Concept Architecture
Concept
Theoretically, Pairwise Comparison is a preference elicitation method in which respondents evaluate two alternatives at a time and indicate which is preferred according to a specified criterion. It is founded on random utility theory and comparative judgement theory, providing a simple framework for eliciting preferences while reducing cognitive burden. In health economics, pairwise comparisons are used in stated preference studies, health state valuation and multi-criteria decision analysis.
Mathematically, Pairwise Comparison models the probability that one alternative is preferred over another as a function of the difference in their underlying utilities. Under random utility theory, observed choices are used to estimate latent preference parameters using discrete choice models such as the conditional logit model.
In practice, Pairwise Comparison is implemented by presenting respondents with repeated pairs of healthcare interventions, health states or treatment attributes and recording the preferred option. The resulting data are analysed to estimate preference weights, willingness-to-pay values or relative importance of attributes for use in economic evaluation and health technology assessment.
Purpose
Used to elicit preferences by comparing two alternatives at a time and to estimate the relative value of healthcare interventions, health states or treatment attributes.
Mathematical Formulae
Primary Formula
Under the conditional logit model:
P(i ? j) = exp(U?) / (exp(U?) + exp(U?))
where:
- P(i ? j) = probability that alternative i is preferred to alternative j
- U? = utility of alternative i
- U? = utility of alternative j
Supporting Formulae
Random utility model:
U? = V? + �?
where:
- V? = systematic utility
- �? = random error component
Related Mathematical Methods
- Random Utility Theory
- Conditional Logit Model
- Multinomial Logit Model
- Discrete Choice Experiment
- Maximum Likelihood Estimation
Example
A preference study asks 500 respondents to choose between two osteoporosis treatments that differ in fracture reduction, dosing frequency and monthly cost. Each respondent completes 12 pairwise comparisons. Conditional logit analysis estimates the utility associated with each attribute level, allowing willingness-to-pay for improved treatment effectiveness to be calculated.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| IF | =IF(B2>C2,1,0) | Records the preferred alternative in each pair |
| COUNTIF | =COUNTIF(D2:D501,1) | Counts the number of times an alternative is preferred |
| SUM | =SUM(D2:D501) | Summarises observed choices before statistical analysis |
| AVERAGE | =AVERAGE(E2:E501) | Calculates mean preference scores where applicable |
VBA (Optional)
Automate the generation of randomised pairwise comparison tasks and export response datasets for discrete choice modelling.
Sources
- McFadden D. Conditional Logit Analysis of Qualitative Choice Behavior. In: Zarembka P, ed. Frontiers in Econometrics. Academic Press.
- Louviere JJ, Hensher DA, Swait JD. Stated Choice Methods: Analysis and Applications. 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.
- Train KE. Discrete Choice Methods with Simulation. Cambridge University Press.
Related Concepts (2)
Library
Publications
3
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 →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.
Frequently Asked Questions (6)
What is a pairwise comparison?
A comparison of exactly two interventions at a time, used as a building block within a fully incremental analysis of several options.
Source: Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press; 2015.
What does a pairwise comparison establish?
The difference in cost and in effect between exactly two options, from which an incremental ratio or a net benefit figure can be calculated. It is the elementary unit of economic evaluation, since every incremental measure is a comparison between two alternatives, and analyses of several options are built from a sequence of such comparisons rather than from anything more elaborate. Both incremental measures reduce to it, since a ratio and a net benefit figure are alternative summaries of the same two differences in cost and effect.
Source: Drummond et al. 2015
Why is a pairwise comparison insufficient when several options exist?
Because the relevant comparator for each option is the next best surviving alternative rather than a fixed reference, and that cannot be identified without first establishing which options survive dominance. Comparing every option separately against a common baseline produces ratios that look like incremental figures and cannot be compared against a threshold, and the resulting ranking can select the wrong alternative. The error is easy to make because the arithmetic proceeds normally and the resulting figures look like valid incremental ratios.
Source: Drummond et al. 2015
How does a pairwise comparison fit into a fully incremental analysis?
Options are ordered by increasing effect, dominated and extendedly dominated options are removed, and a pairwise comparison is then made between each surviving option and the one immediately below it. The sequence of pairwise results forms the frontier, along which each step costs more per unit of health than the last. The pairwise calculation is therefore correct at every step, provided the ordering and removal were done first.
Source: Drummond et al. 2015
When is a pairwise comparison sufficient on its own?
Where only two options are genuinely available, which covers most appraisals of a single new technology against established care. It is also sufficient where other alternatives have already been excluded for clinical or practical reasons, provided that exclusion is stated rather than implied. Outside these situations, presenting a pairwise result as though it settled the choice omits the alternatives that were not examined. It is also sufficient where the analysis is being conducted to inform a single yes or no decision about adding one technology to an existing pathway.
Source: Gold, Siegel, Russell & Weinstein 1996
What should a pairwise comparison report?
The incremental cost and incremental effect separately as well as any summary measure, since the two increments identify which quadrant the comparison falls in and a ratio alone does not. The comparator should be named with its dose and setting. And where other options exist but were not compared, they should be listed with the reason, so a reader can judge whether the pair examined was the relevant one.
Source: Drummond et al. 2015
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 7 Aug 2025
Content version: 1.0.0
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- Persistent URI
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- Term code
- HE-EE-CEA-049
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