Abstract

Spatial inequality remains a major structural barrier to equitable healthcare access in low-resource African settings. This study develops a Bayesian Multilayer Causal Framework (BMCF) to quantify how distance, road quality, and facility hierarchy interact to shape accessibility in the Blue Nile Region of Sudan. The framework combines hierarchical Bayesian inference, spatial conditional autoregressive priors, and directed acyclic graphs (DAGs) to decompose accessibility into direct, indirect, and contextual causal effects. Using data from 47 facilities, Hamiltonian Monte Carlo sampling was applied, with diagnostics indicating strong convergence (R̂ = 1.01, ESS > 400, Moran’s I = 0.04). Results show that road quality is a central causal determinant, moderating the negative influence of distance and improving supply-chain reliability. Counterfactual simulations demonstrate that a one-level improvement in road condition increases the probability of accessibility by 12.8%. Facility hierarchy also exerts a positive effect, indicating that service complexity drives patients’ willingness to travel further. The proposed model outperforms non-causal regression and single-level spatial approaches in WAIC, LOOIC, and posterior predictive checks, demonstrating its superior explanatory and predictive capacity. The study highlights the importance of rural road rehabilitation and decentralized supply-chain planning as indirect but powerful health interventions. The BMCF provides a decision-ready framework for policymakers seeking to allocate resources based on causal impact. Future extensions will incorporate temporal dynamics and patient-level data to enable real-time, dynamic causal forecasting in fragile health systems.