Accelerated failure time models for counting processes

We present a natural extension of the conventional accelerated failure time model for survival data to formulate the effects of covariates on the mean function of the counting process for recurrent events. A class of consistent and asymptotically normal rank estimators is developed for estimating the regression parameters of the proposed model. In addition, a Nelson-Aalen-type estimator for the mean function of the counting process is constructed, which is consistent and, properly normalised, converges weakly to a zero-mean Gaussian process. We assess the finite-sample properties of the proposed estimators and the associated inference procedures through Monte Carlo simulation and provide an application to a well-known bladder cancer study.