The Centers for Medicare and Medicaid Services (CMS) has introduced several Episode‐based Payment Models. Episodes are combinations of pre‐acute, acute, and post‐acute services for particular medical conditions. During the year, CMS pays hospitals according to historical norms. At the end of the year, these payments are reconciled against a target price, resulting in either a gain or a loss for the hospital. The hospital may also realize gains or losses from its internal operations. It may incentivize physicians to select certain treatment levels that improve quality and reduce costs by offering to share gains and losses. CMS has placed restrictions on what gains or losses may be shared and implemented stop‐loss and stop‐gain (SLSG) provisions for the hospital and the physicians. In this study, we consider a class of affine gainsharing functions that calculate a physician’s per‐episode share based on both the aggregate performance across all physicians, and the cost and quality outcomes achieved by that physician. We show that when there are no sharing restrictions and no SLSG provisions, an optimal gainsharing function lies in the class of affine functions. In contrast, when there are SLSG constraints, the contract design problem is analytically challenging. Therefore, we perform a series of numerical experiments, which reveal that the hospital SLSG provisions, the maximum savings potential, and the hospital’s risk preferences determine the amount of gains and losses that the hospitals share and the resulting treatment levels. From the CMS perspective, we show that SLSG constraints matter more to hospitals with higher historical average billing and higher risk aversion.

Shall Follow-up Appointments Be Booked in Advance? Appointment systems are ubiquitous, especially in healthcare. By looking into a large data set with over 1.6 million appointments, we observe that many doctors booked a follow-up appointment at the end of their meeting with their patients. This strategy ensures that the patients would follow up but at the risk that the patient may not show up and the appointment ends being wasted. We develop a slotted-service queue model to study if and when such a strategy should be used in three representative appointment systems, respectively. In an open access system, it is optimal to never use this strategy. In a traditional appointment system that allows patients to book in advance, it is optimal to apply this strategy to some patients. While in a hybrid system with both walk-in patients and patients with appointments, whether to use this strategy depends on the load balancing between the two patient queues.