The relative frailty variance and shared frailty models

The relative frailty variance among survivors provides a readily interpretable measure of how the heterogeneity of a population, as represented by a frailty model, evolves over time. We discuss the properties of the relative frailty variance, show that it characterizes frailty distributions and that, suitably rescaled, it may be used to compare patterns of dependence across models and data sets. In shared frailty models, the relative frailty variance is closely related to the cross-ratio function, which is estimable from bivariate survival data. We investigate the possible shapes of the relative frailty variance function for the purpose of model selection, and we review available frailty distribution families in this context. We introduce several new families with contrasting properties, including simple but flexible time varying frailty models. The benefits of the approach that we propose are illustrated with two applications to bivariate current status data obtained from serological surveys.