Abstract: 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. As a byproduct, the structure of the model provides a model selection approach for the submodels that employs hypothesis testing of the model parameters. Numerical studies show that the proposed estimator and the model selection procedure perform well under both noninformative and informative censoring scenarios. Lastly, the methods are applied to data from two transplant cohorts to study the risk of infection after transplantation.

Key words and phrases: Accelerated failure time model, accelerated rate model, Cox model, frailty model, hypothesis testing, model selection, resampling.