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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.

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.

One presentation is the cost-effectiveness plane, with $\Delta E$ horizontally and $\Delta C$ vertically. Plot the point estimate $(45,1800)$ with a joint confidence region or paired bootstrap cloud. Its position shows the tradeoff quadrant, while the cloud shows uncertainty, dependence and possible dominance. A willingness-to-pay threshold $\lambda$ is the line $\Delta C=\lambda \Delta E$ through the origin. Points below that line have positive incremental net monetary benefit, including points in quadrants where a ratio rule would fail. The point-estimated switch occurs at $\lambda =40$ pounds per day.

A second presentation is a cost-effectiveness acceptability curve, giving an uncertainty-based measure of cost-effectiveness for a range of thresholds. For paired bootstrap increments $(\Delta E^{\ast (b)},\Delta C^{\ast (b)})$, plotThis counts positive net benefits, not merely ratios below the threshold, so it handles all quadrants. Using Bayesian inference the curve is the posterior probability that incremental net monetary benefit is positive; a frequentist bootstrap curve is a resampling summary, not literally a probability that a fixed parameter is positive.

Here the estimated incremental net monetary benefit and its standard error areThus a normal approximation uncertainty curve isIt passes through one half at £40 per day. Alternatively display the incremental net monetary benefit curve itself with approximate pointwise $95\%$ bands $45\lambda -1800\pm 1.96s_{\mathrm{INMB}}(\lambda )$. The plane preserves the joint uncertainty; the acceptability curve shows how the threshold changes the cost-effectiveness assessment. Neither presentation chooses society's willingness-to-pay threshold.