Dynamic healthcare demand with informative dropout: evidence from register data

We study the dynamic relationship between outpatient secondary care and emergency secondary care using linked Danish register data on approximately 30,000 individuals with type-2 diabetes followed for 5 years after an emergency hospital admission. The data present 3 challenges: utilization is observed as 2 interrelated count outcomes, attrition is informative because it is largely driven by mortality, and the timing of death is recorded only at the quarterly level. We address these features using a hidden Markov dropout bivariate Poisson model that combines time-varying latent health states with a discrete-time specification for dropout. This framework allows us to separately identify dynamic state dependence and unobserved heterogeneity in both care utilization and survival. Accounting for latent health dynamics substantially alters the estimated relationship between the 2 services: standard random-effects models suggest mild complementarity, whereas the hidden Markov specification indicates substitution. Modelling dropout as informative further refines these estimates and clarifies the role of unobserved heterogeneity, disentangling persistent frailty from time-varying health dynamics. The results reveal substantial heterogeneity in patient trajectories and show that more recent cohorts experience improved survival together with a shift from emergency towards outpatient utilization. The framework is applicable to settings with interdependent recurrent events and endogenous attrition.