Transportability without Graphs: A Bayesian Approach to Identifying s-Admissible Backdoor Sets

Transporting causal information across populations is a critical challenge in clinical decision-making. Causal modeling provides criteria for identifiability and transportability, but these require knowledge of the causal graph, which rarely holds in practice. We propose a Bayesian method that combines observational data from the target domain with experimental data from a different domain to identify s-admissible backdoor sets, which enable unbiased estimation of causal effects across populations, without requiring the causal graph. We prove that if such a set exists, we can always find one within the Markov boundary of the outcome, narrowing the search space, and we establish asymptotic convergence guarantees for our method. We develop a greedy algorithm that reframes transportability as a feature selection problem, selecting conditioning sets that maximize the marginal likelihood of experimental data given observational data. In simulated and semi-synthetic data, our method correctly identifies transportability bias, improves causal effect estimation, and performs favorably against alternatives.