A COMPARISON OF JOINT STATE UTILITY ESTIMATORS USING STANDARD GAMBLES FOR SUBSTANCE USE DISORDER STATES

Background: Co-occurring conditions are common with substance use disorders. Economic evaluation of treatments requires estimation of health state utilities to calculate Quality Adjusted Life Years, the outcome measure used in cost-utility analysis. Methods for estimation of single state utilities are well-defined, however estimation methods for joint states—needed for co-occurring conditions—are less-developed, and existing estimators have not been tested in the substance use disorder context.

Objective: To compare health state utility estimators’ precision in the context of standard gamble (SG) utilities for substance use disorders.  

Methods: We collected SG utilities for single and joint substance use-relevant health states through an internet survey of 2 samples of adults in the US. Respondents evaluated a random subset of 6 single and 4 joint states: injection opioid use, prescription opioid misuse, cocaine use, injection crack use, back pain, depression, cocaine and prescription opioid misuse, injection crack and opioid use, back pain and prescription opioid misuse, and depression and injection opioid use. We calculated predicted utility using joint health state estimators described in the literature and one hypothesized to be useful in this context: additive, multiplicative, minimum, linear index, adjusted decrement, and maximum, respectively. We used 1,000 bootstrap iterations to estimate the bias (and 95% CI) and root mean square error (RMSE) for the predicted utilities for the joint states.

Results: We analyzed 3,892 utilities collected from 1,502 respondents (56% completion rate). Comparing the observed joint and single state utilities, the joint utility was lower than both single state utilities for the cocaine/prescription opioid state; higher than both for the injection crack/opioid use state and the back pain/prescription opioid state; and between the two for the depression/injection opioid state. The minimum estimator was the only one that was unbiased for all 4 joint health states. The smallest RMSE was for the maximum estimator for 2 states (back pain/prescription opioid and injection crack/opioid, 0.0004 and 0.0007, respectively); for the linear index estimator for 1 state (cocaine/prescription opioid, 0.0004); and for the minimum estimator for 1 state (depression/injection opioid, 0.002). The second smallest RMSE for 3 states was the minimum, and for 1 it was the linear index. The additive and multiplicative estimators had the highest RMSEs for all states.

Conclusions: The minimum estimator is a reasonable first choice estimator for substance misuse-related joint utilities because of its consistent lack of bias, although it may not be optimal for every state; the maximum and linear index estimators should be considered among the options. Our data confirm others’ findings that the additive and multiplicative estimators are highly biased. Further research is needed on whether these results are unique to substance use disorders or to low-utility single states, and on estimators for more than 2 co-occurring states.