Strengthening Primary Healthcare Evaluation: Game-Theoretic Weighting of Resident Service Functions in Macao Health Centers

Objective: Existing evaluation studies on community health services in China often face limitations in regional applicability. In Macao, a Special Administrative Region (SAR) with distinctive healthcare system characteristics, it remains difficult to identify an evaluation indicator system specifically tailored to the service functions of local health centers. This study offers a preliminary and exploratory attempt to develop a locally adapted evaluation indicator system, together with the determination of indicator weights, for assessing the resident service functions of Macao health centers. Methods: A systematic literature review and Delphi method were first conducted to select and refine the indicators, thereby establishing an evaluation indicator system suited to the services of Macao health centers. Subsequently, the Analytic Hierarchy Process was applied to construct a hierarchical model, with expert panels generating pairwise comparison matrices to calculate subjective weights. The Entropy Weight Method was then employed to measure the degree of dispersion in the data, thereby deriving the corresponding objective weights. Finally, the Game-Theoretic Combination Weighting Method was introduced, whereby Nash equilibrium principles and minimization of deviations between combined and individual weights were used to determine the optimal combination coefficients and obtain the integrated weights. Results: The final evaluation indicator system comprises three primary indicators and nine secondary indicators, covering the core functions of Macao health centers: "Basic Medical Diagnosis and Treatment", "Preventive Healthcare Services", and "Health Education and Communication". The weighting design of this study was centered on residents' healthcare needs, with particular attention to service functions that, if poorly performed, could directly affect life and health outcomes. Diagnosis and treatment remained the core functions with the highest weights, while disease screening, health management, and vaccination were also highly weighted due to their critical roles in major disease prevention and early detection. The indicator for drug supply focused on the adequacy and accessibility of essential medicines rather than prescription rationality, resulting in a moderate weight. Fertility guidance was assigned a higher weight because of its direct relevance to the health and safety of mothers and newborns - areas characterized by high risk and irreversible consequences. The overall weighting perspective primarily reflected residents' needs, emphasizing diagnosis and examination functions while giving relatively lower importance to publicity and guidance services. If future research shifts toward a governmental or public health perspective, the weighting distribution within the same indicator system may accordingly change. Conclusion: Compared with traditional evaluation approaches, the preliminary indicator system developed in this study based on the Game-Theoretic Combination Weighting Method may, to some extent, offer a possible way to address certain limitations in the current health service evaluations in Macao. Although the system remains in its early stage of development, it can serve as an initial reference for the Macao Special Administrative Region in optimizing resource allocation in health centers and conducting assessments of primary healthcare service functions, while also providing methodological insights for the development of community health service evaluation systems in other regions. Continued empirical validation and practical application will be essential to further strengthen the applicability and reliability of the proposed indicator system.