bayesian survival analysis

Mathematics Subject Classifications:

• 62N01
• 62F15

Acknowledgments

This research was supported by Programa Operacional “Cieˆncia, Tecnologia, Inovação” (POCTI) of the Fundação para a Cieˆncia e a Tecnologia (FCT), cofinanced by the European Community fund FEDER. The authors are grateful to anonymous referees for their important comments.