Utilities should not be multiplied: evidence from the preference-based scores in the United States

Several estimators exist when average utility scores are not available for patient populations with multiple disease conditions. The multiplicative estimator is a widespread choice among them. Our study is to empirically test the accuracy of the multiplicative estimator and compare it with other estimators.

The Medical Expenditure Panel Survey (MEPS) has a nationally representative sample of the US civilian noninstitutionalized population. Using the pooled 2001 and 2003 data, a sample of 40,846 individuals with EQ-5D index scores were categorized into 238 disease condition categories. The study focus was the difference between the estimated and the observed mean scores for each comorbid pair, with the observed one presumed to be the true value.

The scores estimated by multiplying the 2 mean scores of the corresponding disease conditions on average had a statistically significantly larger difference (P < 0.0001) from the observed ones (-0.094) than simply picking the smaller mean of the 2 paired conditions (difference = 0.025), the larger mean of the 2 (difference = 0.071), the average of the 2 means (difference = 0.048), or the mean of the condition with smaller sample size of the pair (difference = 0.049). However, the multiplicative estimator performed better than the additive estimator (sum of the means minus 1, difference = -0.123).

Multiplication is not a good estimate when the average utility score for patients with 2 disease conditions is not readily available. The lower of the 2 utility scores had the least error among those estimators that we compared. Further research with an experimental design is warranted before a specific alternative can be firmly recommended.