Sensitivity Analysis

Sensitivity Analysis in Health Economic Evaluation

In health economic evaluation, sensitivity analysis means running a decision model again with changed inputs or assumptions to find out whether costs, health effects and, above all, the recommended option change. The term covers a family of methods, from one-way and threshold analysis through scenario analysis to probabilistic sensitivity analysis, and health technology assessment bodies such as NICE expect a submission to use several of them. Current methods advice separates two questions that the shared name tends to blur, how sensitive a result is to a chosen change and how uncertain the decision itself is, and that separation decides which method answers which question. The word has a different meaning in diagnostic testing, where sensitivity is a measure of test accuracy that can itself appear as an input in a model of a diagnostic technology.

Sensitivity and uncertainty answer different questions

The second report of the Health Economics Methods Advisory (HEMA), convened by NICE, Canada's Drug Agency (CDA-AMC) and the Institute for Clinical and Economic Review, describes two approaches that have both been called sensitivity analysis. The first, the older of the two, varies the value of one or more uncertain parameters and watches how the ICER responds. This is deterministic sensitivity analysis, and threshold analysis is a variant of it that finds how far an input can move before the new intervention stops being cost-effective.

The report calls the insight from this first approach partial, since arbitrary ranges such as a fixed change of plus or minus 20 per cent show how sensitive a result is without showing how uncertain an input is, and the deterministic sensitivity analysis page sets out its weaknesses in full.

The second approach, which the report says can more accurately be called uncertainty analysis, places the combined uncertainty in all parameters into one distribution of possible cost-effectiveness results. In practice this is probabilistic sensitivity analysis (PSA). The share of that distribution lying on the wrong side of zero net benefit is the probability that the decision is wrong, which is decision uncertainty. The HEMA report states that the purpose of uncertainty analysis is to establish whether variation in model outputs could lead to a decision that fails the health system's objective, with a cost that can be quantified, rather than to describe how widely outputs vary.

The main forms of sensitivity analysis

Each form varies something different and supports a different conclusion. Each has its own page with the detail.

One-way, two-way and threshold analysis are deterministic sensitivity analyses, and the HEMA report also treats scenario analysis as a form of it because it explores alternatives without weighting them, although each scenario can itself be run probabilistically. Global sensitivity analysis is a further family with its own page.

Matching the method to the source of uncertainty

Sensitivity analysis is easier to plan when each test is tied to a named source of uncertainty. The NICE technology appraisal manual (PMG36) asks for an overall assessment describing the relative effect of different types of uncertainty, such as parameter and structural, on cost-effectiveness estimates.

Two things are not uncertainty in this sense. Heterogeneity, the variation between patients that their characteristics explain, calls for subgroup analyses, and the HEMA report says coding errors and avoidable methodological shortcomings should be corrected rather than carried forward as uncertainty.

What NICE asks to see

PMG36 sets out how sensitivity analysis should be used and presented in technology appraisal. The committee's preferred cost-effectiveness estimate should come from a probabilistic analysis when possible, unless the model is linear, and scenario analyses should in general also be probabilistic, with any purely deterministic analysis justified.

Deterministic analyses keep a supporting role, identifying the parameters to which the decision is most sensitive and, for highly uncertain inputs, the switching value at thresholds such as GBP 25,000 and GBP 35,000 per QALY. The manual warns against threshold analysis for parameters highly correlated with other influential parameters, and against using it to justify restricting the population to a subgroup on cost-effectiveness grounds. Analyses built on demonstrably implausible values are useful only to show that a conclusion is robust, as when assuming no resource use and very large resource use both leave the conclusion unchanged.

What the HEMA report recommends

The HEMA report gives advice to HTA organisations rather than binding rules. It recommends probabilistic analysis as the general default for two reasons. Decision models are non-linear in their inputs, so running the model at the mean of each input does not necessarily give the expected costs and health effects, and probabilistic analysis combines all characterised uncertainty into one result.

Deterministic analysis keeps what the report calls a narrower role. Varying one or two inputs at a time helps analysts understand how the model behaves, exposes coding and conceptual errors, and identifies influential inputs, which links it to model validation. The report's summary describes deterministic and scenario analysis as uncertainty diagnostics and as the main current route to structural uncertainty, while noting that neither yields a probability of error or a loss.

