Break-Even Analysis

Break-Even Analysis for Prices, Treatment Effects and Service Volumes

Break-even analysis solves for the value of one variable at which a decision criterion is exactly zero. In health economics the variable is usually a price, a treatment effect or a volume of activity, and the criterion is incremental net benefit, incremental cost or financial surplus. The same arithmetic therefore answers different questions, namely the highest price at which a new technology stays cost-effective at a stated threshold, the price at which it adds nothing to expected spending, and the number of patients a service must treat before its income covers its costs. The NICE manual (PMG36) discusses the calculation under the names threshold analysis and switching value, and the concept is distinct from threshold analysis in general and from the break-even point.

Break-even prices and effects in cost-effectiveness analysis

Every break-even calculation varies one input, holds the others at their base-case values and finds the value of that input at which the decision criterion changes sign. In a cost-effectiveness analysis the criterion is incremental net monetary benefit at a stated threshold, so the break-even value is where the incremental cost-effectiveness ratio equals the threshold; in a cost-neutrality analysis the criterion is incremental cost alone. Price is the input most often solved for, because it enters the cost side of a model in a simple way.

When a new technology is compared with current care, the incremental cost can be split into the acquisition cost of the technology and every other cost difference, such as administration, monitoring and care avoided. The incremental net monetary benefit at a given price is then as follows.

$$INMB(p) = \lambda \Delta E - (u p + \Delta C_{0})$$

where $INMB(p)$ is the incremental net monetary benefit per patient at unit price $p$, $\lambda$ is the cost-effectiveness threshold in money per QALY, $\Delta E$ is the incremental health effect in QALYs, $u$ is the number of units used per patient and $\Delta C_{0}$ is the incremental cost excluding acquisition of the technology, which is negative when the technology avoids more cost than it adds. Setting this expression to zero and solving for $p$ gives the break-even price.

$$p^{*} = \frac{\lambda \Delta E - \Delta C_{0}}{u}$$

where $p^{*}$ is the highest unit price at which the technology is cost-effective at threshold $\lambda$. Setting the incremental cost alone to zero gives the cost-neutral price.

$$p_{0} = \frac{-\Delta C_{0}}{u}$$

where $p_{0}$ is the unit price at which the technology leaves expected cost per patient unchanged. The gap between the two, $\lambda \Delta E / u$, is the money value of the health gain per unit at the threshold, so for a technology that improves health the break-even price always lies above the cost-neutral price.

The same condition can be solved for the health effect.

$$\Delta E^{*} = \frac{\Delta C}{\lambda}$$

where $\Delta E^{*}$ is the break-even incremental effect and $\Delta C$ is the total incremental cost at the price assumed. Price usually enters a model linearly, so its break-even value follows exactly from the formula. Effect parameters such as hazard ratios or transition probabilities usually act through a non-linear model, so their break-even values are found by repeated model runs or a numerical search, as in a one-way sensitivity analysis. In every case the result is read against the plausible range of the input, and a break-even value far outside it means the conclusion does not depend on that input.

Worked example of break-even and cost-neutral prices for a new medicine

The figures below are illustrative. A new medicine given as one course per patient, so $u$ is 1, is compared with standard care over a lifetime horizon, with costs and QALYs discounted and all amounts in pounds per patient. The model estimates a gain of 0.40 QALYs. Apart from the medicine itself, the new pathway adds £2,000 in administration and monitoring and avoids £5,000 of hospital care, so $\Delta C_{0}$ is −£3,000. The proposed net price is £14,000 per course.

1. Calculate the base case. The incremental cost at the proposed net price is as follows.

$$\Delta C = 14000 - 3000 = 11000$$

where $\Delta C$ is the incremental cost. The ratio and the net benefit at an illustrative threshold of £25,000 per QALY follow.

$$ICER = \frac{11000}{0.40} = 27500$$

where $ICER$ is the cost per QALY gained, and

$$INMB = 25000 \times 0.40 - 11000 = -1000$$

where $INMB$ is the incremental net monetary benefit, so at the proposed price the medicine is not cost-effective at this threshold.

