Concept Architecture
Concept
Theoretically, Experimental Design is the systematic process of planning a study to ensure that the effects of one or more interventions can be estimated accurately while minimising bias, confounding and random error. It is founded on the principles of statistical inference, randomisation and controlled comparison, and exists to produce valid and efficient evidence for evaluating causal relationships between interventions and outcomes.
Mathematically, Experimental Design is represented through a statistical design matrix that specifies the allocation of experimental units to treatment conditions and defines the estimable model parameters. The mathematical framework supports unbiased estimation of treatment effects and quantification of uncertainty using statistical models such as analysis of variance, regression and generalised linear models.
In practice, Experimental Design is implemented by defining the study population, selecting interventions and comparators, determining sample size, specifying randomisation procedures, collecting outcome data and analysing treatment effects using appropriate statistical methods. In health economics, experimental designs underpin clinical trials, preference elicitation studies, valuation studies and economic evaluations conducted alongside randomised controlled trials.
Purpose
Used to generate valid evidence on treatment effects, minimise bias, improve statistical efficiency, support causal inference, and provide reliable data for health economic evaluation and decision making.
Mathematical Formulae
Primary Formula
There is no universally recognised canonical mathematical formula.
Supporting Formulae
General linear model:
Y = X? + �
where:
- Y = observed outcomes
- X = design matrix
- ? = model parameters
- � = random error
Related Mathematical Methods
- Randomisation
- Analysis of variance (ANOVA)
- Linear regression
- Generalised linear models (GLMs)
- Factorial design
- Sample size calculation
- Hypothesis testing
Example
A randomised controlled trial compares a new antihypertensive medicine with standard care. Two hundred patients are randomly allocated equally between treatment groups. Costs and QALYs are measured over 12 months, and differences between groups are estimated using regression models adjusted for baseline characteristics. The resulting estimates form the basis of the economic evaluation.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| RAND | =RAND() | Generates random numbers for treatment allocation. |
| RANK | =RANK(A2,$A$2:$A$201) | Creates a randomisation sequence. |
| AVERAGE | =AVERAGE(B2:B101) | Calculates mean outcomes for each treatment group. |
| STDEV.S | =STDEV.S(B2:B101) | Estimates variability within treatment groups. |
| T.TEST | =T.TEST(B2:B101,C2:C101,2,2) | Compares mean outcomes between treatment groups. |
VBA (Optional)
Automate participant randomisation, generation of allocation schedules and production of summary statistics for experimental studies.
Sources
- 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.
- Montgomery DC. Design and Analysis of Experiments.
- NICE. Health Technology Evaluation Manual.
- Husereau D, Drummond M, Augustovski F, et al. CHEERS 2022 Statement. BMJ. 2022.
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 experimental design?
The systematic planning of an empirical study to allow valid causal inference, including decisions about randomisation, control groups, and study conditions.
Source: Fisher 1935
What principles underlie experimental design?
Three, set out in the foundational account and still standard. Randomisation assigns units to conditions by chance, which removes systematic differences between the groups and provides the basis for the statistical inference. Replication provides enough units to estimate the variability against which any difference must be judged. Local control, achieved by grouping similar units before assignment, removes known sources of variation so that the comparison is made within groups rather than across them. Each addresses a different threat, and omitting any one weakens the inference in a different way.
Source: Fisher 1935
Why does experimental design matter for causal inference?
Because it establishes that the groups being compared differ only in the condition applied. Without random assignment, the units receiving each condition differ in ways that may also determine the outcome, and no analysis can distinguish the effect of the condition from the effect of those differences. Design settles this before any data are collected, which is why a well designed study can be analysed simply and a poorly designed one cannot be rescued by sophisticated analysis afterwards.
Source: Fisher 1935
What is a factorial experimental design?
The units assigned are combinations of attribute levels rather than people, and the design determines which combinations are shown and in what groupings. The objective is to vary attributes independently of one another, so that the effect of each can be estimated separately, and to extract the most information from a limited number of questions. Designs are constructed to maximise the precision of the estimated parameters given assumptions about their likely values, which is a different optimisation from the one used in trials but rests on the same principle of controlled variation.
Source: Louviere, Hensher & Swait 2000
What distinguishes a within-subjects from a between-subjects experimental design?
A between-subjects experimental design allocates each participant to a single condition and compares outcomes across groups, whereas a within-subjects design exposes the same participant to several conditions in sequence and compares their responses. The within-subjects form removes variation between individuals and so needs fewer participants for a given precision, but it risks order and carryover effects that the sequence itself introduces. The between-subjects form avoids those effects at the cost of larger samples. Shadish, Cook and Campbell (2002) treat the choice as a trade-off between statistical efficiency and the threats each arrangement admits.
Source: Shadish, Cook & Campbell 2002
What limits experimental design in practice?
Randomisation is frequently impossible where the intervention is a policy or a service configuration applied to whole populations. Replication is limited by cost and by the number of units available, which in cluster designs can be very few. Local control requires knowing in advance which variables to group on. In stated preference work the constraint is different again, since the design can be made as efficient as the analyst wishes and the binding limit is what respondents can process before they begin simplifying.
Source: healtheconomics.wiki
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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- Term code
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