Copula‐based joint modelling of emergency department visits with time‐varying dependence

Jointly modelling multiple correlated count time series is essential in health services research, where outcomes like emergency visits for mental health and substance use often evolve together. Ignoring these dependencies can obscure meaningful trends and limit the effectiveness of policy evaluation. We propose a copula‐based framework that combines negative binomial regression with penalized splines for flexible marginal trends and a smoothly time‐varying copula to capture evolving dependence. Simulations show improved accuracy and uncertainty quantification compared to models assuming constant or no dependence. Applied to monthly emergency visits in Nova Scotia (2017–2023), the model reveals dynamic associations: strong positive correlation prior to COVID‐19, a temporary reversal during lockdowns, and partial recovery post reopening. This approach offers a powerful tool for analyzing complex, time‐varying relationships in healthcare utilization data to inform public health planning.