Three methods tested to model SF-6D health utilities for health states involving comorbidity/co-occurring conditions

Abstract

Objectives: Compare three commonly used methods to combine the impacts of multiple health conditions on SF-6D health utility scores.

Study design and setting: We used data from the 1998-2004 Medicare Health Outcomes Survey to compare three commonly suggested models of multiple health conditions' impacts on health-related quality of life: additive, minimum, and multiplicative. We modeled SF-6D scores using information about 15 health conditions, both unadjusted and adjusted for age, sex, education, and income. Model performance was assessed using mean squared error, mean predictive error by number of health conditions, and mean predictive error for groups with specific combinations of health conditions.

Results: Ninety-five thousand one hundred ninety-five observations were used for model estimation, and 94,794 observations were used for model testing. The adjusted models always had better performance than the unadjusted models. The multiplicative model showed smaller mean predictive error than the other models in both those younger than 65 years and those 65 years and older. Mean predictive error for the multiplicative model was generally within the minimally important difference of the SF-6D.

Conclusion: All tested models are imperfect in these Medicare data, but the multiplicative model performed best.

Figure 1. Distribution of observed SF-6D health utility scores

The theoretical maximum and minimum SF-6D scores are 1.0 and 0.30. The under-65 group, which primary includes individuals with disabilities, reports lower SF-6D scores than the 65-and-older group.

Figure 2. Mean predictive error and mean squared error for each of the three methods in the 65-and-older group

The model using the multiplicative method has the smallest mean predictive error as well as the smallest mean squared error by number of health conditions. The model using the minimum method has the most error.

Figure 3. Mean predictive error for specific combinations of conditions with 50 or more observations. Mean predictive error was calculated for each of the three methods in the 65-and-older group

This figure represents the difference between the mean of actual SF-6D scores and the mean of predicted SF-6D scores for groups with a specific combination of 1 to 5 health conditions. For example, one of the points in the 2 Conditions panel represents those reporting arthritis of the hip or knee and problems hearing and no other conditions. “n” is the number of such groups within a panel. The lowest boundary of the box indicates the 25th percentile, a line within the box marks the median, and the highest boundary of the box indicates the 75th percentile. Whiskers (error bars) above and below the box indicate the 90th and 10th percentiles. Any outlying points are also illustrated. The error in mean estimates for the models using the additive and multiplicative methods is centered around zero and the spread is smaller than the model using the minimum method.