The Generalized Risk-Adjusted Cost-Effectiveness (GRACE) Model for Measuring the Value of Gains in Health: An Exact Formulation

The generalized risk-adjusted cost-effectiveness (GRACE) analysis method modifies standard cost-effectiveness analysis (CEA), the primary method currently used worldwide to value health improvements arising from healthcare interventions. Generalizing standard CEA, GRACE allows for decreasing or even increasing returns to health. Previous presentations of GRACE have relied extensively on Taylor Series expansion methods to specify key model parameters, including those that properly adjust for illness severity and preexisting disability, consequences of uncertain treatment outcomes, and the marginal rate of substitution between life expectancy and health-related quality of life. Standard CEA cannot account for these sources of value or cost in its valuation of medical treatments. However, calculations of GRACE measures based on Taylor Series are approximations, which may be poorly behaved in some contexts. This paper provides a new approach for implementing GRACE, using exact utility functions instead of Taylor Series approximations. While any proper utility function will suffice, we illustrate with three well-known functions: constant relative risk aversion (CRRA) utility; hyperbolic absolute risk aversion (HARA) utility, of which CRRA is a special case; and expo-power (EP) utility, of which constant absolute risk aversion (CARA) is a special case. The analysis then extends from two-period to multiperiod models. We discuss methods to estimate parameters of HARA and EP functions using two different types of data, one from discrete choice experiments and the other from “happiness economics” methods. We conclude with some reflections on how this analysis might affect benefit-cost analysis studies of healthcare interventions.