This is a short paper my doctoral student Tengjiao Xiao and I recently completed.
Here is the abstract: "Risk adjustment is used to calibrate payments to health plans based on the relative health status of insured populations and helps keep the health insurance market competitive. Current risk adjustment models use parameter estimates obtained via regression and are thus subject to estimation error. This paper discusses the impact of parameter uncertainty on risk scoring, and presents an approach to create robust risk scores to incorporate ambiguity and uncertainty in the risk adjustment model. This approach is highly tractable since it involves solving a series of linear programming problems."
The paper also contains, in the section where we motivate the need for robustness, the graph about ranking changes using proxy and actual Value-Based Purchasing factors that are used to give the about 3,000 hospitals considered bonuses or penalties. A negative ranking change indicates a loss in ranks and a positive one indicates a gain. The interesting thing about this graph is that losses and gains can fluctuate enormously, meaning that some hospitals that would have stood to receive very high bonuses (for the amounts of money considered: every hospital contributes 1% to fund the scheme) under proxy factors found themselves at the very bottom of the ranking, and vice-versa. To the best of our knowledge, this is not something that has received much if any attention in the media.
The core of the short paper is to show how robust risk scores can be computed by solving a series of linear programming problems, with the aim of minimizing worst-case regret between the actual risk scores, used to implement transfer payments between health payers, and the true scores, which we don't know. We show on a simple test case with 10 insurers that the change in payments can be substantial.