Joint modelling of in-hospital mortality and length of stay: a copula additive distributional regression analysis of COVID-19 patient data

Abstract In-hospital mortality and length of stay are fundamental metrics for evaluating healthcare quality, patient outcomes, and resource utilization. While length of stay reflects hospital efficiency and capacity management, mortality provides insights into patient safety and the effectiveness of clinical interventions. These outcomes are interdependent, and demographic, clinical and laboratory factors simultaneously influence both hospitalization duration and mortality. To address this, a copula additive distributional regression framework is employed, enabling the joint modelling of these hospital metrics as functions of covariate effects. Application to COVID-19 data demonstrates that key predictors, including age, oxygenation and inflammation markers, modulate the dependence between mortality and hospitalization duration. The joint modelling approach provides a probabilistic, patient-level characterization of the interplay between these indicators, supporting risk stratification, resource planning and actionable clinical decision-making.