Concept Architecture
Concept
Theoretically, D-Efficient Design is an experimental design methodology that selects combinations of attribute levels to maximise the statistical efficiency of parameter estimation in stated preference studies, including discrete choice experiments. It is founded on optimal experimental design theory and information theory, and exists to minimise the uncertainty of estimated model parameters while reducing respondent burden.
Mathematically, D-Efficient Design is based on maximising the information contained within the design matrix by minimising the determinant of the variance-covariance matrix of the estimated parameters. The resulting design provides the most precise parameter estimates for a given sample size and set of design constraints, often incorporating prior parameter estimates to further improve efficiency.
In practice, D-Efficient Designs are generated using specialised design software before data collection. They are widely used in health economics for discrete choice experiments, conjoint analysis and preference elicitation studies to estimate preferences, willingness to pay and trade-offs between healthcare attributes with greater statistical precision than traditional orthogonal designs.
Purpose
Used to construct statistically efficient experimental designs, minimise parameter uncertainty, reduce sample size requirements, improve estimation precision, and support preference elicitation in health economics.
Mathematical Formulae
Primary Formula
D-efficiency = |I(?)??|^(1/p)
or, equivalently, optimisation seeks to minimise:
|I(?)??|
where:
- I(?) = Fisher information matrix
- p = number of estimated parameters
Supporting Formulae
I(?) = X?WX
where:
- X = design matrix
- W = weighting matrix determined by the assumed choice model
Related Mathematical Methods
- Optimal experimental design
- Fisher information matrix
- Discrete Choice Experiment (DCE)
- Multinomial logit model
- Bayesian D-efficient design
- Utility maximisation
Example
A discrete choice experiment is being developed to evaluate patient preferences for treatments defined by five attributes. Rather than using every possible attribute combination, a D-efficient algorithm selects 24 choice sets that minimise the determinant of the parameter variance-covariance matrix. The resulting design achieves more precise utility estimates than an orthogonal design using the same number of respondents.
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 of the information matrix. |
| 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 construction and evaluation of candidate D-efficient experimental designs by comparing alternative design matrices and selecting the design with the highest statistical efficiency.
Sources
- Rose JM, Bliemer MCJ. Constructing Efficient Stated Choice Experimental Designs. Transport Reviews. 2009.
- Bridges JFP, Hauber AB, Marshall D, et al. Conjoint Analysis Applications in Health: A Checklist. Value in Health. 2011.
- Louviere JJ, Hensher DA, Swait JD. Stated Choice Methods: Analysis and Applications. 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.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
Related Concepts (3)
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 a D-efficient design?
An experimental design for a discrete choice experiment built to minimise the statistical variance of estimated attribute parameters for a fixed number of tasks.
Source: Huber & Zwerina 1996
How does a D-efficient design differ from an orthogonal one?
An orthogonal design varies attributes independently of one another, which is the classical criterion and treats every parameter as equally worth estimating. A D-efficient design instead minimises a summary of the variance of the estimated parameters, which requires assumptions about their likely values before the data are collected. Where those assumptions are roughly correct, the D-efficient design yields more precise estimates from the same number of tasks. Where they are badly wrong, it can perform worse than a simple orthogonal design, so the gain is conditional rather than guaranteed.
Source: Huber & Zwerina 1996
What prior information does a D-efficient design require?
It requires an assumed value for each parameter, since the variance being minimised depends on where the parameters actually lie. Priors are usually taken from a pilot study, from published estimates for similar attributes, or from the expected sign alone where nothing better exists. Designs built on the sign of each coefficient without a magnitude are common and capture part of the available gain. The priors should be reported, because a reader cannot otherwise judge how much the design depended on them.
Source: Huber & Zwerina 1996
What does a D-efficient design achieve in practice?
It reduces the number of respondents or tasks needed for a given precision, which matters where recruitment is expensive or the population is small. It also avoids the dominated pairs that random or orthogonal construction can generate, since a choice set in which one option is better on every attribute yields no information about trade-offs. The improvement is real but modest in most applications, and it is smaller than the improvement available from reducing the number of attributes to something respondents can process.
Source: Lancsar & Louviere 2008
What are the limitations of a D-efficient design?
Efficiency is defined for a specified model, so a design optimised for a simple additive specification may not suit a model allowing preferences to vary between respondents. Optimising for statistical precision can produce choice sets that are difficult for respondents, since the most informative comparisons are the closest ones. And the criterion says nothing about whether the alternatives presented are plausible, so plausibility constraints must be imposed separately and will reduce the achievable efficiency.
Source: healtheconomics.wiki
What should a study report about its D-efficient design?
The design criterion used, the priors assumed and their source, the number of choice sets and how they were blocked across respondents, and any constraints imposed to exclude implausible or dominated combinations. Reporting the efficiency measure itself is less useful than reporting these inputs, since the measure cannot be interpreted without them and is not comparable between studies with different attributes. Providing the design itself, or the software and settings used to generate it, allows another analyst to reproduce it, which published choice experiments rarely permit.
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
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/d-efficient-design
- Term code
- HE-EE-CBA-015
Stable URI · Machine-readable · Resolvable · CC BY 4.0