Concept Architecture
Concept
Theoretically, Two-Way Sensitivity Analysis is a deterministic sensitivity analysis method that evaluates the combined effect of simultaneously varying two uncertain model parameters while all remaining parameters are held constant. It extends one-way sensitivity analysis by assessing whether interactions between two influential parameters alter model conclusions. In health economics, two-way sensitivity analysis is commonly used to examine combinations of treatment costs, clinical effectiveness, utility values or other key inputs that influence reimbursement decisions.
Mathematically, two-way sensitivity analysis recalculates model outcomes across all combinations of two varying parameters over predefined ranges. The resulting matrix of outcomes identifies regions in which the preferred intervention changes and may be used to determine combinations of parameter values satisfying specified decision criteria, such as cost-effectiveness thresholds or net monetary benefit equal to zero.
In practice, plausible ranges for two influential parameters are obtained from confidence intervals, published evidence or expert opinion. Model outcomes are calculated for every parameter combination and presented as two-dimensional tables, contour plots, heat maps or threshold diagrams, enabling decision-makers to evaluate how simultaneous changes in both parameters affect health economic conclusions.
Purpose
Used to evaluate the combined influence of two uncertain parameters on model outcomes, identify interaction effects and determine combinations of values that alter health economic decisions.
Mathematical Formulae
Primary Formula
There is no universally recognised canonical mathematical formula.
Supporting Formulae
Incremental Cost-Effectiveness Ratio:
ICER = ?C / ?E
Net Monetary Benefit:
NMB = ?E ? C
Incremental Net Monetary Benefit:
INMB = ??E ? ?C
Threshold condition:
INMB = 0
Related Mathematical Methods
- One-Way Sensitivity Analysis
- Deterministic Sensitivity Analysis
- Threshold Analysis
- Scenario Analysis
- Net Monetary Benefit
- Incremental Cost-Effectiveness Ratio
Example
A health economic model simultaneously varies annual treatment cost between �6,000 and �10,000 and treatment effectiveness between 0.20 and 0.35 QALYs. The resulting two-way sensitivity analysis demonstrates that the intervention remains cost-effective when effectiveness exceeds 0.27 QALYs at treatment costs below �8,500, but becomes not cost-effective outside this region.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| Data Table | Two-variable Data Table | Recalculate model outcomes for every combination of two uncertain parameters. |
| IF | =IF(B2<=30000,"Cost-effective","Not cost-effective") | Identify cost-effectiveness for each parameter combination. |
| INDEX | =INDEX(ResultMatrix,Row,Column) | Retrieve model outcomes from the two-way sensitivity table. |
| MATCH | =MATCH(TargetValue,ParameterRange,1) | Locate threshold parameter combinations within the analysis. |
VBA (Optional)
VBA can automate two-way sensitivity analyses, populate parameter grids and generate contour plots or threshold diagrams illustrating regions of cost-effectiveness.
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.
- NICE. NICE Health Technology Evaluations: The Manual.
- 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.
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 two-way sensitivity analysis?
An analysis varying two parameters together across a grid of combinations, typically shown as a contour plot or heat map of results.
Source: Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006. doi:10.1093/oso/9780198526629.001.0001.
What does a two-way sensitivity analysis show across a grid of values?
A two-way sensitivity analysis runs the model across a grid formed by every combination of two inputs' values, producing a result for each pair. Displayed as a contour plot or coloured map, the grid shows which regions of the two-input space give one conclusion and which give another, with a line marking where the decision changes. This reveals not just that the two inputs matter but how they trade off against each other in shaping the result. The map turns two dimensions of uncertainty into a readable picture. Briggs and colleagues (2006) describe this display.
Source: Briggs et al. 2006
How is two-way sensitivity analysis displayed?
Two-way sensitivity analysis is displayed by mapping the result across a grid of the two parameters' values, often as a contour plot, where lines join combinations giving the same result, or a heat map, where colour indicates the result's magnitude. A common display divides the plane into regions where different decisions are preferred, with a boundary marking where the conclusion changes. These displays convey how the result or decision depends on the two parameters jointly, making the combined effect and any interaction visible across their ranges.
Source: Briggs, Claxton & Sculpher 2006
Why is two-way sensitivity analysis used?
Two-way sensitivity analysis is used to examine how a result depends on two parameters jointly, which matters when the parameters interact or when a decision hinges on both, since their combined effect can differ from what separate one-way analyses suggest. Displaying the result across a grid shows the combinations supporting each conclusion and where the decision changes. Being limited to two parameters, it stays interpretable and can be plotted clearly, making it a practical tool for understanding the joint influence of a chosen pair of inputs.
Source: Drummond et al. 2015
What does a two-way sensitivity analysis reveal?
A two-way sensitivity analysis reveals how the result or preferred decision changes across the joint range of two parameters, including any interaction between them and the combinations at which the conclusion switches. A contour plot or heat map shows where the result is higher or lower, and a decision map shows which option is preferred across the plane. This indicates whether the conclusion is robust to joint changes in the pair and identifies the regions of their values that support each decision.
Source: Briggs, Claxton & Sculpher 2006
What are the limitations of two-way sensitivity analysis?
Two-way sensitivity analysis is limited to two parameters, so it cannot capture the joint effect of more than two changing together, and it uses fixed values across a grid rather than full distributions, holding other inputs at base case, so it does not convey overall uncertainty or probabilities. The results depend on the chosen ranges and grid. These limitations mean it is applied to a pair of particular interest, with probabilistic sensitivity analysis used to represent the combined uncertainty of all inputs through their distributions.
Source: Briggs, Claxton & Sculpher 2006
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Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 30 Oct 2025
Content version: 1.0.0
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