Concept Architecture
Concept
Theoretically, Threshold Analysis is a deterministic sensitivity analysis method used to identify the value of an uncertain parameter at which a decision changes from one preferred option to another. It determines the critical parameter value that causes an intervention to become cost-effective or not cost-effective under a specified decision rule. In health economics, threshold analysis is widely used to evaluate the robustness of reimbursement decisions and identify parameters that have the greatest influence on model conclusions.
Mathematically, threshold analysis involves solving for the value of an uncertain parameter that satisfies a predefined decision criterion. This is commonly achieved by identifying the parameter value at which the incremental net monetary benefit equals zero or the incremental cost-effectiveness ratio equals the willingness-to-pay threshold. Numerical methods are frequently required because many health economic models do not have closed-form analytical solutions.
In practice, threshold analysis is performed by varying one uncertain parameter while holding all other model inputs constant until the decision criterion changes. The resulting threshold value is used to determine whether existing evidence provides sufficient confidence for decision-making or whether additional research should focus on reducing uncertainty surrounding that parameter.
Purpose
Used to identify the critical value of an uncertain parameter at which a health economic decision changes, supporting assessment of model robustness and research prioritisation.
Mathematical Formulae
Primary Formula
INMB = ??E ? ?C
Threshold occurs when:
INMB = 0
Supporting Formulae
Incremental Cost-Effectiveness Ratio:
ICER = ?C / ?E
Threshold condition:
ICER = ?
where:
? = willingness-to-pay threshold
Related Mathematical Methods
- One-Way Sensitivity Analysis
- Deterministic Sensitivity Analysis
- Scenario Analysis
- Net Monetary Benefit
- Incremental Net Benefit
- Incremental Cost-Effectiveness Ratio
Example
A new treatment has an incremental cost of �8,000 and an incremental benefit of 0.30 QALYs. The ICER is �26,667 per QALY. At a willingness-to-pay threshold of �30,000 per QALY, the intervention is cost-effective. Threshold analysis shows that if the treatment cost increases above �9,000 while all other parameters remain unchanged, the ICER exceeds �30,000 per QALY and the reimbursement decision changes.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| Goal Seek | What-If Analysis ? Goal Seek | Determine the parameter value at which INMB equals zero or the ICER equals the decision threshold. |
| IF | =IF(B2<=30000,"Cost-effective","Not cost-effective") | Identify whether the intervention remains cost-effective after parameter variation. |
| DATA TABLE | =TABLE(ParameterCell,) | Evaluate model outcomes across a range of parameter values. |
| MATCH | =MATCH(TRUE,B2:B100>30000,0) | Identify the first parameter value exceeding the willingness-to-pay threshold. |
VBA (Optional)
VBA can automate iterative threshold searches for multiple parameters and generate reports identifying the critical values at which reimbursement decisions change.
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.
- ISPOR-SMDM Modeling Good Research Practices Task Force Reports.
Related Concepts (2)
Library
Publications
1
Statistical Analysis of Cost-Effectiveness Data — Willan & Briggs, 1st Edition ed., 2006 (John Wiley & Sons)
A synthesis of statistical methods for analysing cost-effectiveness data, including net-benefit regression, confidence intervals for the ICER, cost-effectiveness acceptability curves, and covariate adjustment. Part of the Wiley Statistics in Practice series.
BookView source →
Frequently Asked Questions (6)
What is threshold analysis?
A sensitivity analysis technique identifying the value at which an input parameter would need to be set for a model's conclusion to change.
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 question does threshold analysis answer?
Threshold analysis turns the usual sensitivity question around. Instead of asking what the result is at a given input value, it asks how far an uncertain input would have to move before the conclusion changed, such as the price at which a treatment stops being cost-effective. This locates the tipping point directly, which is useful when the exact input value is unknown but a decision-maker wants to know whether the true value is likely to fall on one side of it. It finds the value that flips the decision. Briggs and colleagues (2006) describe it.
Source: Briggs et al. 2006
How is threshold analysis performed?
Threshold analysis is performed by varying the parameter of interest and finding the value at which the result reaches the point where the conclusion changes, for example where the incremental cost-effectiveness ratio equals the decision threshold. This critical value is the threshold. It can be found by solving for the value that equates the result to the decision boundary or by searching across the parameter's range. The threshold is then compared with the plausible range of the parameter to judge whether the conclusion is likely to hold.
Source: Briggs, Claxton & Sculpher 2006
Why is threshold analysis used?
Threshold analysis is used to understand how far an uncertain parameter could change before a conclusion is overturned, giving a clear sense of the robustness of a decision to that input. It is especially useful for parameters such as price, where the threshold value, the price at which an intervention becomes cost-effective, is directly informative for negotiation or decision making. By identifying the critical value and comparing it with plausible ranges, threshold analysis conveys whether the parameter is likely to fall on the side supporting the conclusion.
Source: Drummond et al. 2015
What does a threshold value represent?
A threshold value represents the value of an input parameter at which the model's conclusion changes, marking the boundary between one decision and another, such as the effectiveness or cost at which an intervention's incremental cost-effectiveness ratio equals the decision threshold. On one side of this value the intervention is judged cost-effective and on the other it is not. The threshold thus locates the critical point for that parameter, indicating how much it would need to change from its estimate to alter the decision.
Source: Briggs, Claxton & Sculpher 2006
What are the limitations of threshold analysis?
Threshold analysis typically considers one parameter at a time, so it does not capture how several parameters changing together could alter the conclusion, for which multi-way threshold analysis is needed, and it identifies where the conclusion changes without conveying the probability of reaching the threshold. Its result depends on holding other inputs fixed. These limitations mean threshold analysis is interpreted alongside knowledge of the parameter's plausible range and, for combined effects, with multi-way analysis, while probabilistic analysis quantifies the overall probability of each conclusion.
Source: Briggs, Claxton & Sculpher 2006
Trust Record
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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