The variance of length of stay and the optimal DRG outlier payments.

Prospective payment schemes in health care often include supply-side insurance for cost outliers. In hospital reimbursement, prospective payments for patient discharges, based on their classification into diagnosis related group (DRGs), are complemented by outlier payments for long stay patients. The outlier scheme fixes the length of stay (LOS) threshold, constraining the profit risk of the hospitals. In most DRG systems, this threshold increases with the standard deviation of the LOS distribution. The present paper addresses the adequacy of this DRG outlier threshold rule for risk-averse hospitals with preferences depending on the expected value and the variance of profits. It first shows that the optimal threshold solves the hospital's tradeoff between higher profit risk and lower premium loading payments. It then demonstrates for normally distributed truncated LOS that the optimal outlier threshold indeed decreases with an increase in the standard deviation.