A nonparametric test for the equality of counting processes with panel count data

This paper considers the problem of nonparametric comparison of counting processes with panel count data, which arise naturally when recurrent events are considered. For the problem considered, we construct a new nonparametric test statistic based on the nonparametric maximum likelihood estimator of the mean function of the counting processes over observation times. The asymptotic distribution of the proposed statistic is derived and its finite-sample property is examined through Monte Carlo simulations. The simulation results show that the proposed method is good for practical use and also more powerful than the existing nonparametric tests based on the nonparametric maximum pseudo-likelihood estimator. A set of panel count data from a floating gallstone study is analyzed and presented as an illustrative example.