Evaluating the efficiency of the private healthcare facilities in Italy : a game cross-efficiency DEA modeling framework

This study evaluates the operational efficiency of accredited private healthcare facilities in Italy, a sector increasingly complementing the public National Health Service. Unlike previous studies that aggregate public and private providers, this research focuses exclusively on private facilities, providing a consistent and detailed evaluation of their performance. Utilizing game-theoretic cross-efficiency Data Envelopment Analysis (DEA) combined with Classification and Regression Tree (CART) analysis, this study identifies endogenous and exogenous efficiency drivers. Results indicate that private facilities operate at high efficiency levels (mean cross-efficiency = 0.923), with smaller facilities outperforming larger ones, though resources remain underutilized. Inactive ward and bed non-occupancy rates emerge as key inefficiency factors. Regional analysis highlights minimal disparities between the north-center and south, but significant local variations persist, shaped by governance, funding allocation, and institutional frameworks. This study also identifies an "efficiency paradox", as in deficit regions, private expenditure correlates with higher efficiency, whereas in surplus regions, greater spending does not necessarily improve performance. These findings provide actionable insights for healthcare managers and policymakers, emphasizing the need to maximize capacity utilization, optimize staffing, and structure public-private partnerships strategically. Methodologically, integrating game cross-efficiency DEA with CART strengthens accuracy, offering a robust tool for benchmarking and improving private healthcare performance.