Generalized scale-change models for recurrent event processes under informative censoring

Two major challenges arise in regression analyses of recurrent event data. First, popular existing models, such as the Cox proportional rates model, may not fully capture the covariate effects on the underlying recurrent event process. Second, the censoring time remains informative about the risk of experiencing recurrent events after accounting for covariates. We address both challenges using a general class of semiparametric scale-change models that allow both scale-change and multiplicative covariate effects. The proposed model is flexible, and includes several existing models as special cases, including the popular proportional rates model, accelerated mean model, and accelerated rate model. Moreover, it accommodates informative censoring through a subject-level latent frailty, the distribution of which is left unspecified. A robust estimation procedure is proposed to estimate the model parameters that does not require a parametric assumption on the distribution of the frailty, or a Poisson assumption on the recurrent event process. The asymptotic properties of the resulting estimator are established, with the asymptotic variance estimated using a novel resampling approach. Statistica Sinica: Preprint doi:10.5705/ss.202018.0224