Sufficient dimension reduction on partially nonlinear index models with applications to medical costs analysis

Modeling medical costs is a crucial task in health economics, especially when high-dimensional covariates and nonlinear effects are present. In this study, we propose a partially nonlinear index model (PNIM) that integrates partially sufficient dimension reduction with a rapid instrumental variable pilot estimation method. Through simulations, we demonstrate that the proposed model excels at capturing significant nonlinear relationships. When applying the model to the Medical Expenditure Panel Survey (MEPS) dataset, we identify important nonlinear age effects on medical costs and highlight key factors such as hospitalization, cardiovascular diseases, and supplemental insurance coverage. These findings provide valuable insights for healthcare policy, including targeted interventions for specific age groups and enhanced management of chronic conditions. Overall, the proposed method offers a flexible and computationally efficient framework for analyzing complex medical cost data, with broad applicability in health economics.