A general class of semiparametric models for recurrent event data

We propose a general class of semiparametric models for analyzing recurrent event data that takes into account the change in age of a unit due to interventions; allows for the possibility of the unit receiving a life supplement after being repaired; and provides a mechanism for researchers to incorporate time-dependent covariates. The class of models includes as special cases many other models that have been proposed for analyzing recurrent event data. Models belonging to the class can be easily generalized and new models can be created to accommodate a variety of practical considerations. A partial maximum likelihood estimator of the regression parameter and a Nelson–Aalen type estimator of the baseline cumulative intensity are given. Asymptotic properties of the estimators are established and the finite sample properties are investigated via a simulation study. The statistical analysis of a real data set is used to illustrate the class of models.