Estimating CE ratios under second-order uncertainty: the mean ratio versus the ratio of means

Two methods have been presented for estimating cost-effectiveness ratios under conditions of second-order (model) uncertainty: one method estimates a mean ratio of cost to effect (the "mean ratio" approach), and the other estimates a ratio of mean cost to mean effect (the "ratio of means" approach). However, the question of which estimate is theoretically correct has not been formally addressed. The authors show that the "ratio of means" approach follows directly from the theoretical foundations of cost-effectiveness analysis, has attractive internal consistency properties, and is consistent with a simple vector algebra approach to the problem. In contrast, the "mean ratio" approach has not been shown to follow from first principles, is internally inconsistent, and can prescribe economically inefficient choices. It is concluded that the "ratio of means" procedure should be preferred unless persuasive arguments are presented to the contrary.