Asymptotic convergence in distribution of the area bounded by prevalence-weighted Kaplan–Meier curves using empirical process modelling

The Kaplan–Meier product-limit estimator is a simple and powerful tool in time to event analysis. An extension exists for populations stratified into cohorts where a population survival curve is generated by weighted averaging of cohort-level survival curves. For making population-level comparisons using this statistic, we analyse the statistics of the area between two such weighted survival curves. We derive the large sample behaviour of this statistic based on an empirical process of product-limit estimators. This estimator was used by an interdisciplinary National Institutes of Health–Social Security Administration team in the identification of medical conditions to prioritize for adjudication in disability benefits processing.