2. Solve for the break-even price. Subtracting a negative $\Delta C_{0}$ adds £3,000 to the value of the health gain. The calculation at £25,000 per QALY is shown below.

$$p^{*} = \frac{25000 \times 0.40 + 3000}{1} = 13000$$

where $p^{*}$ is the break-even price per course. At £35,000 per QALY the result is as follows.

$$p^{*} = \frac{35000 \times 0.40 + 3000}{1} = 17000$$

where only the threshold has changed. A reduction of £1,000, about 7% of the proposed price, makes the medicine cost-effective at the lower threshold, and the proposed price is already below the break-even price at the higher one.

3. Solve for the cost-neutral price and the break-even effect.

$$p_{0} = \frac{3000}{1} = 3000$$

where $p_{0}$ is the cost-neutral price per course. Only at £3,000 would the hospital care avoided fully offset the medicine. At the proposed price the figures are as follows.

$$\Delta E^{*} = \frac{11000}{25000} = 0.44$$

where $\Delta E^{*}$ is in QALYs. The gain would need to be 0.04 QALYs, or 10%, larger than the current estimate for the proposed price to be cost-effective at £25,000 per QALY.

4. Interpret the result. At the £13,000 break-even price, a year's cohort of 1,000 patients would add £10 million in discounted lifetime costs. A break-even price makes a technology acceptable at the threshold; it does not make it affordable, which is the question a budget impact analysis addresses.

How NICE PMG36 treats threshold analysis and switching values

Chapter 4 of the NICE manual for technology appraisal and highly specialised technologies (PMG36) discusses this calculation under the name threshold analysis. It defines a switching value as the value an input would need to take for the decision on whether a technology is a good use of NHS resources to change at a given threshold, giving £25,000 and £35,000 per QALY gained as examples. Its guidance applies directly to break-even prices and effects.

• Threshold analysis can be used to explore highly uncertain parameters when a switching value would inform decision makers, and the analysis should show how far the switching value is from the current best estimate of the parameter (section 4.7.22).
• It is not suitable for parameters that are highly correlated with other influential parameters, and it should not be used to justify restricting the population to a subgroup on cost-effectiveness grounds (section 4.7.23).
• If the parameter value at which a cost-effectiveness estimate reaches a threshold is implausible, the threshold analysis is still presented, alongside information on the plausible range for the parameter (section 4.6.29).
• Deterministic threshold analysis might inform decisions when parameters are influential but highly uncertain, although deterministic analysis is less appropriate for decision making when the model is non-linear (section 4.7.17).

The manual also asks for reference-case analyses to use the prices the NHS actually pays, including known price reductions such as patient access schemes (section 4.4.4). A break-even price is therefore compared with the net price available to the NHS, not with the list price.

Break-even prices in pricing, early assessment and budget planning

The break-even price is also used before and after appraisal, wherever a price has to be judged against the value of a technology. Its interpretation rests on what the threshold stands for, and in the arguments below it stands for the health displaced elsewhere in the system by new spending, the opportunity cost of that spending.

In the case for value-based pricing of NHS medicines, Claxton and colleagues showed that a price at which the ICER just equals the threshold leaves the NHS with zero net health benefit, because the health gained is offset by the health displaced elsewhere, so the benefit of the innovation goes to the manufacturer as revenue. A price below the break-even price shares that gain with the health system as net health benefit. Because expected gains differ between subgroups, so do break-even prices, and the same authors proposed allowing higher prices only when guidance restricts use to the more cost-effective subgroups.

In early health technology assessment the calculation is made while a technology is still in development, under the name headroom analysis. A 2023 systematic review described headroom analysis as quantifying the highest price at which an intervention may still be cost-effective. Of the 42 studies it identified, a third assumed perfect effectiveness, and 10% solved for the effect needed at a given price instead of the price allowed for a given effect.