Because scenario analysis carries most of the uncertainty that is not parameterised, the report asks that scenarios be specified before results are seen and span the range the evidence supports rather than a pair of convenient extremes. It recommends that every scenario analysis be accompanied by a probabilistic analysis of that scenario and, at a minimum, the expected value of perfect information, and that reports state which parameters, correlations or other sources of uncertainty were left out of the probabilistic analysis.

Worked example with one model read four ways

All numbers in this example are illustrative. A new treatment is compared with standard care at a threshold of GBP 25,000 per QALY. The base-case incremental QALY gain is 0.30 per patient and the incremental cost is GBP 6,000. Results are expressed as incremental net health benefit, which the HEMA report recommends reporting alongside the ICER.

$$\Delta NHB = \Delta E - \frac{\Delta C}{\lambda} = 0.30 - \frac{6000}{25000} = 0.30 - 0.24 = 0.06$$

where $\Delta E$ is the incremental health gain in QALYs, $\Delta C$ is the incremental cost in GBP, $\lambda$ is the cost-effectiveness threshold in GBP per QALY and $\Delta NHB$ is the incremental net health benefit in QALYs. The expected gain of 0.06 QALY per patient equals GBP 1,500 of net monetary benefit at GBP 25,000 per QALY, so the base case favours the treatment.

One-way analysis with an evidence-based range. Suppose the evidence supports a range of 0.20 to 0.40 QALYs for the incremental gain. At 0.20 the net health benefit is 0.20 minus 0.24, or minus 0.04 QALY, and at 0.40 it is 0.40 minus 0.24, or 0.16 QALY. The decision changes inside the range, so the health gain is a candidate driver.

One-way analysis with a conventional range. Varying the incremental cost by 20 per cent either way gives GBP 4,800 to GBP 7,200. Divided by GBP 25,000 these cost 0.192 and 0.288 QALY, giving net health benefits of 0.108 and 0.012 QALY. The decision does not change, but the 20 per cent range says nothing about how uncertain the cost estimate is.

Threshold analysis. The decision switches when the health gain equals the incremental cost divided by the threshold, which is 6,000 divided by 25,000, or 0.24 QALY. The switching value is 0.06 QALY below the best estimate. At GBP 35,000 per QALY it falls to 6,000 divided by 35,000, about 0.171 QALY.

Probabilistic analysis. A real PSA uses enough draws to keep Monte Carlo error small, but five equally likely joint draws show the logic, as in the HEMA report's own five-possibility example.

The mean health gain is 1.50 divided by 5, or 0.30, and the mean cost is GBP 30,000 divided by 5, or GBP 6,000, matching the base case. The mean net health benefit is 0.30 divided by 5, or 0.06 QALY, so adoption remains the better choice. Two of the five draws are negative, so the probability that adopting is the wrong decision is 0.4.

If the true draw were known in advance, the treatment would be adopted only when its net health benefit was positive. The expected net health benefit with perfect information is then the sum of 0.14, 0.07 and 0.15 divided by 5, or 0.072 QALY. The difference of 0.072 minus 0.06, or 0.012 QALY per patient (GBP 300 at GBP 25,000 per QALY), is the expected cost of the uncertainty, the per-patient expected value of perfect information. Only the joint analysis gave both the probability and the health consequence of a wrong decision.

Common misreadings of sensitivity analysis

The finding that matters is whether the preferred option changes, since an output can move a long way while net benefit stays positive. Most errors come from reading a deterministic result as if it measured uncertainty, or a probabilistic result as if it covered everything. The ISPOR-SMDM task force considered it appropriate to report both kinds in one evaluation, with every range or distribution disclosed and justified against the evidence.

• A long tornado bar may reflect a wide or poorly justified range rather than an important input, and the HEMA report notes that tornado diagrams generally do not preserve correlations.
• A decision that survives every one-way test can still be uncertain, because one-way analysis does not capture joint variation.
• A scenario shows whether the decision changes under its assumptions, and says nothing about how likely those assumptions are.
• A PSA still rests on judgement. The HEMA report notes that its distributions and correlations draw on the same evidence and modelling assumptions as everything else.
• The probability of cost-effectiveness alone can mislead. The HEMA report shows a case in which it would point to the option with the lower expected net benefit, and recommends showing expected loss alongside the acceptability curve.

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; 2022, last updated 13 October 2026. Section 4.7, Exploring uncertainty. https://www.nice.org.uk/process/pmg36/chapter/economic-evaluation-2
• 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, 4.2 to 4.7 and 6.4. https://hemamethods.org/wp-content/uploads/2026/10/HEMA-Report-2_For-Publication_100726.pdf