Threshold Analysis

Threshold Analysis and Switching Values in Health Economic Models

Threshold analysis in a health economic model works backwards from the decision. It solves for the value an uncertain input would need to take for the preferred option to change, a figure the NICE technology appraisal manual (PMG36) calls the switching value, and sets that figure beside what the evidence says is plausible. A switching value far outside the plausible range shows that the decision does not hinge on that input, while one close to the best estimate marks an input the decision is sensitive to. The method is a form of deterministic sensitivity analysis, and the same reasoning is used to test recommendations drawn from a network meta-analysis and to set probability thresholds for treating or testing in clinical decision analysis.

Solving net benefit for the switching value

A decision model ranks options by expected net benefit at a stated cost-effectiveness threshold, and threshold analysis asks where that ranking breaks. One input, written $\theta$, is treated as unknown while every other input stays at its base case value. The switching value is the value of $\theta$ at which the best option ties with its closest rival.

$$\lambda E_{j}(\theta^{*}) - C_{j}(\theta^{*}) = \max_{k \neq j} \left[ \lambda E_{k}(\theta^{*}) - C_{k}(\theta^{*}) \right]$$

where $\theta^{*}$ is the switching value, $j$ is the option preferred at the base case, $k$ indexes the other options, $E$ and $C$ are the expected QALYs and costs per patient of each option, and $\lambda$ is the threshold in GBP per QALY. With two options this reduces to setting incremental net monetary benefit to zero, which for a more effective and more costly option is the same as its ICER equalling $\lambda$.

When the input enters the model linearly, as an acquisition cost or a fixed QALY gain usually does, the switching value has a closed form.

$$\Delta E^{*} = \frac{\Delta C}{\lambda}, \qquad \Delta C^{*} = \lambda \, \Delta E$$

where $\Delta E^{*}$ is the switching incremental QALY gain with costs held at base case, $\Delta C^{*}$ is the switching incremental cost with QALYs held at base case, and $\Delta E$ and $\Delta C$ are the base-case incremental QALYs and costs. Run on the threshold itself, the analysis returns the ICER, since the decision between two options changes when $\lambda$ crosses it.

Most clinical inputs act non-linearly. A hazard ratio or transition probability in a Markov model changes costs and QALYs over many discounted cycles, so the switching value is found by re-running the model and searching for the value at which net benefit changes sign, for example by bisection or a spreadsheet goal-seek routine. A non-linear input can have no switching value within its possible range, or more than one, so the search has to cover the whole range.

How NICE uses switching values in technology appraisal

PMG36 treats threshold analysis as an option for highly uncertain parameters when a switching value may inform decision makers (section 4.7.22). It ties the switching value to thresholds such as GBP 25,000 and GBP 35,000 per QALY gained and asks the analysis to show how far the switching value is from the current best estimate. Section 4.7.17 adds that deterministic threshold analysis might inform decisions on influential but highly uncertain parameters, while deterministic analysis is less appropriate for decision making if the model is non-linear.

An implausible switching value is still presented, alongside the plausible range for the parameter (section 4.6.29). Threshold analysis is unsuitable for parameters highly correlated with other influential parameters, and it should not be used to justify restricting the population to a subgroup on cost-effectiveness grounds (section 4.7.23). The break-even analysis page applies these provisions to prices and treatment effects.

Reading a switching value against the evidence

A switching value means little until it is compared with the evidence on the input, such as a confidence interval. The ISPOR-SMDM task force on parameter estimation and uncertainty (Working Group 6) places threshold analysis among the analyses that need no formal ascertainment of parameter uncertainty, and links it to "even if" approaches, which identify extreme values that still leave the decision unchanged.

The task force notes that one-way threshold results are easily reported in text, as an ICER that stays below a stated value as long as an input stays above another, and that threshold values can be marked on the bars of a tornado diagram.

