The Kaplan-Meier Estimator as a Sum over Units
Malte C. Tichy
TL;DR
This paper introduces a sum-wise formulation of the Kaplan-Meier estimator, allowing for a clearer understanding of individual contributions of units to the overall survival estimate, especially in censored data scenarios.
Contribution
It presents a novel sum-over-units representation of the Kaplan-Meier estimator, enhancing interpretability and visualization of individual data contributions.
Findings
The formulation enables visualization of failed vs. censored units' contributions.
It provides an intuitive decomposition of the population estimator.
The approach improves understanding of survival data analysis.
Abstract
A sum-wise formulation is proposed for the Kaplan-Meier product limit estimator of partially right-censored survival data. The derived representation permits to write the population's estimator as a sum over its individual units' semi-empirical estimators. This intuitive decomposition is applied to visualize the different contributions of failed and censored units to the overall population estimator.
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Taxonomy
TopicsStatistical Methods and Inference · Census and Population Estimation · Statistical Distribution Estimation and Applications