NONPARAMETRIC ESTIMATION AND TESTING FOR PANEL COUNT DATA WITH INFORMATIVE TERMINAL EVENT.

Informative terminal events often occur in the long term recurrent event follow-up studies. To reflect their effects on recurrent event processes explicitly, we propose a reversed 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. The consistency, convergence rate and asymptotic normality of the proposed nonparametric estimator are established. Then we construct a class of new statistics for two-sample test. The asymptotic properties of the new tests are established and evaluated by extensive simulation studies. Panel count data from Chinese Longitudinal Healthy Longevity study are analyzed using the proposed method for illustration.