Some Models and Tests for Carryover Effects and Trends in Recurrent Event Processes

Abstract

Recurrent events experienced by individual units or systems occur in many fields. The main target of this thesis is to develop formal tests for certain features of recurrent event processes, and to discuss their properties. In particular, carryover effects and time trends are considered. The former is related to clustering of events together in time, and the latter refers to a tendency for the rate of event occurrence to change over time in some systematic way. Score tests are developed for models incorporating carryover effects or time trends. The tests considered are easily interpreted and based on simple models but have good robustness properties against a range of carryover and trend alternatives. Asymptotic properties of test statistics are discussed when the number of processes approaches infinity as well as when one process is under observation for a long time. In applications involving multiple systems or individuals, heterogeneity is often apparent, and there is a need for tests developed for such cases. Allowance for heterogeneity is, therefore, considered. Methods are applied to data sets from industry and medicine. The results are supported by simulation studies.