In budget planning, a lifetime discounted cost-neutral price can still raise spending in the early years of a budget impact forecast, because acquisition costs are paid at once while avoided care accrues later, a timing question closer to the payback period.

The fixed and variable cost form for a health service

The older form of break-even analysis comes from management accounting, where it is part of cost-volume-profit analysis. It asks how much activity a service paid per unit of activity needs before its income covers its fixed and variable costs. The break-even volume and margin of safety are given below.

$$Q^{*} = \frac{F}{P - V}, \quad MS = \frac{Q_{e} - Q^{*}}{Q_{e}}$$

where $Q^{*}$ is the break-even volume, $F$ is the fixed cost for the period, $P$ is the price or tariff per unit, $V$ is the variable cost per unit, $P - V$ is the contribution per unit, $MS$ is the margin of safety and $Q_{e}$ is expected activity.

In an illustrative day unit paid £160 per attendance, with variable costs of £70 and fixed costs of £270,000 a year, the contribution is £90 and the break-even volume is $Q^{*} = 270000 / 90 = 3000$ attendances. With 3,600 attendances expected, the margin of safety is $MS = (3600 - 3000) / 3600 = 0.167$, about 17%, and the surplus is £54,000. If growth beyond a capacity of 4,000 needs a second team costing £120,000 a year, the unit only just covers its costs again at 4,334 attendances, and expansion beats staying at 4,000, with its £90,000 surplus, only above 5,333 attendances. Because costs step up in blocks like this, decisions about extra activity rest on marginal cost, not on an average cost that includes a share of fixed costs.

Choices that move a break-even value

A break-even value is conditional on every input held fixed while one is varied. A report should therefore state the choices that produced it.

The threshold acts directly on break-even prices, as the move from £13,000 to £17,000 in the example shows. The comparator matters because the break-even price is relative. Against a more effective comparator the incremental gain is smaller and the break-even price lower, and with several options the relevant comparison is with the next option on the efficient frontier. Time horizon and discounting matter because gains that arrive late are discounted more heavily than acquisition costs paid early. Holding other inputs at base-case values assumes they are independent of the one being varied, which is why the NICE manual warns against threshold analysis for highly correlated parameters.

Break-even analysis, threshold analysis and the break-even point

Several neighbouring terms describe parts of the same idea. The table sets out how they differ and which question each answers.

The break-even point is the result and break-even analysis is the method that produces it, so the two concepts are distinct.

Common misreadings of break-even results

Break-even results are simple to calculate and easy to misread. Most errors come from treating a boundary as a target or from forgetting what was held fixed.

A break-even price is the most a payer could pay without losing health overall, not a fair or target price, since at that price the net benefit to the health system is zero. A cost-effective price and a cost-neutral price are different figures, £10,000 apart in the example at £25,000 per QALY, so a technology priced at its break-even level still needs funding. A break-even value calculated from expected values says nothing about how likely the conclusion is to hold, which is the role of probabilistic sensitivity analysis; in a non-linear model it can also differ from the value that would make the probabilistic mean net benefit zero.

Sources

• Boudewijns EA, Otten TM, Gobianidze M, Ramaekers BL, van Schayck OCP, Joore MA. Headroom analysis for early economic evaluation: a systematic review. Applied Health Economics and Health Policy. 2023;21(2):195-204. https://doi.org/10.1007/s40258-022-00774-5
• Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford: Oxford University Press; 2006.
• Claxton K, Briggs A, Buxton MJ, Culyer AJ, McCabe C, Walker S, Sculpher MJ. Value based pricing for NHS drugs: an opportunity not to be missed? BMJ. 2008;336(7638):251-254. https://doi.org/10.1136/bmj.39434.500185.25
• Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford: Oxford University Press; 2015.
• Horngren CT, Datar SM, Rajan MV. Cost Accounting: A Managerial Emphasis. 15th ed. Boston: Pearson; 2015.
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). London: NICE; 2022, last updated 13 October 2026. Sections 4.4.4, 4.6.29, 4.7.17, 4.7.22 and 4.7.23.