Concept Architecture
Concept Architecture
Expected value analysis
Expected value analysis is a decision-analytic method that calculates the probability-weighted mean of the possible outcomes associated with a decision option.
This page explains how expected values are calculated, how they support comparisons between healthcare options and why expected value is different from the most likely outcome. It also shows how expected costs, expected health outcomes and expected net benefit are used in health-economic models.
What expected value analysis tells us
Expected value analysis combines the possible consequences of a decision with their probabilities. It provides the long-run average value that would be obtained if the same uncertain decision could be repeated many times under the stated assumptions.
Expected value does not predict the outcome that will occur for one individual or on one occasion. Instead, it provides a consistent basis for comparing decision options under uncertainty.
- Expected value analysis includes every mutually exclusive outcome represented in the model.
- Each outcome contributes to expected value according to its probability.
- Outcome probabilities must sum to one within each complete set of possible outcomes.
- Outcome values may represent costs, health outcomes, utility or net monetary benefit.
How expected value is calculated
Expected value is calculated by multiplying every possible outcome value by its probability and then adding the resulting weighted values. The outcome values must use the same units and interpretation.
EV(X) = Σ pᵢxᵢ
where:
- EV(X) is the expected value of outcome X.
- pᵢ is the probability of outcome i.
- xᵢ is the value associated with outcome i.
- Σpᵢ = 1 means that the probabilities for all mutually exclusive outcomes sum to one.
A simple healthcare example
Suppose a new screening programme has two possible net monetary benefit outcomes. There is an 80% probability of producing £15,000 in net monetary benefit and a 20% probability of producing a £5,000 net monetary loss.
Expected value = (0.80 × £15,000) + (0.20 × −£5,000)
Expected value = £12,000 − £1,000 = £11,000
The programme therefore has an expected net monetary benefit of £11,000 under these assumptions. That expected value can be compared with the expected net monetary benefit of other relevant options.
Expected value is not the most likely outcome
The most likely outcome is the individual outcome with the greatest probability. Expected value instead incorporates every represented outcome and reflects both its probability and its magnitude.
In the screening example, £15,000 is the most likely individual outcome, but £11,000 is the expected value. The expected value does not have to equal any outcome that could actually occur.
Calculating expected costs and health outcomes
Health-economic models commonly calculate expected costs and expected health outcomes separately for every alternative. These values may be generated through a decision tree, state-transition model or another decision-analytic structure.
For alternative j:
E[Cⱼ] = Σ pᵢⱼCᵢⱼ
E[Qⱼ] = Σ pᵢⱼQᵢⱼ
In these formulas, E[Cⱼ] is the expected cost and E[Qⱼ] is the expected health outcome for alternative j. The probabilities and consequences must refer to a complete and internally consistent set of possible pathways or outcomes.
Connecting expected values to expected net benefit
Expected costs and expected health outcomes can be combined using a cost-effectiveness threshold. This produces expected net monetary benefit and allows alternatives to be compared using a common outcome measure.
Expected NMBⱼ = (λ × E[Qⱼ]) − E[Cⱼ]
The preferred alternative on expected cost-effectiveness grounds is the alternative with the greatest expected net benefit at the stated threshold.
Choosing the preferred option
The correct decision rule depends on what the expected value represents. A larger numerical value is not automatically preferable for every type of outcome.
- The alternative with the greatest expected health outcome is preferred when only health is being maximized.
- The alternative with the lowest expected cost is preferred when outcomes are equivalent and only costs are being compared.
- The alternative with the greatest expected utility is preferred in an expected-utility analysis.
- The alternative with the greatest expected net benefit is preferred under the expected net-benefit decision rule.
Expected value analysis does not establish affordability, equity, implementation feasibility or overall adoption. Those considerations may require budget impact analysis and a broader health technology assessment.
How expected value analysis is used in decision models
Expected value calculations are embedded throughout health-economic decision models. Each chance node in a decision tree is evaluated by multiplying downstream consequences by their probabilities and summing the results.
State-transition models use the same underlying principle when combining state occupancy probabilities with state-specific costs and health outcomes. Probabilistic sensitivity analysis estimates expected results by averaging outputs across simulations drawn from parameter distributions.
Expected value and expected utility are not identical
Expected value analysis can be applied to money, costs, health outcomes, net benefit or other numerical consequences. Expected utility analysis specifically applies probabilities to utility values representing preferences over uncertain outcomes.
Selecting the option with the greatest expected monetary value assumes that monetary outcomes are valued linearly. When attitudes toward risk or nonlinear preferences matter, expected utility may provide a more appropriate framework.
