A Class of Tests for Trend in Time Censored Recurrent Event Data

Statistical tests for trend in recurrent event data not following a Poisson process are generally constructed for event censored data. However, time censored data are more frequently encountered in practice. In this article, we contribute to filling an important gap in the literature on trend testing by presenting a class of statistical tests for trend in time censored recurrent event data, based on the null hypothesis of a renewal process. The class of tests is constructed by an adaption of a functional central limit theorem for renewal processes. By this approach a number of tests for time censored recurrent event data can be constructed, including among others a version of the classical Lewis–Robinson trend test and an Anderson–Darling type test. The latter test turns out to have attractive properties for general use by having good power properties against both monotonic and nonmonotonic trends. Extensions to situations with several processes are considered. Properties of the tests are studied by simulations and some asymptotic calculations, and the approach is illustrated in data examples.