Modified Kaplan–Meier Estimator and Nelson–Aalen Estimator with Geographical Weighting for Survival Data

Abstract

The Kaplan–Meier and Nelson–Aalen estimators are universally used methods in clinical studies. In a public health study, people often collect data from different locations of the medical services provider. When some studies need to consider survival curves from different locations, traditional estimators simply estimate the marginal survival curves using stratification. In this article, we use the idea from geographically weighted regression to add geographical weights to the observations to get modified versions of the Kaplan–Meier and Nelson–Aalen estimators which can represent the local survival curve and cumulative hazard. We use counting process methods to derive these modified estimators and to estimate their variances. In addition, we discuss some general spatial weighting functions which can be used in computing these estimators. Furthermore, we present simulation results to illustrate the performance of the modified estimators. Finally, we apply our method to prostate cancer data from the SEER cancer registry for the state of Louisiana.