Survival Models for Heterogeneity Using the Non-Central Chi-Squared Distribution with Zero Degrees of Freedom

Abstract

The existence of homogeneity between individuals for given covariate values is an assumption which is usually made in the analysis of survival data. Nevertheless, there is an increasing concern about the impact of unobserved heterogeneity due, for instance, to the fact that it may not have been possible to record all relevant risk factors. This has led to the development of frailty models. The multiplicative model has been widely used with several choices for the frailty distribution. Here, we consider an alternative model, where frailty acts additively on the hazard function. Also, in order to develop a survival model for heterogeneity which allows for a non-susceptible group of individuals, we propose the non-central chi-squared distribution with zero degrees of freedom as a frailty distribution. Its basic properties, together with the results obtained by its application to the additive model, as well as to the multiplicative one, will be presented.