Purpose: To develop and validate a simple predictive model that combines the trade-offs (1- utility) accepted by individual patients for two single health states in order to predict their expected trade-off when the health states occur jointly. Predicting utilities for joint health states is an important issue for cost-effectiveness analysis especially in elderly patients where such joint-states are common.

Methods: Our model encompasses all traditional models – additive, multiplicative, and minimum - used for predicting utilities for joint health states. The parameters of this model are specified to be generic for any joint health states, thereby increasing generalizability. They are estimated using individual level time-trade-off utilities for the following joint states: impotence and watchful waiting, impotence and incontinence, and impotence and post-prostatectomy, and the corresponding single health states. Subjects were patients referred for prostate biopsy due to elevated risk of having prostate cancer. We use the method of non-linear least squares for estimation and an iterated, bootstrapped split-sample approach for validation.

Results: Based on the estimates of our encompassing model all the traditional models are rejected at the 5% level. The new model puts more weight on the accepted trade-off for the more severe health state. Additionally, it calculates a correction factor that represents the overlap in preferences when two health states occur jointly. We propose a simple linear index based on the estimates of our encompassing model. Based on out-of-sample predictions, this new simple model produces 17 – 35% reduction in MSE compared to traditional models and, more importantly, consistent prediction across the distribution of joint state utilities, which the traditional models do not.

Conclusion: Direct elicitation of utilities for all joint health states may pose substantial interview burden. Our previous work has shown that traditional models used to predict these joint-state utilities based on single-state utilities are inconsistent, at least in the context of prostate cancer. The new model proposed here provides direct evidence on the inconsistency of these traditional models. Additionally, it has a theoretical basis in prospect theory by emphasizing the more severe component of a joint health state, and provides a simple linear index to generate consistent predictions of utilities for joint health states. Further validation of this function in other joint health states in other diseases is warranted.