The value of a health state is typically described relative to the value of an optimal state, specifically as a ratio ranging from unity (equal to optimal health) to negative infinity. Incorporating potentially infinite values is a challenging issue in the econometrics of health valuation.
In this paper, we apply a directional statistics approach based on the assumption of wavering preference. Unlike ratio statistics, directional statistics are based on polar coordinates (angle, radius). The range of angles is bounded between 45 degrees (unity) and negative 90 degrees (i.e., negative infinity); therefore, mean angles are well behaved and negate the impetus behind arbitrary data manipulations. Using time trade-off (TTO) responses from the seminal Measurement and Valuation of Health study, we estimate 243 EQ-5D health state values by minimizing circular variance with and without radial weights.
For states with published values greater than zero (i.e., better-than-death), the radially weighted estimates are nearly identical to the published values (Mean Absolute Difference 0.07; Lin's rho 0.94). For worse-than-death states, the estimates are substantially lower than the published values (Mean Absolute Difference 0.186; Lin's rho 0.576). For the worst EQ-5D state (33333), the published value is -0.59 and the directional estimate is -1.11.
By taking a directional statistics approach, we circumvent problems inherent to ratio statistics and the systematic bias introduced by arbitrary data manipulations. The predictions suggest that published estimates overvalue severe states. This paper examines TTO responses; however, it may be extended to all forms of health valuation.