A switching value carries no probability. The second report of the Health Economics Methods Advisory (HEMA), convened by NICE, Canada's Drug Agency and the Institute for Clinical and Economic Review, calls threshold analysis a variant of deterministic sensitivity analysis and says deterministic and scenario analysis yield neither a probability of error nor a loss. PMG36 (section 4.7.21) notes that probabilistic univariate analysis may incorporate the likelihood of a parameter taking its bound values. The probability that the decision is wrong across all inputs comes from probabilistic sensitivity analysis, and the value of resolving one input first is measured by the expected value of partial perfect information.

Two-way and multi-way threshold analysis

Varying two inputs together turns a switching value into a switching line. The ISPOR-SMDM task force describes displays in which the axes carry the values of the two inputs and the plane is partitioned into regions, with boundaries at stated ICER thresholds or at thresholds of dominance, each region showing which option is preferred. Threshold curves for a few discrete values of a third input can be overlaid, though the task force warns this often leads to visual overload and confusion. A two-way sensitivity analysis shows results across the whole grid, whereas a two-way threshold analysis keeps only the boundary.

The task force calls threshold analyses especially useful, perhaps necessary, when deterministic results involve three or more comparators, because the question becomes which option is cost-effective at a given threshold. A switching value computed against standard care alone can then mislead, since the option that takes over may be another active treatment.

Worked example with three options and one uncertain health gain

All numbers in this example are illustrative. Two new treatments, T1 and T2, are compared with standard care S at GBP 25,000 per QALY. Against S, T1 adds GBP 6,000 and 0.30 QALYs per patient, and T2 adds GBP 11,000 and a best-estimate 0.56 QALYs. The uncertain input is T2's health gain, written $g$.

1. Net benefit at the base case. Against S, whose net benefit is set at zero, T1 has 25,000 × 0.30 minus 6,000 = GBP 1,500 and T2 has 25,000 × 0.56 minus 11,000 = GBP 3,000 per patient, so T2 is preferred.

2. Switching value against standard care. T2 beats S while 25,000 × $g$ exceeds 11,000, which holds above $g$ = 11,000 ÷ 25,000 = 0.44.

3. Switching value against the best rival. T2 beats T1 while 25,000 × $g$ minus 11,000 exceeds 1,500, which holds above $g$ = 12,500 ÷ 25,000 = 0.50. The binding switching value is 0.50, which is 0.06 below the best estimate, and an analysis against S alone would have put it at 0.44 and overstated the margin.

4. The upper end of the NICE range. At GBP 35,000 per QALY, T1's net benefit is 35,000 × 0.30 minus 6,000 = GBP 4,500, and the switching value for $g$ is (11,000 + 4,500) ÷ 35,000 = 0.443.

5. Comparison with the evidence. Suppose $g$ has a mean of 0.56 and a standard error of 0.05, giving a 95% interval of 0.56 ± 1.96 × 0.05, about 0.46 to 0.66. At GBP 25,000 the switching value of 0.50 lies inside the interval, so the choice between T1 and T2 is sensitive to $g$. At GBP 35,000 the switching value of 0.443 lies below it, and even at $g$ = 0.46 T2's net benefit is 35,000 × 0.46 minus 11,000 = GBP 5,100, above T1's GBP 4,500.

6. A probability for one input. If $g$ is normally distributed, the probability that it lies below 0.50 is $\Phi((0.50 - 0.56)/0.05) = \Phi(-1.2) = 0.115$. That is the chance this one input falls on the wrong side with every other input fixed, not the probability that the decision is wrong.

7. A two-way switching line. If T2's incremental cost $c$ is also uncertain, T2 stays preferred over T1 while $c$ is below 25,000 × $g$ minus 1,500 at GBP 25,000 per QALY, or below 35,000 × $g$ minus 4,500 at GBP 35,000.

At the best-estimate gain, T2's incremental cost could rise by GBP 1,500 to GBP 12,500 before T1 took over at GBP 25,000 per QALY, while at the lower end of the interval it would need to fall by GBP 1,000 to GBP 10,000. Solving the same line for a unit price gives a threshold price.

