Bayesian Spatial Split-Population Models for the Social Sciences

Abstract

Survival data often include an “immune” or cured fraction of units that will never experience an event and conversely, an “at risk” fraction that can fail or die. It is also plausible that spatial clustering (i.e., spatial autocorrelation) in latent or unmeasured risk factors among adjacent units can affect their odds of being immune and survival time of interest. To address these methodological challenges, this article introduces a class of parametric Spatial split-population survival models—also denoted as Spatial cure models—that explicitly accounts for the influence of spatial autocorrelation among the underlying risk propensities of units on not only their probability of being immune but also their risk of experiencing the event of interest. Our approach is Bayesian in that we account for spatial autocorrelation in unmeasured risk factors across adjacent units in the cure model’s split-stage (cure rate portion) and survival stage via the conditional autoregressive prior (CAR) prior. The article also presents a set of parametric split-population survival models with non-spatial i.i.d frailties and without frailties, and time-varying covariates can be included in all the models mentioned above. Bayesian inference of the non-spatial and spatial cure models is conducted via a hybrid Markov Chain Monte Carlo (MCMC) algorithm. The relevant full conditional distributions required for MCMC sampling are also derived and presented in the paper. We fit all the models to survival data on post-civil war peace to demonstrate their main applicability and main features.