  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 paper 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 non-monotonic trends.
Extensions to situations with several processes are considered. Properties of
the tests are studied by simulations, and the approach is illustrated in two
data examples.
