Bayesian hierarchical bootstrap framework for causal subgroup estimation with a time-to-event outcome

Abstract

Causal estimation of treatment effects within prespecified subgroups, such as biomarker-defined strata, disease phenotypes, or demographic groups are often of clinical interest. Bayesian approaches are attractive for subgroup effect estimation because flexible priors can represent complex treatment heterogeneity and propagate posterior uncertainty. Frequentist methods for prespecified causal subgroup analysis with time-to-event outcomes are also available, including propensity-score weighting approaches that emphasize subgroup-level covariate balance. In the posterior g-formula, subgroup survival estimands also depend on the subgroup-specific distribution of baseline covariates, which may be unstable when some subgroups are small or unevenly represented. Right censoring separately reduces information for the outcome-model component of the estimand, increasing overall uncertainty in subgroup causal survival contrasts. We extend the hierarchical Bayesian bootstrap (HBB) to subgroup causal inference with right-censored time-to-event outcomes. The HBB places a nonparametric hierarchical prior on subgroup-specific baseline covariate distributions, enabling principled borrowing of information across related subgroups while preserving subgroup-specific structure. We combine this distributional regularization with a Bayesian accelerated failure time model and right censoring to perform a posterior g-formula that propagates uncertainty from both the survival model and the subgroup covariate distribution. The resulting framework stabilizes subgroup causal survival estimands in sparse strata without imposing parametric assumptions on the covariate distribution. Simulation studies examine performance across varying degrees of subgroup sparsity and censoring and compare the proposed approach to the popular Bayesian additive regression tree for heterogeneous survival effects.