Estimation of cluster-specific causal effects on spatially associated survival data using SoftBART

Abstract

We propose a novel Bayesian approach to estimate causal effects in spatially clustered survival data. Using Soft Bayesian Additive Regression Trees (SBART), we introduce a nonparametric regression for a log-Normal survival model that accommodates spatial associations among unknown cluster effects through a directed acyclic graph autoregressive (DAGAR) model. We employ a two-stage approach, which entails estimating the propensity score in the first step and incorporating it as a confounder of the outcome model in the second step. In our simulation study, we compare our method with existing approaches under various simulation scenarios, including both correctly specified and misspecified outcome models, to demonstrate the superior performance of our method. We then apply our method to analyze the causal effect of treatment delay (TD) on posttreatment survival of breast cancer patients from the Florida Cancer Registry (FCR). Our analysis produces the county-specific as well as state-wide assessment of the causal effects while accommodating spatial association among counties.