Semiparametric regression of panel count data with informative terminal event

We study a semiparametric model for robust analysis of panel count data with an informative terminal event. To explore the explicit effect of the terminal event on recurrent events of interest, we propose a conditional mean model for a reversed counting process anchoring at the terminal event. Treating the distribution function of the terminal event as a nuisance functional parameter, we develop a predicted least squares-based two-stage estimation procedure with the spline-based sieve estimation technique, and derive the convergence rate of the proposed estimator. Furthermore, overcoming the difficulties caused by the convergence rate slower than 1/root n, we establish the asymptotic normality for the estimator of the finite-dimensional parameter and a functional of the estimator of the infinite-dimensional parameter. The proposed method is evaluated through extensive simulation studies and illustrated with an application to the Longitudinal Healthy Longevity Survey study on elder people in China.