It might be premature to reject the assumption of a power curve relationship between VAS and SG data: three comments on Stevens, McCabe and Brazier's ‘Mapping between VAS and SG data; results from the UK HUI Index 2 valuation survey’

Abstract

In a recent paper in Health Economics, Stevens, McCabe and Brazier (Health Econ. 2006; 15: 527-533.) found that the cubic relationship between Visual Analog Scale (VAS) values and standard gamble (SG) utilities was superior to other functional forms in terms of explanatory power and predictive ability. Consequently, they question the reliance on the assumption of a power curve relationship, which was established, theoretically and empirically, in earlier works. This note argues that: (1) SMB's conclusions are incorrect. The estimated cubic function overfits the four data points, and is questionable with respect to the implied attitude toward relative risk. (2) The evaluation of the functional forms in terms of the individual predictions' mean absolute error is misleading and (3) correcting for heteroscedasticity improves the precision of the estimates and of the predictions.