Concept Architecture
Concept
Theoretically, Tornado Diagram is a graphical method used to present the results of deterministic sensitivity analysis by ranking uncertain model parameters according to their influence on a selected model outcome. The diagram provides a visual summary of parameter importance and enables rapid identification of the variables that contribute most to decision uncertainty. In health economics, tornado diagrams are routinely used to communicate the results of one-way sensitivity analyses in economic evaluations and health technology assessments.
Mathematically, a tornado diagram is constructed by calculating the change in a model outcome resulting from varying each parameter individually across a predefined range while holding all other parameters constant. Parameters are ranked according to the magnitude of the resulting change, typically measured as the difference between the upper and lower model outcomes. The graphical representation itself does not introduce additional mathematical modelling but summarises the results of deterministic sensitivity analysis.
In practice, tornado diagrams are produced after performing one-way sensitivity analyses using plausible parameter ranges derived from confidence intervals, standard errors, published evidence or expert judgement. The longest horizontal bars identify the parameters exerting the greatest influence on costs, QALYs, net monetary benefit or incremental cost-effectiveness ratios, thereby helping analysts prioritise further research and communicate model uncertainty.
Purpose
Used to rank uncertain parameters according to their influence on model outcomes and provide a clear visual summary of deterministic sensitivity analysis in health economic evaluations.
Mathematical Formulae
Primary Formula
There is no universally recognised canonical mathematical formula.
Supporting Formulae
Parameter impact:
?Y? = Y?,high ? Y?,low
Absolute impact:
|?Y?| = |Y?,high ? Y?,low|
Ranking criterion:
|?Y?| � |?Y?| � ? � |?Y?|
Related Mathematical Methods
- One-Way Sensitivity Analysis
- Deterministic Sensitivity Analysis
- Threshold Analysis
- Scenario Analysis
- Sensitivity Analysis
Example
A one-way sensitivity analysis varies treatment cost, treatment efficacy, utility values and discount rate individually. Treatment cost changes the ICER by �9,400 per QALY, treatment efficacy by �6,100 per QALY, utility values by �2,300 per QALY and discount rate by �900 per QALY. The tornado diagram ranks these parameters from largest to smallest impact, demonstrating that treatment cost is the principal driver of model uncertainty.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| ABS | =ABS(C2-B2) | Calculate the absolute change in the model outcome for each parameter. |
| SORT | =SORT(A2:D20,4,-1) | Rank parameters by magnitude of impact before plotting the tornado diagram. |
| MAX | =MAX(B2:C2) | Determine the upper value of each sensitivity range. |
| MIN | =MIN(B2:C2) | Determine the lower value of each sensitivity range. |
| BAR CHART | Insert ? Bar Chart | Produce the tornado diagram using ranked parameter ranges. |
VBA (Optional)
VBA can automate one-way sensitivity analyses, rank parameter impacts and generate formatted tornado diagrams directly from model outputs.
Sources
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
- 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. Medical Decision Making. 2012;32(5):722?732.
- NICE. NICE Health Technology Evaluations: The Manual.
Related Concepts (2)
Library
Tools & Resources
1
SAVI — Sheffield Accelerated Value of Information — Mark Strong, Jeremy Oakley & Penny Breeze (University of Sheffield), Web application ed., 2024 (University of Sheffield)
A free, open-access web calculator that computes value-of-information measures (EVPI, partial EVPI/EVPPI and EVSI) directly from a model’s probabilistic sensitivity analysis output — no need to re-run the model. Also reports payer strategy-specific and uncertainty burden.
Web Tool (R Shiny)View source →
Frequently Asked Questions (6)
What is a tornado diagram?
A horizontal bar chart displaying one-way sensitivity analysis results, bars ranked from largest to smallest range, resembling a tornado shape.
Source: Eschenbach 1992
Why are the bars in a tornado diagram ordered by length?
The bars of a tornado diagram are arranged from longest at the top to shortest at the bottom precisely so that the inputs with the greatest influence on the result appear first and stand out. This ordering turns the chart into an immediate ranking of importance, letting a reader see at once which parameters drive the conclusion and which barely affect it. The tapering shape that gives the diagram its name is a direct consequence of this sorting. The order carries the message. Briggs and colleagues (2006) describe this display.
Source: Briggs et al. 2006
How is a tornado diagram constructed?
A tornado diagram is constructed by performing a one-way sensitivity analysis for each parameter, varying it between plausible low and high values while others stay at base case, and recording the resulting range of the output. Each parameter's range is drawn as a horizontal bar, usually centred on the base-case result, and the bars are sorted by width, widest at the top. The ordering by width produces the characteristic tapering, tornado-like shape, with the most influential parameters at the top.
Source: Briggs, Claxton & Sculpher 2006
What does a tornado diagram show?
A tornado diagram shows which input parameters most influence a model's result: the length of each bar represents the range over which the result moves as that parameter is varied individually, so longer bars mark more influential parameters, and the ordering places the most influential at the top. It summarises many one-way analyses in one picture, quickly conveying the relative importance of the inputs. It does not show interactions or joint effects, since each bar reflects one parameter varied alone, but it highlights the individual drivers of the result.
Source: Eschenbach 1992
Why is a tornado diagram used?
A tornado diagram is used to communicate the results of one-way sensitivity analyses clearly, showing the relative influence of the inputs in a single, intuitive picture that highlights which parameters matter most. This helps focus attention and further data collection on the influential parameters and conveys to decision makers how the result depends on individual inputs. Its ranked bars make comparisons immediate. As a transparent visual summary, the tornado diagram is a standard way to present deterministic one-way sensitivity analysis.
Source: Briggs, Claxton & Sculpher 2006
What are the limitations of a tornado diagram?
A tornado diagram displays only one-way sensitivity analyses, so it shows each parameter's individual effect but not interactions or the combined effect of several parameters changing together, and it depends on the chosen high and low values, which affect the bar lengths. It gives no probabilities and holds other inputs at base case, so it can understate overall uncertainty. These limitations mean the tornado diagram is used to convey individual sensitivities, complemented by multi-way and probabilistic analyses that capture joint effects and the full uncertainty.
Source: Eschenbach 1992
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 30 Oct 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/tornado-diagram
- Term code
- HE-EM-UA-076
Stable URI · Machine-readable · Resolvable · CC BY 4.0