Signature
theta_jS = theta_jL - INMB_jL * (theta_jU - theta_jL) / (INMB_jU - INMB_jL)
| Inputs | Definition | Unit |
|---|---|---|
theta_jL | Lower endpoint of the range tested for input j | the unit of input j |
INMB_jL | Incremental net monetary benefit at the stated threshold with input j at its lower value | currency per person |
theta_jU | Upper endpoint of the range tested for input j | the unit of input j |
INMB_jU | Incremental net monetary benefit at the stated threshold with input j at its upper value | currency per person |
theta_jS | Value of input j at which incremental net monetary benefit is zero and the preferred option changes | the unit of input j |
|---|
Function
One-way sensitivity function
Maps a model output to its value when a single input j is set to a stated value while every other input stays at its base-case value. Running it at the input's lower and upper values gives the endpoints of one bar in a tornado diagram.
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Implementations
Excel
Switching value from two endpoint runs
Excel interpolates the input value at which incremental net monetary benefit is zero from the stored endpoint results in named cells.
=LowValue-LowINMB*(HighValue-LowValue)/(HighINMB-LowINMB)
Assumptions
Net benefit linear in the input
Incremental net monetary benefit is linear in input j between and beyond the endpoints. In the Quintavel model this holds for the relative risk, baseline risk, acquisition cost and QALY loss per event; otherwise the value is found with a root finder or a fine grid, and the method is reported.
Distinct endpoint results
INMB_jU differs from INMB_jL. When both have the same sign, the switching value lies outside the tested range and is reported as such.
Input not tied to other influential inputs
The analysis moves one input with the others at base case, so it is not used for parameters that are highly correlated with other influential parameters.
Worked examples
Switching relative risk for Quintavel
At £30,000 per QALY, incremental net monetary benefit is £9,375 at a relative risk of 0.45 and minus £5,500 at 0.80. Interpolation gives a switching relative risk of about 0.6706, inside the tested range. Because net benefit is linear in the relative risk, this equals the analytic switching value of about 0.671 in the article.
theta_jL = 0.45; theta_jU = 0.80; INMB_jL = 9375; INMB_jU = -5500; theta_jS = 0.6706
Switching acquisition cost outside the range
Incremental net monetary benefit is £5,000 at an acquisition cost of £11,000 and £1,000 at £15,000. The switching value is £16,000, outside the tested range, so no tested price changes the decision. The result is exact because net benefit falls by £1 for every £1 of price.
theta_jL = 11000; theta_jU = 15000; INMB_jL = 5000; INMB_jU = 1000; theta_jS = 16000
Common errors
Interpolating the ICER instead of net benefit
The ICER is not linear in the relative risk. Interpolating the Quintavel ICERs of £16,364 and £52,000 to £30,000 per QALY gives a relative risk of about 0.584, while the correct switching value is about 0.671.
Using a switching value for a correlated input
A switching value found with correlated inputs held fixed describes a combination of values that may be implausible, and it cannot justify restricting the population to a subgroup on cost-effectiveness grounds.
Sources
NICE manual on switching values
National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 31 March 2026. Chapter 4 Economic evaluation, sections 4.7.22 (a switching value is the value an input would need to take for the decision at a given threshold to change, with its distance from the current best estimate) and 4.7.23 (not suitable for parameters highly correlated with other influential parameters, or to justify restricting the population to a subgroup).
Decision modelling textbook on threshold analysis
Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford: Oxford University Press; 2006.
Canonical Identity
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