Cost-effectiveness analysis

Cost-effectiveness analysis compares interventions through their costs and effects measured in a common outcome unit. Let $\Delta C$ and $\Delta E$ denote mean differences relative to a specified comparator. A positive effect increment with nonpositive cost increment gives dominance; the reverse signs give a dominated intervention. A tradeoff in the positive-positive quadrant requires a willingness-to-pay threshold per outcome unit. Randomized controlled trials can estimate these differences, but their joint sampling distribution is needed to express uncertainty. Outcome units, time horizon and costing perspective must be specified; a survival-day increment is not automatically a quality-adjusted outcome.

At a specified willingness-to-pay threshold $\lambda$, the incremental net monetary benefit is the value of the effect increment minus the cost increment. It avoids dividing by a potentially near-zero or negative effect estimate. For estimates with variances $v_E,v_C$ and covariance $v_{CE}$, its estimated variance is ${\lambda }^2{v}_E+v_C-2\lambda v_{CE}$. A normal approximation therefore gives a confidence interval directly on the net-benefit scale. The economic sign criterion does not require a positive effect increment.

A cost-effectiveness acceptability curve displays the probability of positive incremental net monetary benefit as a function of the willingness-to-pay threshold. Under a posterior distribution this is a posterior probability. A frequentist paired bootstrap version displays the fraction of replicates for which the net benefit is positive, a resampling measure of uncertainty rather than literally a probability that a fixed true parameter is positive. Using the sign of net benefit handles all quadrants of the cost-effectiveness plane; counting only replicates whose ratio is below the threshold does not.

The cost-effectiveness plane plots an effect increment horizontally and a cost increment vertically. The southeast quadrant represents greater effectiveness at lower cost, while the northwest quadrant represents lower effectiveness at greater cost. A threshold $\lambda$ corresponds to the line $\Delta C=\lambda \Delta E$; points below the line have positive incremental net monetary benefit, in every quadrant. A joint confidence region or paired bootstrap cloud reveals uncertainty and preserves the dependence between cost and effect estimates.

The incremental cost-effectiveness ratio divides an intervention's additional mean cost by its additional mean effect relative to a comparator. Its units are cost per outcome unit. When both increments are positive, comparison with a threshold $\lambda$ is equivalent to checking whether the incremental net monetary benefit $\lambda \Delta E-\Delta C$ is positive. When $\Delta E<0$ the inequality reverses on division, and when $\Delta E=0$ the ratio is undefined. A ratio alone cannot identify the quadrant of the cost-effectiveness plane.