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

TL;DR

This paper introduces a new class of statistical tests for detecting trends in time censored recurrent event data, filling a gap for non-Poisson processes using renewal process theory.

Contribution

It develops a unified framework for trend testing in time censored recurrent data, including classical and novel tests with strong power properties.

Findings

The tests perform well in simulations.

The Anderson-Darling type test has good power against various trends.

Extensions to multiple processes are feasible.

Abstract

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.