A general class of additive semiparametric models for recurrent event data

Abstract

Recurrent event data is a special case of multivariate lifetime data that is present in a large variety of studies from numerous disciplines. Due to its pervasiveness, it is essential that appropriate models and inference procedures exist for its analysis. We propose a general class of additive semiparametric models for examining recurrent event data that uses an effective age process to take into account the impact of interventions applied to units after an event occurrence. The effect of covariates is additive instead of the common multiplicative assumption. We derive estimators of the regression parameter, baseline cumulative hazard function, and baseline survival function. We also establish the asymptotic properties of the estimators using tools from empirical process theory. Simulation studies indicate that the asymptotic properties of the regression parameter closely approximate its finite sample properties. The analysis of a real data set consisting of indolent lymphoma recurrence times provides a practical illustration of the class of models and is used to examine the impact of the effective age process. The importance of the effective age process is also demonstrated via the modeling of a data set of failure times for the hydraulic subsystems of load–haul–dump machines used in mining.