Frailty Models and Frailty-Mixture Models for Recurrent Event Times
The analysis of recurrent event times faces three challenges: between-subject heterogeneity (frailty), within-subject event dependence, and the possibility of a cured fraction. Frailty can be handled by including a latent random-effects term in a Cox-type model. Event dependence may be considered as contributing to the intervention effect, or it may be considered as a source of nuisance, depending on the analysts’ specific research questions. If it is seen as a nuisance, the analysis can stratify the recurrent event times according to event order. If it is seen as contributing to the intervention effect, stratification should not be used. Models with and without stratification for event order estimate two types of treatment effects. They are analogous to per-protocol analysis and intention-to-treat analysis, respectively. In the context of chronic disease treatment, we want to estimate whether there is a cured fraction; for infectious disease prevention, this is called a nonsusceptible fraction. In infectious disease prevention, we want to understand whether an intervention protects each of its recipients to some extent (“leaky” model) or whether it totally protects some recipients but offers no protection to the rest (“all-or-none” model). The truth may be a mixture of the two modes of protection. We describe a class of regression models that can handle all three issues in the analysis of recurrent event times. The model parameters are estimated by the expectation-maximization algorithm, and their variances are estimated by Louis's formula. We provide a new command, strmcure, for implementing these models.