Geographically Weighted Cox Regression for Prostate Cancer Survival Data in Louisiana

TL;DR

This paper introduces a geographically weighted Cox regression model with a stochastic neighborhood scheme to analyze spatially varying effects in prostate cancer survival data from Louisiana, supported by theoretical and empirical validation.

Contribution

It proposes a novel geographically weighted Cox model with a stochastic neighborhood approach and discusses model selection using TIC, advancing spatial survival analysis methods.

Findings

The model effectively captures spatial heterogeneity in survival data.

Simulation studies demonstrate the method's robustness and accuracy.

Application to Louisiana prostate cancer data reveals spatially varying covariate effects.

Abstract

The Cox proportional hazard model is one of the most popular tools in analyzing time-to-event data in public health studies. When outcomes observed in clinical data from different regions yield a varying pattern correlated with location, it is often of great interest to investigate spatially varying effects of covariates. In this paper, we propose a geographically weighted Cox regression model for sparse spatial survival data. In addition, a stochastic neighborhood weighting scheme is introduced at the county level. Theoretical properties of the proposed geographically weighted estimators are examined in detail. A model selection scheme based on the Takeuchi's model robust information criteria (TIC) is discussed. Extensive simulation studies are carried out to examine the empirical performance of the proposed methods. We further apply the proposed methodology to analyze real data on prostate cancer from the Surveillance, Epidemiology, and End Results cancer registry for the state of Louisiana.