Modeling county level breast cancer survival data using a covariate-adjusted frailty proportional hazards model

TL;DR

This paper introduces a flexible covariate-adjusted frailty model for clustered survival data, applied to breast cancer survival, revealing complex temporal and geographic survival trends linked to socioeconomic factors.

Contribution

It develops a novel Bayesian nonparametric frailty model that allows frailty distributions to vary with covariates, enhancing analysis of clustered survival data.

Findings

Rural counties showed better survival in the 1990s, contrary to expectations.

Urban and affluent areas had worse survival in the same period, possibly due to hormone therapy.

Model fitting was straightforward with existing R packages.

Abstract

Understanding the factors that explain differences in survival times is an important issue for establishing policies to improve national health systems. Motivated by breast cancer data arising from the Surveillance Epidemiology and End Results program, we propose a covariate-adjusted proportional hazards frailty model for the analysis of clustered right-censored data. Rather than incorporating exchangeable frailties in the linear predictor of commonly-used survival models, we allow the frailty distribution to flexibly change with both continuous and categorical cluster-level covariates and model them using a dependent Bayesian nonparametric model. The resulting process is flexible and easy to fit using an existing R package. The application of the model to our motivating example showed that, contrary to intuition, those diagnosed during a period of time in the 1990s in more rural and less affluent Iowan counties survived breast cancer better. Additional analyses showed the opposite trend for earlier time windows. We conjecture that this anomaly has to be due to increased hormone replacement therapy treatments prescribed to more urban and affluent subpopulations.