Partially Linear Additive Reversed Mean Model for Panel Count Data With Informative Terminal Event

This article investigates a partially linear additive reversed mean model for panel count data with an informative terminal event. By anchoring the time origin at the terminal event, the proposed model characterizes the recurrent event process prior to the occurrence of the terminal event. The partially linear additive form provides a flexible framework for modeling covariate effects. The B-spline sieve approximation is employed for both the baseline reversed mean function and the link function. To make the optimization of the loss function feasible, we treat the distribution function of the terminal event as a nuisance functional parameter and develop a two-stage estimation procedure. We establish the asymptotic properties of the proposed estimator, including consistency, convergence rate, and asymptotic distribution. Simulation studies demonstrate that the proposed estimator performs well in finite-sample settings. The proposed method is further illustrated through an application to the Chinese longitudinal healthy longevity survey (CLHLS).