Testing for Monotone Trend in Recurrent Event Processes

Abstract

Tests for the presence of monotone trends in recurrent event processes have been proposed and studied by many authors. However, a general concept of trend is elusive, and the dependence of the behavior of tests on the assumed definitions of “no trend” and “trend,” and on the observation periods for the processes, has been largely ignored. We discuss these issues and study them through analytical results and simulation studies. The article also presents robust tests for trend across multiple processes, extends them to deal with interval-censored event times, and compares them and other well-known trend tests with respect to the issues mentioned.

Keywords:

• Lewis–Robinson test
• Rank tests
• Rate functions
• Repairable systems
• Renewal processes
• Robust tests.

ACKNOWLEDGMENTS

This research was supported by the Natural Sciences and Engineering Research Council of Canada (RJC, JFL), by the Canadian Institutes for Health Research (RJC), and by Cancer Care Ontario and the Ontario Institute for Cancer Research (through funding provided by the Ministry of Health and Long-Term Care and the Ministry of Research & Innovation of the Government of Ontario) (CÇ).