Efficiency loss with binary pre-processing of continuous monitoring data

In studies with a recurrent event outcome, events may be captured as counts during subsequent intervals or follow-up times either by design or for ease of analysis. In many cases, recurrent events may be further coarsened such that only an indicator of one or more events in an interval is observed at the follow-up time, resulting in a loss of information relative to a record of all events. In this paper, we examine efficiency loss when coarsening longitudinally observed counts to binary indicators and aspects of the design which impact the ability to estimate a treatment effect of interest. The investigation was motivated by a study of patients with cardiac implantable electronic devices in which investigators aimed to examine the effect of a treatment on events detected by the devices over time. In order to study components of such a recurrent event process impacted by data coarsening, we derive the asymptotic relative efficiency (ARE) of a treatment effect estimator utilizing a coarsened binary outcome relative to an alternative estimator using the count outcome. We compare the efficiencies and consider conditions where the binary process maintains good efficiency in estimating a treatment effect. We present an application of the methods to a data set consisting of seizure counts in a sample of patients with epilepsy.