A Multi-linear Multi-Attribute Utility Function for the Health Utilities Index Mark 3 System
- Presenter:
Chair: Albert Okunade; Discussant: Albert Okunade Wed June 7, 2006 9:45-11:15 Room 225
Rationale and Objectives. Estimated multi-attribute utility functions have relied on linear additive or multiplicative functional forms that assume respectively a lack of preference interactions among attributes or only one type of preference interaction. Are there quantitatively important and statistically significant interactions in preferences among attributes in the Health Utilities Index Mark 3 (HUI3) system? How would the performance of the less restrictive multi-linear model compare to the performance of the multiplicative model?
Methodology. HUI3 has 8 attributes, vision, hearing, speech, ambulation, dexterity, emotion, cognition, and pain, with 5 or 6 levels per attribute. A preference survey was conducted of a random sample of the general population (n = 256) using a one-half 2 to the eight power fractional factorial design plan. The same survey provided scores for the estimation of a multiplicative multi-attribute utility function. A parallel survey (n = 248) provided directly measured standard gamble utility scores for 73 HUI3 health states. The fractional factorial design permits the identification of all 8 main effects, 26 of 28 two-way interactions, and 4 of 56 three-way interactions terms. The estimated equation was forced to pass through 0 (for the health state with all attributes at lowest functional level) and 1 (all attributes at highest level). Agreement between directly measured scores from the second sample and scores from the multi-linear and multiplicative utility functions was assessed using an intra-class correlation coefficient.
Results. For the multi-linear model, the adjusted R-squared was 0.63. All 8 main effects were quantitatively important (coefficient >0.024) and statistically significant (p < 0.10). Two-way interaction terms indicating preference complementarity were quantitatively important and statistically significant in 18 cases and insignificant in 2 cases. Two-way interaction terms indicating preference substitutes were important and significant in 4 cases and insignificant in 2 cases. All 4 three-way interaction terms were important and significant. Agreement between directly measured scores and scores from the multiplicative function was much higher than agreement between directly measured scores and scores from the multi-linear function.
Conclusions. There are quantitatively important and statistically significant interactions in preferences among attributes of health status. These results call into question the use of linear additive multi-attribute utility functions. The multiplicative function out performed the multi-linear function in out-of-sample prediction. The omnibus interaction term of the multiplicative function indicates preference complementarity and appears to handle the preference interactions more than adequately.