Using expected value analysis in a spreadsheet
A spreadsheet can calculate expected value transparently when probabilities and outcome values are stored in separate columns. The probability total should always be checked before interpreting the result.
| Task | Example Excel formula | Purpose |
|---|---|---|
| Calculate expected value | =SUMPRODUCT(B2:B6,C2:C6) | Multiplies each probability by its outcome value and adds the results. |
| Check probability total | =SUM(B2:B6) | Confirms whether the represented probabilities sum to one. |
| Test the probability total | =IF(ABS(SUM(B2:B6)-1)<0.000001,"Valid","Check probabilities") | Flags an incomplete or invalid probability set. |
| Identify the greatest expected benefit | =IF(D2=MAX($D$2:$D$5),"Preferred","") | Identifies the largest expected benefit, utility or net benefit. |
| Identify the lowest expected cost | =IF(D2=MIN($D$2:$D$5),"Preferred","") | Identifies the lowest expected cost when outcomes are equivalent. |
Important assumptions and limitations
Expected value analysis is only as reliable as the probabilities, outcome values and model structure used in the calculation. Missing outcomes, dependent events treated as independent or probabilities that do not sum correctly can produce misleading results.
Expected value can also conceal the distribution of possible outcomes. Two alternatives may have the same expected value while having very different levels of uncertainty, downside risk or consequences for different population groups.
Common mistakes
These mistakes can cause expected value calculations or their interpretation to be incorrect. Every analysis should report the alternatives, possible outcomes, probabilities, units and decision rule.
- Expected value should not be confused with the most likely outcome.
- Probabilities for a complete set of mutually exclusive outcomes should sum to one.
- Costs, health outcomes and net benefits should not be combined without a valid conversion or decision rule.
- The alternative with the largest expected cost should not be selected as though cost were a benefit.
- Expected monetary value and expected utility should not be treated as interchangeable.
- Expected value does not describe the uncertainty or range surrounding the average.
- A decision based on expected value alone does not establish affordability or guarantee adoption.
Further learning
These Library resources explain expected value calculations, decision modelling and healthcare decision-making under uncertainty. Final website links must use the confirmed Library destination for expected-value-analysis rather than a guessed URL.
- Methods for the Economic Evaluation of Health Care Programmes — LIB-000001
- Applied Methods of Cost-Effectiveness Analysis in Healthcare — LIB-000003
- Decision Modelling for Health Economic Evaluation — use the confirmed existing Library record
- NICE Health Technology Evaluations: The Manual — LIB-000099
Media & tools (1)
Expected Net Benefit and Probability Explorer
Change scenario probabilities, costs, QALYs and the threshold to compare expected-value and probability rankings.
Open tool →Related Concepts (3)
Library
Publications
8
Methods for the Economic Evaluation of Health Care Programmes — Drummond, Sculpher, Claxton, Stoddart & Torrance, 4th Edition ed., 2015 (Oxford University Press)
The standard international reference text for economic evaluation methods in health care, covering cost-effectiveness, cost-utility and cost-benefit analysis, measurement of costs and outcomes, evidence synthesis, and the characterisation of uncertainty.
BookView source →Applied Methods of Cost-Effectiveness Analysis in Healthcare — Gray, Clarke, Wolstenholme & Wordsworth, 1st Edition ed., 2011 (Oxford University Press)
A practical, worked-example guide to conducting cost-effectiveness analysis, structured around outcomes, costs, modelling with decision trees and Markov models, and presenting results. Volume 3 in the Handbooks in Health Economic Evaluation series, developed from the University of Oxford course.
BookView source →Cost-Effectiveness in Health and Medicine — Neumann, Sanders, Russell, Siegel & Ganiats, 2nd Edition ed., 2016 (Oxford University Press)
The revised report of the Second Panel on Cost-Effectiveness in Health and Medicine, providing methodological benchmarks for CEA including the reference case, perspectives, discounting, and the valuation of health outcomes.
BookView source →NICE DSU Technical Support Document 11: Alternatives to EQ-5D for Generating Health State Utility Values — Brazier, Rowen, TSD 11 ed., 2011 (NICE Decision Support Unit (University of Sheffield))
Guidance on alternatives to EQ-5D — including SF-6D, HUI, condition-specific preference-based measures, direct valuation and vignette methods — for generating health-state utility values.
NICE Health Technology Evaluations: The Manual (PMG36) — National Institute for Health and Care Excellence, PMG36 ed., 2022 (NICE)
NICE’s consolidated methods and processes manual for health technology evaluation, defining the reference case for economic evaluation (perspective, comparators, time horizon, discounting, EQ-5D, cost-effectiveness thresholds and the severity modifier) — the authoritative HTA methods reference for the English NHS.
