Abstract: We study semiparametric regression for a recurrent event process with an informative terminal event, where observations are taken only at discrete time points, rather than continuously over time. To account for the effect of a terminal event on the recurrent event process, we propose a semiparametric reversed mean model, for which we develop a two-stage sieve likelihood-based method to estimate the baseline mean function and the covariate effects. Our approach overcomes the computational difficulties arising from the nuisance functional parameter in the assumption that the likelihood is based on a Poisson process. We establish the consistency, convergence rate, and asymptotic normality of the proposed two- stage estimator, which is robust against the assumption of an underlying Poisson process. The proposed method is evaluated using extensive simulation studies, and demonstrated using panel count data from a longitudinal healthy longevity study and data from a bladder tumor study.

Key words and phrases: Counting process, expected log-likelihood, reversed mean model, semiparametric M-estimator, terminal event.