The Demand of Primary and Secondary Care: A Bayesian Hierarchical Approach

Health systems increasingly face the dual challenge of rising demand and persistent inequalities in access to care. Understanding how patients use different services—particularly the balance between primary and secondary care—is essential for informing policy. This study develops a Bayesian hierarchical bivariate Poisson model to jointly analyze general practitioner consultations and emergency department visits among older adults newly diagnosed with hypertension, using data from the UK Clinical Practice Research Datalink. The framework accounts for both individual-level heterogeneity and practice-level fixed effects, capturing substitution or complementarity between services. Results show that multimorbidity strongly drives both utilization, while socioeconomic deprivation is mainly associated with higher emergency care use, pointing to persistent inequalities. We also find substantial heterogeneity across GP practices, suggesting that organizational and contextual factors significantly shape care pathways.