Abstract: A major complication in the analysis of recurrent event data from medical studies is the presence of death. We consider the marginal mean function for the cumulative number of recurrent events over time, acknowledging the fact that death precludes further recurrences. We specify that covariates have multiplicative effects on an arbitrary baseline mean function while leaving the stochastic structure of the recurrent event process completely unspecified. We then propose estimators for the regression parameters and the baseline mean function under this semiparametric model. The asymptotic properties of these estimators are established. Joint inferences about recurrent events and death are also discussed. The finite-sample behavior of the proposed inference procedures is assessed through simulation studies. An application to a well-known bladder tumor study is provided.
Key words and phrases: Censoring, competing risks, counting process, empirical process, multiple events, survival analysis.