Horseshoe Forests for High-Dimensional Causal Survival Analysis

We develop a Bayesian tree ensemble model to estimate heterogeneous treatment effects in censored survival data with high-dimensional covariates. Instead of imposing sparsity through the tree structure, we place a horseshoe prior directly on the step heights to achieve adaptive global-local shrinkage. This strategy allows flexible regularisation and reduces noise. We develop a reversible jump Gibbs sampler to accommodate the non-conjugate horseshoe prior within the tree ensemble framework. We show through extensive simulations that the method accurately estimates treatment effects in high-dimensional covariate spaces, at various sparsity levels, and under non-linear treatment effect functions. We further illustrate the practical utility of the proposed approach by a re-analysis of pancreatic ductal adenocarcinoma (PDAC) survival data from The Cancer Genome Atlas.