A novel approach for analyzing data on recurrent events with duration to estimate the combined cumulative rate of both variables over time

Recurrent adverse events, once occur often continue for some duration of time in clinical trials; and the number of events along with their durations is clinically considered as a measure of severity of a disease under study. While there are methods available for analyzing recurrent events or durations or for analyzing both side by side, no effort has been made so far to combine them and present as a single measure. However, this single-valued combined measure may help clinicians assess the wholesome effect of recurrence of incident comprising events and durations. Non-parametric approach is adapted here to develop an estimator for estimating the combined rate of both, the recurrence of events as well as the event-continuation, that is the duration per event. The proposed estimator produces a single numerical value, the interpretation and meaningfulness of which are discussed through the analysis of a real-life clinical dataset. The algebraic expression of variance is derived, asymptotic normality of the estimator is noted, and demonstration is provided on how the estimator can be used in the setup of testing of statistical hypothesis. Further possible development of the estimator is also noted, to adjust for the dependence of event occurrences on the history of the process generating recurrent events through covariates and for the case of dependent censoring. Keywords: Recurrent events, Duration per event, Intensity, Nelson-aalen estimator