Concept Architecture
Concept
Theoretically, Part-Worth Utility is the numerical value assigned to an individual attribute level in a stated preference model, representing its contribution to the overall utility of an alternative. It is founded on random utility theory and conjoint measurement theory, where the total utility of a healthcare intervention is decomposed into the sum of the utilities associated with its individual attributes. In health economics, part-worth utilities are estimated to quantify patient, clinician or public preferences for healthcare interventions and health technologies.
Mathematically, Part-Worth Utility is represented as a component of the systematic utility function in a discrete choice model. Each attribute level is assigned a coefficient estimated from observed choices, and the sum of these coefficients represents the systematic utility of an alternative. The coefficients are typically estimated using maximum likelihood methods within conditional logit, mixed logit or related econometric models.
In practice, Part-Worth Utilities are estimated from data collected in discrete choice experiments or conjoint analyses. The estimated utilities are used to calculate attribute importance, predict choices, estimate willingness-to-pay and inform health technology assessment and reimbursement decisions.
Purpose
Used to quantify the contribution of individual attribute levels to overall utility, enabling estimation of preferences, prediction of choices and calculation of willingness-to-pay in health economics.
Mathematical Formulae
Primary Formula
V? = ?? + ????? ??x??
where:
- V? = systematic utility of alternative i
- ?? = part-worth utility associated with attribute level k
- x?? = indicator or coded variable for attribute level k
Supporting Formulae
Random utility model:
U? = V? + �?
Conditional choice probability:
P(i) = exp(V?) / ?? exp(V?)
Related Mathematical Methods
- Random Utility Theory
- Conditional Logit Model
- Mixed Logit Model
- Maximum Likelihood Estimation
- Conjoint Analysis
- Discrete Choice Experiment
Example
A discrete choice experiment evaluates preferences for diabetes treatments using attributes for HbA1c reduction, dosing frequency, risk of hypoglycaemia and monthly cost. The estimated part-worth utility for once-weekly dosing is 0.62, while the utility for daily dosing is 0.00. Combined with the utilities of the remaining attributes, these coefficients are summed to predict treatment choice probabilities and estimate willingness-to-pay.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| SUMPRODUCT | =SUMPRODUCT(B2:E2,B10:E10) | Calculates systematic utility from estimated part-worth utilities |
| SUM | =SUM(B10:E10) | Sums utility contributions across attribute levels |
| EXP | =EXP(F2) | Calculates the exponential utility for logit choice probabilities |
| IF | =IF(F2>F3,""Choose A"",""Choose B"") | Illustrates deterministic comparison of predicted utilities |
VBA (Optional)
Automate calculation of total utilities and predicted choice probabilities for multiple respondent profiles using estimated part-worth utilities.
Sources
- Louviere JJ, Hensher DA, Swait JD. Stated Choice Methods: Analysis and Applications. Cambridge University Press.
- Train KE. Discrete Choice Methods with Simulation. Cambridge University Press.
- Bridges JFP, Hauber AB, Marshall D, et al. Conjoint Analysis Applications in Health: A Checklist. Value in Health.
- ISPOR Conjoint Analysis Good Research Practices Task Force Reports.
- McFadden D. Conditional Logit Analysis of Qualitative Choice Behavior. In: Frontiers in Econometrics. Academic Press.
Related Concepts (2)
Library
Publications
1
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.
Frequently Asked Questions (6)
What is part-worth utility?
The contribution of a single attribute level to an individual's overall utility for a good, estimated from a conjoint or choice experiment.
Source: Luce & Tukey 1964
How is a part-worth utility estimated?
From the pattern of choices respondents make between alternatives described by combinations of attribute levels. The model assumes each level contributes a fixed amount to the overall attractiveness of an option, and estimation recovers those contributions from the observed choices. The result is a weight for every level of every attribute, expressed on an arbitrary scale whose units have no meaning in themselves. The estimated values are identified only up to scale, so their absolute size carries no meaning and only the relations between them can be interpreted.
Source: Luce & Tukey 1964
How is a part-worth utility interpreted?
Only in relation to other part-worths, since the scale has no natural units. Differences between levels within an attribute show how much that change matters; comparing the range across attributes shows their relative importance. Dividing a part-worth by the coefficient on cost expresses it in money, and dividing by a health coefficient expresses it in health, which is how the arbitrary scale is converted into something interpretable.
Source: Louviere, Hensher & Swait 2000
What does the range of part-worth utilities indicate?
The importance of an attribute within the design, calculated as the difference between its highest and lowest part-worth. This is a property of the levels presented as much as of preferences, since an attribute varied across a narrow range will show a small range of part-worths regardless of how much it matters. Comparisons of importance are therefore conditional on the design and should not be reported without the levels used.
Source: Lancsar & Louviere 2008
Do part-worth utilities vary between respondents?
Almost always, and models assuming a single set of part-worths for everyone usually describe the data poorly. Specifications allowing the weights to vary across individuals, or positing a small number of groups with distinct preferences, generally fit better and reveal heterogeneity that an average conceals. Reporting only mean part-worths can therefore describe a preference structure that no respondent actually holds. Reporting the distribution of part-worths across respondents, rather than the mean alone, is therefore the more informative presentation where heterogeneity is present.
Source: Greene & Hensher 2003
What are the limitations of part-worth utility estimates?
They apply only at the levels presented, so interpolation between them and extrapolation beyond them are unsupported by the design. They are distorted where respondents ignored an attribute rather than trading it off. And they describe stated choices in a hypothetical setting, so their relation to behaviour under real consequences remains uncertain. They also depend on the attributes included, so any characteristic omitted from the design is implicitly assigned no weight at all.
Source: Bridges et al. 2011
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 1 Aug 2025
Content version: 1.0.0
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- Persistent URI
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- Term code
- HE-EE-CBA-039
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