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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.

The incremental cost-effectiveness ratio must be read with the signs of both increments. A negative ratio can mean either greater effectiveness at lower cost, which is favorable, or lower effectiveness at greater cost, which is unfavorable. A positive ratio can likewise lie in either the more-costly/more-effective or cheaper/less-effective quadrant. Thus ordering ratio values without locating the cost-effectiveness plane quadrant can reverse a decision.

The incremental cost-effectiveness ratio is undefined at a zero effect increment and extremely unstable near it. Its sampling distribution can be highly skewed and its mean may fail to exist; a usual symmetric confidence interval or an interval spanning positive and negative ratios can conceal that instability. Cost-effect correlation must be retained, as the Fieller confidence set calculation illustrates.

Interpretation also requires a specified comparator, effect unit, costing perspective, follow-up horizon and willingness-to-pay threshold. Different comparator choices give different incremental ratios, and lower ratios alone do not settle decisions across differently scaled outcomes. Longer survival need not mean a proportional quality-of-life gain; extrapolation, censored outcomes and omitted costs can affect the increments. Point estimates conceal both sampling uncertainty and uncertainty in these assumptions.

For a positive effect increment, comparison with a threshold $\lambda$ is equivalent to $\Delta C/\Delta E<\lambda$. For negative effect increments that inequality reverses when multiplied by $\Delta E$, so a rule that blindly compares all ratios with $\lambda$ is wrong. Use the signs and joint cost/effect uncertainty, or the incremental net monetary benefit $\lambda \Delta E-\Delta C$, rather than the ratio alone. No particular threshold is given in the paper, so the point estimate does not establish whether reimbursement should occur.

Let $\Delta C$ and $\Delta E$ be the new-minus-standard mean cost and survival increments. The incremental cost-effectiveness ratio isUsing $365$ days per year, this is £14,600 per additional life-year. It is not cost per quality-adjusted life-year because no quality-of-life adjustment is supplied. Both point-estimated increments are positive, so the new intervention exchanges higher cost for longer survival; this is not dominance.