A Copula-Based Joint Modeling Framework for Hospitalization Costs and Length of Stay in Massive Healthcare Data

In large-scale medical data, the connection between hospital length of stay and medical expenses shows a complex and nonlinear relationship instead of a straightforward positive link. This study proposes a Cox–Log-Logistic–Copula joint modeling framework to describe the marginal distributions and latent dependence between the two variables. Specifically, a semi-parametric Cox proportional hazards model is used for hospitalization duration, while a Log-Logistic model handles medical costs. The two margins are flexibly coupled through a Copula function to capture dynamic variations in cost levels during different hospitalization stages. To address computational challenges in large datasets, this study also includes subsample correction and one-step adjustment algorithms, combined with parallel computing strategies, to enhance estimation efficiency and accuracy. Empirical results show that the length of hospital stays and medical costs are not always positively related. In some cases, higher medical expenses occur during shorter stays, suggesting possible over-treatment or uneven resource distribution. The proposed framework proves to have strong explanatory power in identifying nonlinear patterns in healthcare behavior and offers a new quantitative tool for optimizing medical resource allocation and controlling costs.