Pay for performance in health care: a new best practice tariff-based tool using a log-linear piecewise frontier function and a dual-primal approach for unique solutions

Health care systems worldwide have faced a problem of resources scarcity that, in turn, should be allocated to the health care providers according to the corresponding population needs. Such an allocation should be as much as effective and efficient as possible to guarantee the sustainability of those systems. One alternative to reach that goal is through (prospective) payments due to the providers for their clinical procedures. The way that such payments are computed is frequently unknown and arguably far from being optimal. For instance, in Portugal, public hospitals are clustered based on criteria related to size, consumed resources, and volume of medical acts, and payments associated with the inpatient services are equal to the smallest unitary cost within each cluster. First, there is no reason to impose a single benchmark for each inefficient hospital. Second, this approach disregards dimensions like quality (and access) and the environment, which are paramount for fair comparisons and benchmarking exercises. This paper proposes an innovative tool to achieve best-practices tariff. This tool merges both quality and financial sustainability concepts, attributing a hospital-specific tariff that can be different from hospital to hospital. That payment results from the combination of costs related to a set of potential benchmarks, keeping quality as high as possible and higher than a user-predefined threshold, and being able to generate considerable cost savings. To obtain those coefficients we propose and detail a log-linear piecewise frontier function as well as a dual-primal approach for unique solutions.