Semiparametric additive rates model for recurrent events data with intermittent gaps

Statistical methods for analyzing recurrent events have attracted significant attention. The majority of existing works consider situations in which subjects are observed over time periods and events of interest that occurred during the course of follow-up are recorded. In some applications, a subject may leave the study for a period of time and then resume due to various reasons. During the absence, which is referred to as an intermittent gap in this study, it may be impossible to observe a recording of the event. A naive analysis disregards gaps and considers events to be a typical recurrent event dataset. However, this may result in biased estimations and misleading results. In this study, we build an additive rates model for recurrent event data considering intermittent gaps. We provide the asymptotic theories behind the proposed model, as well as the goodness of fit between observed and modeled values. Simulation studies reveal that the estimations perform well if intermittent gaps are taken into account. In addition, we utilized the longitudinal cohort of elderly patients who have type 2 diabetes and at least one record of a severe recurrent complication, hypoglycemia, from the National Health Insurance Research Database in Taiwan to demonstrate the proposed method.