Referral mechanisms coordinating hierarchic healthcare system: subsidy scheme versus penalty scheme

In the context of healthcare services, a variety of reforms have been performed in some countries to coordinate supply and demand. For example, China has implemented a hierarchic healthcare system for this end. As a core challenge pertaining to such reforms, a healthcare referral mechanism needs to be implemented and calibrated efficiently. We consider a hierarchic healthcare system where each patient permitted at a high-level hospital decides whether to be transferred to a low-level hospital, based on their expected utility maximization. In particular, this paper examines two typical mechanisms and their coordination efficiency of referral service: the subsidy scheme and the penalty scheme. Methodologically, by modeling a three-stage Stackelberg game within a queueing framework, we investigate the healthcare referral rate determined by both the high-level hospital and its patients, as well as the reimbursement rate, subsidy rate, and penalty rate determined by the funder alongside the profit- and welfare-maximizing objectives of the high-level hospital. By deriving and comparing the equilibrium outcomes (e.g., referral rate, reimbursement rate, funder’s welfare, patient/social welfare, operating profit, and waiting time) associated with each scheme and the two different objectives of the high-level hospital, we reveal that: (i) when the budget is relatively sufficient (i.e., above a certain threshold), the high-level hospital always transfers out more patients under the welfare-maximizing criterion than that under the profit-maximizing criterion; however, the optimal referral rates under the welfare-maximization and profit-maximizing objectives are respectively above and below that under the social welfare maximization criterion. (ii) The penalty scheme generally dominates the subsidy scheme in terms of higher social/patient welfare, higher funder’s welfare, shorter waiting times, and lower patient referral rates. (iii) When the budget is sufficient and the difference between the prices charged by the high-level and low-level hospitals is relatively small, the funder is recommended to encourage a welfare-maximizing hospital to refer out its patients. In contrast, when the budget is relatively limited, a penalty scheme for a profit-maximizing high-level hospital should be adopted. Finally, extensive numerical experiments have been performed to glean more insights, such as the outperformance of the penalty scheme over the subsidy scheme under different scenarios of available budget levels. These insights can readily facilitate policymakers and regulators in developing a coordinating scheme.