Modelling physician visit frequency and costs using a copula additive distributional regression approach

Abstract This paper introduces a copula additive distributional regression framework for mixed count–continuous outcomes, with a focus on simultaneous modelling of the number and cost of physician visits. Traditionally analysed separately, these outcomes are inherently interdependent, and modelling them jointly uncovers relationships that would otherwise be overlooked. The approach employs a zero-truncated count distribution for visit frequency, a continuous skewed distribution with positive support for costs, allows for flexible covariate effects through additive predictors and captures the dependence between the responses using copulae. Alongside model development, model-based statistics, such as conditional expectations, are derived to improve interpretability. Applied to Medical Expenditure Panel Survey data, the methodology provides valuable insights into the determinants of visit frequency and healthcare costs, as well as their association, highlighting its potential as a useful tool for decision-makers. To enhance reproducibility and transparency, the modelling framework has been incorporated into the R package GJRM.