Concept Architecture
Concept
Theoretically, Randomization is the assignment of study participants to treatment groups using a chance mechanism that is independent of participant characteristics, investigator judgement and anticipated outcomes. It is grounded in probability theory and experimental design and exists to prevent systematic allocation bias, balance known and unknown prognostic factors on average and support valid causal inference. In health economics, randomisation strengthens the internal validity of clinical-effectiveness evidence used to estimate costs, health outcomes and cost-effectiveness.
Mathematically, randomisation represents treatment assignment as a random variable with predefined allocation probabilities. For participant i and treatment group k, the probability of assignment is expressed as P(Z? = k) = p?, where the group probabilities sum to one. Under equal allocation between two groups, each participant has probability 0.5 of assignment to either group, while restricted procedures such as block or stratified randomisation modify the assignment mechanism to improve balance without removing its probabilistic basis.
In practice, randomisation is implemented using validated computer-generated sequences, central randomisation services, interactive response technologies or securely prepared allocation schedules. The method may use simple, block, stratified, minimisation-based or response-adaptive procedures, depending on the trial design. Health economic analyses generally preserve randomised treatment groups through intention-to-treat analysis when estimating comparative resource use, costs and health outcomes.
Purpose
Used to prevent allocation bias, balance prognostic characteristics between comparison groups, support unbiased estimation of treatment effects and strengthen the clinical evidence underlying health economic evaluation.
Mathematical Formulae
Primary Formula
P(Z? = k) = p?
????? p? = 1
Supporting Formulae
Equal allocation between two groups:
P(Z? = 1) = P(Z? = 2) = 0.5
Allocation ratio for two groups:
p? / p? = r
Expected number assigned to group k:
E(n?) = np?
Related Mathematical Methods
- Simple randomisation
- Block randomisation
- Stratified randomisation
- Permuted-block randomisation
- Covariate-adaptive randomisation
- Response-adaptive randomisation
- Random permutation
- Intention-to-treat analysis
Example
A randomised controlled trial compares a new diabetes treatment with standard care in 400 participants using equal allocation.
P(New Treatment) = 0.5
P(Standard Care) = 0.5
Expected participants per group = 400 ? 0.5 = 200
The randomisation sequence assigns approximately 200 participants to each group. Differences in treatment costs, quality-adjusted life-years and clinical outcomes are then estimated according to the randomised groups.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| RAND | =RAND() | Generates a uniform random number used to support simple random assignment. |
| IF | =IF(RAND()<0.5,"New Treatment","Standard Care") | Assigns participants between two groups with equal probability. |
| RANK.EQ | =RANK.EQ(B2,$B$2:$B$401,1) | Creates a random ordering of participants from generated random numbers. |
| SORTBY | =SORTBY(A2:A401,RANDARRAY(400)) | Produces a randomly ordered participant list before group allocation. |
| RANDARRAY | =RANDARRAY(400,1) | Generates random values for a complete participant allocation schedule. |
| COUNTIF | =COUNTIF(C2:C401,"New Treatment") | Checks the realised number of participants allocated to a treatment group. |
VBA (Optional)
VBA may automate generation of reproducible randomisation schedules, allocation concealment files and balance checks across treatment groups and strata.
Sources
- Friedman LM, Furberg CD, DeMets DL, Reboussin DM, Granger CB. Fundamentals of Clinical Trials.
- Pocock SJ. Clinical Trials: A Practical Approach.
- Rosenberger WF, Lachin JM. Randomization in Clinical Trials: Theory and Practice.
- Schulz KF, Grimes DA. Generation of allocation sequences in randomised trials: chance, not choice. The Lancet. 2002.
- International Council for Harmonisation. ICH E9: Statistical Principles for Clinical Trials.
- NICE. Health Technology Evaluation Manual.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
Related Concepts (2)
Frequently Asked Questions (6)
What is randomisation?
The process of assigning trial participants to treatment groups by chance, producing groups comparable on both known and unknown influencing factors.
Source: Fisher 1935
Why does randomisation balance even unknown factors?
Assigning patients to groups by chance means that, in a large enough trial, every characteristic, whether recorded or not, tends to be spread evenly between the groups. This is randomisation's great strength, since it balances the confounders a researcher knows to measure and, just as importantly, those they have never thought of or cannot measure, which no statistical adjustment could handle. The groups therefore start alike in every respect except the treatment, so a difference in outcome can be attributed to the treatment. Chance balances the unknown. Schulz and Grimes (2002) explain this.
Source: Schulz & Grimes 2002
How does randomisation work?
Randomisation works by using a chance mechanism, such as random number generation, to allocate participants to treatment groups, so that the assignment is not determined by the participant's or investigator's choice. Methods include simple randomisation, block randomisation to balance group sizes, and stratified randomisation to balance important factors. The allocation is concealed until enrolment to prevent bias. Because assignment is by chance, the groups tend to be similar in all characteristics, both measured and unmeasured, so any difference in outcome can be attributed to the treatments rather than to systematic differences between the groups.
Source: Friedman, Furberg & DeMets 2015
Why is randomisation important?
Randomisation is important because it balances both known and unknown confounding factors across treatment groups, creating comparable groups so that differences in outcome can be attributed to the treatments rather than to pre-existing differences. This is what allows randomised trials to establish causal effects with less bias than observational studies, where groups may differ systematically. Randomisation also supports valid statistical inference and, with allocation concealment, prevents selection bias in forming the groups. Because it underpins the internal validity of a trial, randomisation is the key feature distinguishing experiments from observational studies.
Source: Fisher 1935
How does randomisation control confounding?
Randomisation controls confounding by allocating participants to groups purely by chance, so that confounding factors, whether measured or unmeasured, known or unknown, tend to be distributed similarly across the groups rather than being associated with the treatment. Because the groups are comparable on these factors on average, they cannot systematically bias the comparison, so the difference in outcomes reflects the treatments. This ability to balance unknown as well as known confounders is unique to randomisation, distinguishing it from analytic adjustment, which can address only measured confounders, and giving randomised trials their strength for causal inference.
Source: Fisher 1935
What are the limitations of randomisation?
The limitations of randomisation include that it balances confounders only on average, so with small samples chance imbalances can still occur, which stratified or block randomisation can reduce; that it ensures comparability at baseline but must be protected by allocation concealment and maintained by proper conduct; and that it does not address biases arising after randomisation, such as differential dropout, which require other measures. Randomisation also does not guarantee generalisability. These limitations mean randomisation is combined with adequate sample size, concealment, blinding, and appropriate analysis to realise its benefits fully.
Source: Friedman, Furberg & DeMets 2015
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 18 Nov 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/randomization
- Term code
- HE-ES-CTM-075
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