Guidelines for the Economic Evaluation of Health Technologies: Canada, 4th Edition — Canadian Agency for Drugs and Technologies in Health (CADTH), 4th Edition ed., 2017 (CADTH / CDA-AMC)
CADTH’s national methods guidelines for the economic evaluation of health technologies in Canada — reference case, comparators, modelling, effectiveness, discounting and uncertainty — a major national HTA methods reference (co-authored with Sculpher and other leading health economists).
Net Health Benefits: A New Framework for the Analysis of Uncertainty in Cost-Effectiveness Analysis — Aaron A. Stinnett and John Mullahy, 18(2 Suppl):S68–S80 ed., 1998 (Medical Decision Making)
Foundational net-health-benefit framework for cost-effectiveness decisions under uncertainty.
Journal ArticleView source →Representing Uncertainty: The Role of Cost-Effectiveness Acceptability Curves — Elisabeth Fenwick, Karl Claxton and Mark Sculpher, 10(8):779–787 ed., 2001 (Health Economics)
Foundational explanation of cost-effectiveness acceptability curves and their proper role alongside expected net benefit.
Journal ArticleView source →
Economic evaluation — National Institute for Health and Care Excellence, Technology appraisal and highly specialised technologies guidance manual ed., 2026 (NICE)
Official methods guidance for comparative economic evaluation, including incremental analysis, ICERs, comparators and the treatment of dominated options.
Web GuidanceView source →
Frequently Asked Questions (6)
What is expected net benefit?
The expected value of an intervention's monetary benefit minus its cost, calculated by converting health outcomes into money at a set willingness-to-pay threshold.
Source: Stinnett & Mullahy 1998
How is expected net benefit calculated?
The health gain is multiplied by the willingness-to-pay threshold to express it in money, and the cost is subtracted, giving a single monetary figure for each option. Where the analysis is probabilistic, the calculation is performed for every simulation and the results averaged, which is what makes the measure an expectation rather than a point estimate. An option with positive expected net benefit produces more value than it consumes at the stated threshold, and the option with the highest figure is the one that should be chosen. Because the calculation produces money rather than a ratio, options can be ranked directly by the figure without any further comparison step.
Source: Stinnett & Mullahy 1998
Why is expected net benefit preferred to a ratio?
Because ratios become unstable as the difference in effect approaches zero, since the denominator vanishes and the ratio tends to infinity regardless of the cost difference. Ratios also cannot distinguish an option that is cheaper and less effective from one that is dearer and more effective, since both produce a positive value. Net benefit avoids both problems by producing a quantity that is linear in the underlying parameters, which means it can be averaged, compared and analysed statistically in ways a ratio cannot. The measure also handles the case where an option is both cheaper and more effective without special treatment, since it simply returns a larger positive value.
Source: Stinnett & Mullahy 1998
How does expected net benefit handle uncertainty?
Because the measure is linear, the expected value of net benefit across simulations equals net benefit calculated at the expected values of the parameters, which is not true of ratios. That property allows the distribution of net benefit to be summarised directly, and the proportion of simulations in which each option has the highest value gives the acceptability at that threshold. The decision follows the highest expected net benefit rather than the highest probability of being best, and the two can differ where distributions are skewed. This linearity is the reason net benefit rather than the ratio is used whenever probabilistic results are being summarised or combined.
Source: Briggs, Claxton & Sculpher 2006
Can expected net benefit be expressed in health rather than money?
Yes, and the two formulations are equivalent. Dividing the cost by the threshold converts it into the health that would be displaced elsewhere, which is then subtracted from the health gained to give net health benefit. This version avoids monetising health and states the result in the units the decision actually concerns, which many find more intuitive. The choice between the two is presentational, since the ordering of options is identical under both. Reporting both forms is common, since the monetary version communicates to finance audiences and the health version to clinical ones without either changing the conclusion.
Source: Stinnett & Mullahy 1998
What does expected net benefit depend on?
The threshold, since the health gain is valued at it and a different threshold changes both the magnitude and potentially the ranking. Results are therefore reported across a range of thresholds rather than at one, which is what the acceptability curve displays. It also depends on all the usual choices in an evaluation, including the comparator, the perspective and the horizon, so a net benefit figure is no more transferable than the ratio it replaces. Reporting the figure at a single threshold without the surrounding range therefore conceals how sensitive the recommendation is to a quantity the analysis did not establish.
Source: Drummond et al. 2015
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Verified by Dr Darrin Baines
British health economist
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Verification date: 12 Sep 2026, 02:07 UTC
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