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

## TL;DR

This paper analyzes the asymptotic distribution of the area between prevalence-weighted Kaplan-Meier survival curves, providing theoretical insights into their large sample behavior for population comparisons.

## Contribution

It extends empirical process modeling to the area between weighted Kaplan-Meier curves, offering new theoretical results for population-level survival analysis.

## Key findings

- Derived the asymptotic distribution of the area statistic
- Applied empirical process theory to weighted survival curves
- Supported by NIH-SSA medical condition prioritization case

## Abstract

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.