New Multi - Sample Nonparametric Tests for Panel Count Data

This paper considers the problem of multi-sample nonparametric comparison of counting processes with panel count data, which arise naturally when recurrent events are considered. Such data frequently occur in medical follow-up studies and reliability experiments, for example. For the problem considered, we construct two new classes of nonparametric test statistics based on the accumulated weighted differences between the rates of increase of the estimated mean functions of the counting processes over observation times, wherein the nonparametric maximum likelihood approach is used to estimate the mean function instead of the nonparametric maximum pseudo-likelihood. The asymptotic distributions of the proposed statistics are derived and their finite-sample properties are examined through Monte Carlo simulations. The simulation results show that the proposed methods work quite well and are more powerful than the existing test procedures. Two real data sets are analyzed and presented as illustrative examples. 1. Introduction. Consider a study that concerns some recurrent event, and suppose that each subject in the study gives rise to a counting process N (t), denoting the total number of occurrences of the event of interest up to time t. Also suppose that for each subject, observations include only the values of N (t) at discrete observation times or the numbers of occurrences of the event between the observation times. Such data are usually referred to as panel count data [Sun and Kalbfleisch (1995), Wellner and Zhang (2000)]. Our focus here will be on the situation when such a study involves k (≥ 2) groups. Let Λ l (t) denote the mean function of N (t) corresponding to the lth group for l = 1,. .. , k. The problem of interest is then to test the hypothesis H 0 : Λ 1 (t) = · · · = Λ k (t).