Mutual referral policy for coordinating health care systems of different scales

We develop a model to formulate the mutual referral process in a health care system involving a city hospital and a community hospital, and derive the optimal mutual referral strategy between them in the subordination situation as a benchmark. We also concentrate on the subcontracting situation, where the city hospital plays a dominating role, offering contracts to induce the community hospital to follow the optimal mutual referral strategy. We introduce two complex contracts: fee-for-service via cost sharing (FFS-CS) and pay-for-performance via cost sharing (P4P-CS) to coordinate, and find that both contracts coordinate effectively, regardless of the scale of the system. In addition, we discuss four extreme cases: fee-for-service via no cost sharing (FFS-NCS), fee-for-service via total cost sharing (FFS-TCS), pay-for-performance via no cost sharing (P4P-NCS), and pay-for-performance via total cost sharing (P4P-TCS) and find that some can coordinate the health care system under certain circumstances, whereas others cannot. Through the numerical examples we discuss the applicability of the coordinating contracts and further find that FFS-CS outperforms P4P-CS in terms of applicability.