Threshold analysis of the evidence behind guideline recommendations

Threshold analysis can be applied to the evidence that feeds a decision as well as to model inputs. Phillippo and colleagues, in 2018, proposed methods for network meta-analysis that derive bias-adjustment thresholds, the smallest changes to the data that would change the treatment decision, for individual studies or aggregate treatment contrasts in fixed-effect and random-effects models.

In 2019 Phillippo and colleagues argued that GRADE approaches proposed for network meta-analysis are insufficient for guideline development because they do not take account of the influence of the evidence on the final recommendation, and they demonstrated threshold analysis on two NICE clinical guidelines. The method quantifies how much the evidence could change, through bias, sampling variation or any other reason, before the recommendation changes, and what the revised recommendation would be. If the evidence could not plausibly change by that much, the recommendation is considered secure.

Threshold probabilities in clinical decision analysis

Clinical decision analysis applies the same idea to the care of individual patients. Pauker and Kassirer, in 1980, derived two threshold probabilities of disease, a testing threshold and a test-treatment threshold, set from the reliability and risks of the diagnostic test and the benefits and risks of the treatment. Treatment is withheld below the testing threshold and given without further testing above the test-treatment threshold, and the test is done only between the two. The probability of disease is the uncertain input, and the two thresholds are its switching values in a decision tree with three options.

Boundaries with nearby methods

Several neighbouring methods share the arithmetic but answer different questions. A one-way sensitivity analysis reports the result across a chosen range of one input, whereas threshold analysis reports only the point at which the decision changes. Break-even analysis is threshold analysis applied to a price, a treatment effect or a volume of activity, and the threshold price is its application to the unit price of a technology. The cost-effectiveness threshold $\lambda$ is an input that values health, while the output of threshold analysis is a value of some other input.

Limitations and common misreadings

Every switching value is conditional on the other inputs at base case, so two inputs that each stay short of their switching values can together reverse a decision. In a non-linear model the switching value found around the deterministic base case can also differ from the value at which probabilistic mean net benefit changes sign.

Distance alone is easily misread. A switching value close to the best estimate matters less for a precisely estimated input than for a poorly estimated one, so the gap has to be judged in units of the input's uncertainty, as in step 5, and a distant switching value says nothing about structural assumptions. The ISPOR-SMDM task force asks that ICERs with negative incremental costs and health effects be distinguished from those with positive increments. When both increments are negative an ICER above the threshold favours the new option, so a switching value found by setting the ICER equal to $\lambda$ can be read the wrong way round, which net benefit avoids.

Sources

• 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. https://doi.org/10.1177/0272989X12458348
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). London: NICE; published 31 January 2022, last updated 13 October 2026. Sections 4.6.29 and 4.7.17 to 4.7.23. https://www.nice.org.uk/process/pmg36/chapter/economic-evaluation-2
• Pauker SG, Kassirer JP. The threshold approach to clinical decision making. New England Journal of Medicine. 1980;302(20):1109-1117. https://doi.org/10.1056/NEJM198005153022003
• Phillippo DM, Dias S, Ades AE, Didelez V, Welton NJ. Sensitivity of treatment recommendations to bias in network meta-analysis. Journal of the Royal Statistical Society Series A. 2018;181(3):843-867. https://doi.org/10.1111/rssa.12341
• Phillippo DM, Dias S, Welton NJ, Caldwell DM, Taske N, Ades AE. Threshold analysis as an alternative to GRADE for assessing confidence in guideline recommendations based on network meta-analyses. Annals of Internal Medicine. 2019;170(8):538-546. https://doi.org/10.7326/M18-3542
• Steuten L, Thavorn K, Cipriano LE, Guertin JR, McQueen B, Schmidler G, Sullivan S, Wailoo A, Sculpher M. Methods to Analyze and Present Uncertainty in Economic Evaluation to Support HTA Decisions. HEMA Report 2. Health Economics Methods Advisory; 2026. Executive summary and sections 2.2 and 4.7. https://hemamethods.org/wp-content/uploads/2026/10/HEMA-Report-2_For-Publication_100726.pdf