Signature
p_star = (lambda * Delta_E - Delta_C_0) / u; p_0 = -Delta_C_0 / u
| Inputs | Definition | Unit |
|---|---|---|
lambda | Cost-effectiveness threshold, the value placed on one QALY | money per QALY |
Delta_E | Incremental health effect per patient against the comparator, discounted over the model horizon | QALYs per patient |
Delta_C_0 | Incremental cost per patient other than acquisition of the technology, such as administration, monitoring and care avoided, discounted; negative when cost avoided exceeds cost added | money per patient |
u | Number of units of the technology used per patient over the horizon | units per patient, above zero |
p_star | Highest price per unit at which incremental net monetary benefit is not negative at threshold lambda | money per unit of the technology |
|---|---|---|
p_0 | Price per unit at which the technology leaves expected cost per patient unchanged | money per unit of the technology |
Function
Break-even price, cost-neutral price and service volume function
Solves for the value of one input at which a decision criterion is exactly zero, holding every other input at its base-case value. For a new health technology the input is the unit price and the criterion is incremental net monetary benefit at a stated threshold (the break-even price) or incremental cost alone (the cost-neutral price). For a service paid per unit of activity the input is volume and the criterion is the surplus of income over fixed and variable costs (the break-even volume). The records follow the notation of the Break-Even Analysis article. NICE's manual (PMG36) calls the general calculation threshold analysis and its result a switching value; the switching value of a non-linear input by interpolation is HE-FM-OWSA-002, and the payer's maximum price per patient in price negotiation is HE-FM-BARG-002.
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Implementations
Excel
Break-even unit price from named threshold, effect and cost cells
Excel subtracts the named cell holding the incremental cost other than acquisition from the threshold multiplied by the incremental QALYs, and divides by the named cell holding the units per patient.
=(Threshold*DeltaE-DeltaCOther)/UnitsPerPatient
Excel
Cost-neutral unit price from named cost and unit cells
Excel reverses the sign of the named cell holding the incremental cost other than acquisition and divides by the units per patient.
=-DeltaCOther/UnitsPerPatient
Assumptions
Price enters the incremental cost linearly
The incremental cost per patient is u times the unit price plus Delta_C_0, and neither Delta_E nor Delta_C_0 depends on the price. Inputs that act through a non-linear model, such as hazard ratios, need repeated model runs or a numerical search.
Other inputs held at their base-case values
Every other input stays at its base case while the price varies. PMG36 (section 4.7.23) states that threshold analysis is not suitable for parameters highly correlated with other influential parameters, and should not be used to justify restricting the population to a subgroup on cost-effectiveness grounds.
Break-even price compared with the net price paid by the NHS
The result is compared with the price the NHS would actually pay, including known price reductions such as patient access schemes, which PMG36 (section 4.4.4) requires in reference-case analyses, not with the list price.
Worked examples
Break-even and cost-neutral prices of one course at 25,000 pounds per QALY
In the article's illustrative medicine, one course per patient gains 0.40 QALYs, and the rest of the pathway adds £2,000 and avoids £5,000, so Delta_C_0 is -£3,000. At £25,000 per QALY the break-even price is £13,000 per course, against a proposed net price of £14,000, and the cost-neutral price is £3,000.
lambda = 25000; Delta_E = 0.4; Delta_C_0 = -3000; u = 1; p_star = 13000; p_0 = 3000
Break-even price of the same course at 35,000 pounds per QALY
At £35,000 per QALY the break-even price of the same course rises to £17,000, so the proposed net price of £14,000 is already below it; only the threshold has changed.
lambda = 35000; Delta_E = 0.4; Delta_C_0 = -3000; u = 1; p_star = 17000; p_0 = 3000
Break-even price per pack when the course is 12 monthly packs
If the same course were supplied as 12 monthly packs, the break-even price at £25,000 per QALY would be about £1,083.33 per pack and the cost-neutral price £250 per pack (computed here for illustration).
lambda = 25000; Delta_E = 0.4; Delta_C_0 = -3000; u = 12; p_star = 1083.33; p_0 = 250
Common errors
Leaving cost offsets out of the break-even price
Setting the break-even price to the threshold times the QALY gain alone gives £10,000 per course in the article's example instead of £13,000, because the £3,000 of net care avoided is left out; adding the negative Delta_C_0 instead of subtracting it gives £7,000 (computed here for illustration).
Reading the break-even price as a fair or target price
At the break-even price the health gained is just offset by the health displaced elsewhere, so the net health benefit to the health system is zero and, as Claxton and colleagues argue, the benefit of the innovation goes to the manufacturer as revenue. A price below it shares that benefit with the health system.
Treating a cost-effective price as a cost-neutral price
At £25,000 per QALY the break-even price of £13,000 is £10,000 above the cost-neutral price of £3,000, so a technology priced at its break-even level still adds cost: £10 million in discounted lifetime costs for a cohort of 1,000 patients in the article's example. Whether that can be afforded is a budget impact question.
Comparing the break-even price with the list price
PMG36 bases reference-case analyses on the prices paid in the NHS, including patient access schemes, so a list price above the break-even price does not show that the net price is too high.
Sources
Price at which the ICER equals the threshold in value-based pricing
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. Discussion of figure 1: negotiating a price at which the ICER just equals the threshold ensures that the health benefits of the drug are just offset by the health displaced elsewhere in the NHS, so all the benefits of the innovation go to the manufacturer; with lower prices or restricted guidance the NHS shares the benefits.
NICE switching values and threshold analysis
National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). London: NICE; published 31 January 2022, last updated 31 March 2026. Section 4.7.22: a switching value is the value an input would need to take for the decision at a given threshold, for example £25,000 and £35,000 per QALY gained, to change; section 4.7.23: limits of threshold analysis; section 4.4.4: prices that reflect those paid in the NHS, including patient access schemes.
Headroom analysis as the highest cost-effective price
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. Abstract: headroom analysis quantifies the highest price at which an intervention may still be cost effective; of 42 studies, 10% calculated an effectiveness-seeking headroom instead of a cost-seeking one.
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