Concept Architecture
Concept
Theoretically, an Efficient Design is an experimental design constructed to maximise the statistical precision of parameter estimates obtained from stated preference studies while minimising the amount of information required from respondents. It is founded on optimal experimental design theory, information theory and random utility theory, and exists to improve the efficiency of estimating preferences by selecting the most informative combinations of attribute levels.
Mathematically, an Efficient Design is represented by optimisation of the statistical information contained within the design matrix. Efficiency is evaluated using criteria such as D-efficiency, A-efficiency or Bayesian efficiency, which minimise functions of the variance-covariance matrix of the estimated parameters and thereby reduce estimation uncertainty.
In practice, Efficient Designs are generated using specialised experimental design software before data collection. They are widely used in discrete choice experiments, conjoint analysis and health preference studies to reduce sample size requirements, improve estimation precision and produce reliable estimates of preferences and willingness to pay.
Purpose
Used to construct statistically efficient experimental designs, maximise information from preference studies, reduce estimation uncertainty, minimise respondent burden, and improve the precision of health preference estimates.
Mathematical Formulae
Primary Formula
There is no universally recognised canonical mathematical formula.
Supporting Formulae
For D-efficiency:
D-efficiency = |I(?)??|^(1/p)
where:
- I(?) = Fisher information matrix
- p = number of estimated parameters
Information matrix:
I(?) = X?WX
where:
- X = design matrix
- W = weighting matrix
Related Mathematical Methods
- D-efficient design
- Bayesian efficient design
- A-efficient design
- Fisher information matrix
- Random utility theory
- Discrete Choice Experiment (DCE)
Example
A discrete choice experiment is designed to estimate patient preferences for five treatment attributes. Rather than using every possible attribute combination, an efficient design algorithm selects 24 choice sets that maximise statistical information while maintaining respondent feasibility. The resulting design produces more precise parameter estimates than a conventional orthogonal design using the same sample size.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| MMULT | =MMULT(TRANSPOSE(A2:E25),A2:E25) | Forms the information matrix from the design matrix. |
| MDETERM | =MDETERM(F2:J6) | Calculates the determinant used to assess design efficiency. |
| MINVERSE | =MINVERSE(F2:J6) | Computes the inverse information matrix for variance estimation. |
| TRANSPOSE | =TRANSPOSE(A2:E25) | Creates the transposed design matrix for matrix calculations. |
VBA (Optional)
Automate evaluation of candidate experimental designs and identify the design with the highest statistical efficiency according to the selected optimality criterion.
Sources
- Rose JM, Bliemer MCJ. Constructing Efficient Stated Choice Experimental Designs. Transport Reviews. 2009.
- 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. 2011.
- Train KE. Discrete Choice Methods with Simulation. Cambridge University Press.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
Related Concepts (3)
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 an efficient design?
An experimental design built to maximise the statistical information obtained from a given number of choice tasks.
Source: Huber & Zwerina 1996
What does an efficient design optimise?
It minimises a summary of the variance of the parameters to be estimated, so that a fixed number of choice tasks yields the most precise estimates available. That requires assumptions about where the parameters lie, since the variance depends on their values, which is why priors from a pilot or from published work are needed before the design is generated. Priors expressing only the expected sign of each coefficient, without a magnitude, capture part of the available gain and are common where no pilot has been run.
Source: Huber & Zwerina 1996
How does an efficient design differ from an orthogonal one?
An orthogonal design varies attributes independently of one another and treats every parameter as equally worth estimating, which requires no prior information. An efficient design uses priors to concentrate precision where it is wanted. Where the priors are roughly right the efficient design performs better; where they are badly wrong it can perform worse. The practical position is that an efficient design is worth generating whenever any prior information exists, and that an orthogonal design remains a defensible fallback when none does.
Source: Huber & Zwerina 1996
What practical gains does an efficient design deliver?
It reduces the sample or the number of tasks needed for a given precision, which matters where recruitment is costly or the population is small. It also avoids dominated pairs, since a choice set in which one alternative is better on every attribute yields no information about trade-offs. The improvement is real and usually smaller than the gain from reducing the number of attributes to what respondents can process.
Source: Lancsar & Louviere 2008
What are the limitations of an efficient design?
Efficiency is defined for a specified model, so a design optimised for a simple additive specification may not suit one allowing preferences to vary between respondents. Optimising for precision can produce difficult choice sets, since the most informative comparisons are the closest ones. And the criterion says nothing about plausibility, so constraints excluding implausible combinations must be imposed separately. Efficiency also says nothing about whether respondents can complete the task, so a statistically excellent design can still fail if it exceeds what people will engage with.
Source: Louviere, Hensher & Swait 2000
What should be reported about an efficient design?
The criterion used, the priors assumed and their source, the number of choice sets and how they were divided among respondents, and any constraints applied to exclude implausible or dominated combinations. Supplying the design itself allows another analyst to reproduce the study, which published choice experiments rarely permit. Reporting the efficiency measure itself adds little, since it cannot be interpreted without the priors and is not comparable between studies with different attributes.
Source: Bridges et al. 2011
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 31 Jul 2025
Content version: 1.0.0
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- Persistent URI
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- Term code
- HE-EE-CBA-017
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