NEW MULTI-SAMPLE NONPARAMETRIC TESTS FOR PANEL COUNT DATA

By Narayanaswamy Balakrishnan, Xingqiu Zhao. 2009

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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 difierences 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 pseudolikelihood. The asymptotic distributions of the proposed statistics are derived and their flnite-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 Kalb∞eisch [13], Wellner and Zhang [17]). Our focus here will be on the situation when such a study involves k (‚ 2) groups. Let ⁄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 H0 : ⁄1(t) = ¢¢¢ = ⁄k(t). A number of authors have discussed the analysis of recurrent event data when each subject in the study is observed continuously over an interval or when the exact times of occurrences of the recurrent event are known. For example, the book by Andersen, Borgan, Gill and Keiding [1] presents

Subfields: Finance, Statistics and Probability

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