Abstract: Informative terminal events often occur in long-term recurrent event follow-up studies. To explicitly reflect the effects of such events on recurrent event processes, we propose a reverse nonparametric mean model for panel count data, with a terminal event subject to right censoring. This model enjoys meaningful interpretation for applications and robustness for statistical inference. Treating the distribution of the right-censored terminal event time as a nuisance functional parameter, we develop a two-stage estimation procedure by combining the Kaplan-Meier estimator and nonparametric sieve estimation techniques. We establish the consistency, convergence rate, and asymptotic normality of the proposed nonparametric estimator, and construct a class of new statistics for a two-sample test. We also establish the asymptotic properties of the new tests and evaluate their performance using extensive simulation studies. Lastly, we demonstrate the proposed method by applying it to panel count data from a Chinese longitudinal healthy longevity study.

Key words and phrases: Monotone polynomial spline, nonparametric test, panel count data, terminal event, two-stage estimation.