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In statistical models for the analysis of time-to-event data, individualheterogeneity is usually accounted for by means of one or more random effects,also known as frailties. In the vast majority of the literature, the randomeffect is assumed to follow a continuous probability distribution. However, insome areas of application, a discrete frailty distribution may be moreappropriate. We investigate and compare various existing families of discreteunivariate and shared frailty models by taking as our focus the variance of therelative frailty distribution in survivors. The relative frailty variance (RFV)among survivors provides a readily interpretable measure of how theheterogeneity of a population, as represented by a frailty model, evolves overtime. We explore the shape of the RFV for the purpose of model selection andreview available discrete random effect distributions in this context. We findnon-monotone trajectories of the RFV for discrete univariate and shared frailtymodels, which is a rare property. Furthermore, we proof that for discretetime-invariant univariate and shared frailty models with (without) an atom atzero, the limit of the RFV approaches infinity (zero), if the support of thediscrete distribution can be arranged in ascending order. Through theone-to-one relationship of the RFV with the cross-ratio function in sharedfrailty models, which we generalize to the higher-variate case, our resultsalso apply to patterns of association within a cluster. Extensions andcontrasts to discrete time-varying frailty models and contrasts to correlateddiscrete frailty models are discussed.

The shape of the relative frailty variance induced by discrete random effect distributions in univariate and multivariate survival models