Concept Architecture
Concept
Theoretically, a Utility Function is a mathematical representation of an individual's preferences over alternative bundles of goods, services or health states. It originates from consumer choice theory and expected utility theory, providing a formal framework for ranking alternatives according to the utility they generate. In health economics, utility functions underpin models of individual decision-making, health state valuation, willingness-to-pay analysis and expected utility under uncertainty.
Mathematically, a utility function assigns a numerical value to each alternative while preserving preference ordering. A utility function may be expressed in general form as U(x), where x represents a vector of goods, health attributes or outcomes. Utility functions are used to represent optimisation problems in which individuals maximise utility subject to budget, time or resource constraints.
In practice, utility functions are specified within economic and decision-analytic models and estimated using revealed preference data, stated preference methods, discrete choice experiments, contingent valuation, standard gamble, time trade-off or econometric estimation. Estimated utility functions are subsequently used to predict behaviour, derive willingness-to-pay, estimate demand, value health outcomes and support health economic evaluation.
Purpose
Used to represent preferences mathematically, model individual decision-making, estimate behavioural responses, derive demand functions, value health outcomes, analyse choices under uncertainty and support economic evaluation and health technology assessment.
Mathematical Formulae
Primary Formula
U = U(x?, x?, ?, x?)
where U denotes utility and x?, ?, x? represent goods, services, health states or attributes.
Supporting Formulae
Expected utility:
EU = ????� p?U(x?)
Utility maximisation:
max U(x)
Subject to:
????� p?x? � M
where M is available income or resources.
Related Mathematical Methods
- Utility maximisation
- Constrained optimisation
- Expected utility theory
- Random utility models
- Discrete choice modelling
- Econometric estimation
- Willingness-to-pay estimation
Example
A patient chooses between two treatment options.
Treatment A provides a utility of 0.82.
Treatment B provides a utility of 0.74.
The patient prefers Treatment A because:
0.82 > 0.74
If Treatment A has a 70% probability of success and Treatment B has a 90% probability of success with utility 0.74, expected utility for Treatment A is:
EU = 0.70 ? 0.82 = 0.574
Expected utility for Treatment B is:
EU = 0.90 ? 0.74 = 0.666
Despite its lower health-state utility, Treatment B provides greater expected utility because of its higher probability of success.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| SUMPRODUCT | =SUMPRODUCT(B2:B6,C2:C6) | Calculate expected utility from probabilities and utilities |
| MAX | =MAX(B2:B5) | Identify the preferred alternative |
| INDEX | =INDEX(A2:A5,MATCH(MAX(B2:B5),B2:B5,0)) | Return the option with the highest utility |
| Solver | Maximise utility subject to budget constraints | Utility maximisation in constrained optimisation models |
VBA (Optional)
Automate utility maximisation across multiple decision scenarios and generate comparative expected utility analyses for alternative healthcare interventions.
Sources
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- von Neumann J, Morgenstern O. Theory of Games and Economic Behavior. Princeton University Press.
- Fishburn PC. Utility Theory for Decision Making. Wiley.
- ISPOR Good Practice Reports.
- NICE. Health Technology Evaluation Manual.
Related Concepts (2)
Library
Publications
1
Conjoint Analysis Applications in Health — A Checklist: A Report of the ISPOR Good Research Practices for Conjoint Analysis Task Force — Bridges, Hauber, Marshall, Lloyd, Prosser, Regier, Johnson & Mauskopf, Vol. 14, No. 4 ed., 2011 (Value in Health)
The ISPOR good-practice checklist for conjoint analysis and discrete-choice experiments in health — the stated-preference methods used to elicit patient and public preferences over treatment attributes for value assessment and priority-setting.
Journal ArticleView source →
Frequently Asked Questions (6)
What is an utility function?
A mathematical representation of preferences that assigns a numerical value to each possible outcome, so higher-utility outcomes are preferred.
Source: von Neumann & Morgenstern 1944
What does a utility function represent?
A utility function is a rule that assigns a number to each outcome so that outcomes preferred more receive higher numbers, giving a compact representation of an individual's preferences. It does not measure satisfaction on an absolute scale; it orders outcomes and, under stronger assumptions, reflects the strength of preference between them. In economic evaluation it provides the basis for valuing health states and for combining outcomes under uncertainty, where choices are made over probabilities rather than certain results.
Source: von Neumann & Morgenstern 1944
How does a utility function handle choices under uncertainty?
Where outcomes are uncertain, expected utility theory holds that an option can be valued by the average of its outcome utilities weighted by their probabilities, provided preferences satisfy consistency conditions such as transitivity and independence. The option with the higher expected utility is preferred. This lets a single function represent attitudes to risk as well as to outcomes, since the curvature of the function determines whether an individual accepts or avoids a fair gamble. The approach underlies the valuation of health states by standard gamble.
Source: von Neumann & Morgenstern 1944
How is a utility function used to value health?
In economic evaluation, health states are placed on a utility scale anchored so that death takes the value zero and full health takes one, allowing time in different states to be weighted by their utility. Values are elicited by methods such as the standard gamble, which draws directly on expected utility reasoning, or the time trade-off. The resulting weights let length of life and quality of life be combined into a single measure, most commonly the quality-adjusted life year.
Source: Drummond et al. 2015
What assumptions does a utility function rest on?
Representing preferences by a utility function requires that they are complete, so any two outcomes can be compared, and transitive, so rankings do not cycle. Expected utility adds further conditions, including that preferences over a gamble depend only on its outcomes and their probabilities and not on how it is framed. Observed choices often violate these, since people respond to framing and to how probabilities are presented, which limits how far a single function describes actual behaviour.
Source: von Neumann & Morgenstern 1944
How does a utility function differ from a value function?
A utility function derived from choices under risk encodes attitude to risk as well as preference over certain outcomes, so its scale carries information about how gambles are valued. A value function represents preferences over certain outcomes alone and need not predict choices involving probability. The distinction matters when health-state weights obtained from a risk-based method such as the standard gamble are compared with those from a riskless method such as the time trade-off, since the two need not coincide.
Source: Drummond et al. 2015
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 4 Aug 2025
Content version: 1.0.0
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- Persistent URI
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- Term code
- HE-EE-CBA-051
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