A linear index for predicting joint health-states utilities from single health-states utilities

Direct elicitation of utilities for joint health (JS) states may pose substantial interview burden, while traditional models to predict these utilities from utilities of component single states (SS) are inconsistent with the data. Using individual-level data on utilities for health states associated with prostate cancer, we report the performance of a new model that encompasses three traditional models - additive, multiplicative, and minimum - previously used for predicting utilities for joint health states. Describing utilities in terms of utility losses l(.) relative to prefect health, our final estimated linear index for predicting joint health-state utilities is El(JS)=0.05+0.72 x max l(SS1),l(SS2)+0.33.min x l(SS1),l(SS2)-0.18 x l(SS1) x l(SS2). Based on out-of-sample predictions, this model produces up to 50% reduction in mean-square error compared with traditional models and consistent prediction across different ranges of joint-state utilities, which the traditional models do not. Parameter estimates of the new model proposed here provide direct evidence on the inconsistencies of the traditional models, are grounded in psychological theory by emphasizing the more severe component of a joint health state, and provide a simple linear index to generate consistent predictions of utilities for joint health states. Further validation of this function for joint health states in other clinical scenarios is warranted.