  The distribution of health care payments to insurance plans has substantial
consequences for social policy. Risk adjustment formulas predict spending in
health insurance markets in order to provide fair benefits and health care
coverage for all enrollees, regardless of their health status. Unfortunately,
current risk adjustment formulas are known to underpredict spending for
specific groups of enrollees leading to undercompensated payments to health
insurers. This incentivizes insurers to design their plans such that
individuals in undercompensated groups will be less likely to enroll, impacting
access to health care for these groups. To improve risk adjustment formulas for
undercompensated groups, we expand on concepts from the statistics, computer
science, and health economics literature to develop new fair regression methods
for continuous outcomes by building fairness considerations directly into the
objective function. We additionally propose a novel measure of fairness while
asserting that a suite of metrics is necessary in order to evaluate risk
adjustment formulas more fully. Our data application using the IBM MarketScan
Research Databases and simulation studies demonstrate that these new fair
regression methods may lead to massive improvements in group fairness (e.g.,
98%) with only small reductions in overall fit (e.g., 4%).
