Analysis of Recurrent Event Processes with Dynamic Models for Event Counts

Recurrent events are of interest in many research fields. The analysis of past developments of processes through dynamic covariates is useful to understand the present and future of processes generating recurrent events. In this paper, we consider modelling and estimation of effects of number of prior events and carryover effects on the evolution of recurrent event processes through dynamic models for event counts. These process features are related to monotonic trends in gap times and clustering of events together over time in recurrent event processes, and are frequently seen in biomedical and epidemiology studies involving recurrent events. Insights about the impacts of these features may provide opportunities for treatment improvements and to develop prevention strategies. We discuss issues in the parametric maximum likelihood estimation of these features through multiplicative recurrent event models for event counts. We extend our discussion to the settings in which excess variation in the rate of event occurrences across multiple individuals is present. We illustrate our methods to analyse a dataset from an asthma study involving children.