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Title: A class of tests for trend for time censored recurrent event data not following a Possion process Authors:  Bo Henry Lindqvist - Norwegian University of Science and Technology (Norway)
Jan Terje Kvaloy - University of Stavanger (Norway) [presenting]
Abstract: Many tests for trend have been derived under a Poisson process assumption, but it is well known that such tests are not robust against deviations from the Poisson assumptions commonly seen in practice. Several tests for trend in recurrent event data not following a Poisson process are proposed, but these are generally constructed for event-censored data. However, time censored data are more frequently encountered in practice. Our contribution is to present 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 adaptation 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 new 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 non-monotonic trends. Extensions to situations with several processes are considered. Properties of the tests are illustrated by simulations and applications to real data.