Alternating event processes during lifetimes: population dynamics and statistical inference

In the literature studying recurrent event data, a large amount of work has been focused on univariate recurrent event processes where the occurrence of each event is treated as a single point in time. There are many applications, however, in which univariate recurrent events are insufficient to characterize the feature of the process because patients experience nontrivial durations associated with each event. This results in an alternating event process where the disease status of a patient alternates between exacerbations and remissions. In this paper, we consider the dynamics of a chronic disease and its associated exacerbation-remission process over two time scales: calendar time and time-since-onset. In particular, over calendar time, we explore population dynamics and the relationship between incidence, prevalence and duration for such alternating event processes. We provide nonparametric estimation techniques for characteristic quantities of the process. In some settings, exacerbation processes are observed from an onset time until death; to account for the relationship between the survival and alternating event processes, nonparametric approaches are developed for estimating exacerbation process over lifetime. By understanding the population dynamics and within-process structure, the paper provide a new and general way to study alternating event processes.