Abstract: Panel count data arise when study subjects who may experience certain recurrent events are only observed intermittently at discrete examination times. In addition to the underlying recurrent event process of interest, there usually exist two other nuisance processes, namely the observation and follow-up processes, which may be correlated with the recurrent event process of interest. We propose a general class of random-effects monotonic index models for regression analysis of such panel count data. In order to estimate the regression parameters, we develop a weighted rank (WR) estimation procedure and and establish the consistency and asymptotic normality of the resulting WR estimator. A numerical study and an application of the proposed methodology show that it works well in practice.

Key words and phrases: Informative follow-up time, informative observation process, panel count data, random-effects monotonic index models, weighted rank estimation.