Concept Architecture
Concept
Theoretically, Multi-Attribute Utility is a utility construct that represents preferences for health states described by multiple attributes or dimensions. It is founded on multi-attribute utility theory (MAUT), which assumes that an individual's overall utility can be derived by combining preferences across separate health dimensions according to specified axioms and preference structures. The concept exists to quantify overall health-related utility while accounting for the contribution of multiple aspects of health simultaneously.
Mathematically, multi-attribute utility is represented by a multi-attribute utility function that combines single-attribute utility functions into an overall utility score. Depending on assumptions regarding preferential independence, the function may take additive, multiplicative or multilinear forms. These functions estimate the overall utility associated with a multidimensional health state.
In practice, multi-attribute utility is implemented through preference-based health status instruments such as EQ-5D, HUI, AQoL and 15D. Utility functions are estimated from population preference studies using recognised elicitation methods, including standard gamble, time trade-off and discrete choice experiments. The resulting utility values are used to estimate quality-adjusted life years and inform cost-utility analyses.
Purpose
Used to quantify overall health state utility by combining preferences across multiple health dimensions, supporting quality-adjusted life year estimation, cost-utility analysis and health technology assessment.
Mathematical Formulae
Primary Formula
For an additive multi-attribute utility function:
U(x) = ????� w?u?(x?)
where:
- U(x) = overall utility
- u?(x?) = single-attribute utility for attribute i
- w? = attribute weight
- n = number of attributes
Supporting Formulae
A commonly used multiplicative form is:
1 + kU = ????�(1 + kw?u?)
where:
- k = scaling constant
- U = overall utility
- w? = attribute weight
- u? = single-attribute utility
Related Mathematical Methods
- Multi-attribute utility theory
- Additive utility models
- Multiplicative utility models
- Standard gamble
- Time trade-off
- Discrete choice experiments
- Utility function estimation
Example
A health state is described using three attributes with utilities of 0.90, 0.80 and 0.70 and corresponding weights of 0.40, 0.35 and 0.25. Using an additive multi-attribute utility function:
U = (0.40 ? 0.90) + (0.35 ? 0.80) + (0.25 ? 0.70) = 0.815
The estimated overall utility of 0.815 can then be used in QALY estimation for economic evaluation.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| SUMPRODUCT | =SUMPRODUCT(B2:D2,B$1:D$1) | Calculates an additive multi-attribute utility score from attribute utilities and weights. |
| PRODUCT | =PRODUCT(1+$F$1*B2:D2*B$1:D$1) | Supports implementation of multiplicative utility functions. |
| XLOOKUP | =XLOOKUP(A2,Tariff[Level],Tariff[Utility]) | Retrieves single-attribute utility values from a published tariff. |
| SUM | =SUM(B2:D2) | Aggregates component utilities where appropriate during intermediate calculations. |
VBA (Optional)
Automate the calculation of multi-attribute utility scores from questionnaire responses using published utility functions and value sets.
Sources
- Keeney RL, Raiffa H. Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Wiley.
- Torrance GW. Utility Approach to Measuring Health-Related Quality of Life. Journal of Chronic Diseases. 1987.
- Brazier J, Ratcliffe J, Salomon JA, Tsuchiya A. Measuring and Valuing Health Benefits for 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.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
Related Concepts (2)
Library
Publications
1
Measuring and Valuing Health Benefits for Economic Evaluation — Brazier, Ratcliffe, Salomon & Tsuchiya, 2nd Edition ed., 2017 (Oxford University Press)
The comprehensive text on the measurement and valuation of health benefits for economic evaluation — defining health, valuation techniques (time trade-off, standard gamble), whose values to use, preference-based measures (EQ-5D, SF-6D), and the construction of QALYs.
BookView source →
Frequently Asked Questions (6)
What is multi-attribute utility?
A utility value derived by combining preference weights across several distinct attributes of an outcome into a single overall measure.
Source: Keeney & Raiffa 1976
What problem does multi-attribute utility theory solve?
Directly valuing every possible combination of several health attributes is impractical, because the number of combinations grows quickly and no survey could cover them all. Multi-attribute utility theory addresses this by valuing each attribute's levels separately and specifying a rule for combining those partial values into an overall utility for any state. This lets a scoring formula assign a value to combinations that were never directly presented to respondents. Torrance and colleagues (1996) applied the approach to build health index scoring functions.
Source: Torrance et al. 1996
How is a multi-attribute utility function constructed?
A multi-attribute utility function is constructed by valuing each attribute on its own scale and specifying how the attributes combine, using a form, such as additive or multiplicative, chosen according to how the attributes interact. The combining function requires weights for the attributes and, in the multiplicative form, a parameter capturing their interaction, all derived from preference elicitation. Applying the function to an outcome's levels on each attribute yields its overall utility.
Source: Keeney & Raiffa 1976
When is an additive or multiplicative form used?
An additive form, summing the weighted attribute values, is used when the attributes are preferentially independent in a strong sense, so that the value of one does not depend on the levels of others. A multiplicative form, which allows interaction, is used when this independence holds only weakly, so that the attributes' contributions are not simply additive. Health utility instruments often use a multiplicative form, since health dimensions interact in determining overall health.
Source: Keeney & Raiffa 1976
How is multi-attribute utility applied to health?
In health, multi-attribute utility underlies instruments such as the Health Utilities Index, EQ-5D, and others that describe health on several dimensions and combine the dimension levels into a single utility using a function derived from population preferences. The theory provides the basis for aggregating valuations across dimensions into one index on a scale from death to full health. This allows a multidimensional description of health to be reduced to a single value for economic evaluation.
Source: Keeney & Raiffa 1976
What are the assumptions of multi-attribute utility?
Multi-attribute utility rests on assumptions about the independence of the attributes, which determine the form of the combining function: the additive form requires strong preferential and utility independence, the multiplicative form weaker conditions. These assumptions may not hold exactly, so the chosen form is an approximation of how preferences over the attributes actually combine. Where they fail, the aggregated utility can misrepresent the value of some combinations, which is a limitation of applying the theory.
Source: Keeney & Raiffa 1976
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 1 Sep 2025
Content version: 1.0.0
Canonical Identity
- Term code
- HE-EE-HU-051
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