Signature
R_j = abs(Y_jU - Y_jL)
| Inputs | Definition | Unit |
|---|---|---|
Y_jU | Model output with input j at its upper value and all other inputs at base case | the output unit |
Y_jL | Model output with input j at its lower value and all other inputs at base case | the output unit |
R_j | Width of the output range produced by moving input j between its lower and upper values | the output unit, for example £ per QALY or £ |
|---|
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.
Implementations
Excel
Swing of one input
Excel takes the absolute difference between the stored outputs of the two endpoint runs for one input.
=ABS(HighInputOutput-LowInputOutput)
Excel
Order inputs for the tornado diagram
In Excel 365, SORTBY returns the results table in descending order of swing, keeping each input's label, endpoints and outputs on the same row.
=SORTBY(OWSATable,SwingColumn,-1)
Assumptions
Other inputs held at base case
Each endpoint run changes only input j and the quantities calculated from it, and the base case is restored between runs, so every bar is traceable to two model runs.
Defensible ranges on the estimation scale
The lower and upper values come from the evidence, for example a 95% confidence interval on the scale on which the parameter was estimated. The ranking reflects range width as much as the model, and an arbitrary percentage range measures sensitivity but not uncertainty.
Endpoints recorded rather than inferred
The lower input value does not necessarily give the lower output, so both input endpoints and their outputs are stored with the swing.
Worked examples
Relative risk bar for the fictional drug Quintavel
In the illustrative Quintavel model, the relative risk of the event ranges from 0.45 to 0.80. The ICER is £16,364 per QALY at the lower value and £52,000 per QALY at the upper value, so the swing is £35,636, the widest bar. Quintavel is fictional and every figure is invented, matching the article's worked example.
Y_jL = 16364; Y_jU = 52000; R_j = 35636
Baseline risk bar in net monetary benefit
For the baseline event risk, ranging from 0.40 to 0.60, incremental net monetary benefit at £30,000 per QALY is minus £400 at the lower value and £6,400 at the upper value, a swing of £6,800. The lower endpoint changes the decision, which a marked threshold line on the diagram shows.
Y_jL = -400; Y_jU = 6400; R_j = 6800
Common errors
Treating one-way results as joint uncertainty
One-way analysis holds every other input fixed, so it ignores correlation and interaction and gives no probability of cost-effectiveness. In the Quintavel model, setting baseline risk and relative risk to their unfavourable endpoints together gives an ICER of £66,000 per QALY, which no single bar shows.
Reading bar width as precision of the estimate
A wide bar does not show that a parameter is poorly estimated, and a narrow bar does not show that it is known precisely, because the width combines the model's sensitivity with the chosen range.
Ranking ICER bars when effects approach zero
When incremental effects approach zero or change sign at an endpoint, the ICER becomes unstable or changes meaning, and its swing misranks inputs. Incremental net monetary benefit keeps a consistent meaning across endpoints.
Sources
ISPOR-SMDM report on deterministic sensitivity analysis
Briggs AH, Weinstein MC, Fenwick EAL, Karnon J, Sculpher MJ, Paltiel AD. Model parameter estimation and uncertainty analysis: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force Working Group-6. Medical Decision Making. 2012;32(5):722-732.
NICE manual on one-way analysis
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 4.7.17 (deterministic sensitivity analyses of individual parameters, with tornado diagrams as a presentation) and 4.7.21 (univariate analysis identifies key drivers but becomes less helpful for combined uncertainty as parameters increase).
Canonical Identity
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