  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 analyze the statistics of the area between two such weighted
survival curves. We derive the large sample behavior of this statistic based on
an empirical process of product-limit estimators. This estimator was used by an
interdisciplinary NIH-SSA team in the identification of medical conditions to
prioritize for adjudication in disability benefits processing.
