Nonparametric comparison of recurrent event processes based on panel count data

Recurrent event processes arise in many fields including medical follow-up studies and reliability experiments and many procedures have been developed in the literature for their comparison nonparametrically (Cook and Lawless, 2007; Sun and Zhao, 2013). However, most of them are for either the complete data situation where one observes recurrent event data or the incomplete data situation where one observes panel count data with the same observation process. There also exist a couple of nonparametric comparison procedures for the panel count data situation that allow unequal observation processes, but apply only to limited situations. In this paper, we discuss the latter situation for both univariate and multivariate panel count data and propose a new type of nonparametric procedures that apply to more general situations. The proposed test statistics are shown to have asymptotic normal distributions, and an extensive simulation is conducted and suggests that they work well in practical situations. An application is also provided.