Semiparametric Reversed Mean Model for Recurrent Event Process with Informative Terminal Event

We study semiparametric regression of 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 a nuisance functional parameter involved in the likelihood based on a Poisson process assumption.We establish the consistency, convergence rate and asymptotic normality of the proposed twostage estimator, which is robust against the underlying Poisson process assumption.The proposed method is evaluated with extensive simulation studies and illustrated with panel count data from a longitudinal healthy longevity study and a bladder tumor study.