A comparison of direct and indirect methods for the estimation of health utilities from clinical outcomes

Background: Analysts often need to estimate health state utility values as a function of other outcome measures. Utility values like EQ-5D have several unusual characteristics that make standard statistical methods inappropriate. We have developed a bespoke approach based on mixture models to directly estimate EQ-5D. An indirect method, “response mapping”, first estimates the level on each of the five dimensions of the EQ-5D descriptive system and then calculates the expected tariff score. These methods have never previously been compared.

Methods: We use a large observational database of patients diagnosed with Rheumatoid Arthritis (n=100,398 observations). Direct estimation of UK EQ-5D scores as a function of Health Assessment Questionnaire (HAQ), pain and age was performed using a limited dependent variable mixture model. Indirect modelling was undertaken using a set of generalized ordered probit models with expected tariff scores calculated mathematically. Linear regression was reported for comparison purposes.

Results: The linear model fits poorly, particularly at the extremes of the distribution. Both the bespoke mixture model and the generalized ordered probit approach offer improvements in fit over the entire range of EQ-5D. Mean average error is 10% and 5% lower compared to the linear model respectively. Root mean squared error is 3% and 2% lower. The mixture model demonstrates superior performance to the indirect method across almost the entire range of pain and HAQ.

Limitations: There is limited data from patients in the most extreme HAQ health states.

Conclusions: Modelling of EQ-5D from clinical measures is best performed directly using the bespoke mixture model. This substantially outperforms the indirect method in this example. Linear models are inappropriate, suffer from systematic bias and generate values outside the feasible range.