Test for trends in recurrent events data

Abstract

The aim of this thesis was to analyse how different trend tests perform under various scenarios, with a particular focus on simulated failure truncated data. The research conducted involved simulating failure truncated processes in R and analysing some time truncated real data. Key findings reveal that the choice of \(\hat\sigma\) impacts the performance of the Lewis-Robinson and Anderson-Darling type tests, especially in scenarios with a low number of failures. The Laplace and Military Handbook tests were found unsuitable for Renewal Process (RP) and Trend-Renewal Process (TRP) situations, so they should be limited to scenarios where Poisson process is very highly likely. The Mann-Kendall test was observed to require a more pronounced trend, for increasing trends, when working with Weibull TRP situations. Furthermore, all the tests that were studied had challenges with high variance for less pronounced trends. This indicates a potential limitation of these tests in real-world scenarios where there are high variance.