Concept Architecture
Concept
Theoretically, Equivalence Trial is a randomised clinical trial designed to demonstrate that the difference in effectiveness between two interventions is sufficiently small to be considered clinically unimportant. Unlike superiority trials, which seek to detect differences, equivalence trials aim to show that any true treatment difference lies entirely within pre-specified equivalence margins. The concept is founded on hypothesis testing, confidence interval methodology and clinical trial design. It exists to establish therapeutic equivalence between interventions where comparable efficacy is of primary interest.
Mathematically, Equivalence Trial methodology is based on the Two One-Sided Tests (TOST) procedure. Equivalence is concluded when the confidence interval for the estimated treatment difference lies completely within the predefined lower and upper equivalence margins. The null hypothesis states that the true treatment difference falls outside the equivalence interval, while the alternative hypothesis states that it lies entirely within the interval.
In practice, equivalence margins are specified before the trial begins based on clinical and regulatory considerations. Participants are randomly allocated to treatment groups, and the primary treatment effect is estimated together with its confidence interval. Regulatory agencies generally recommend analysing both the intention-to-treat and per-protocol populations because protocol deviations may bias conclusions towards equivalence. Equivalence trials are widely used in evaluations of generic medicines, biosimilars and alternative treatment formulations, providing evidence for regulatory approval and subsequent health economic evaluation.
Purpose
Used to demonstrate that two interventions produce clinically equivalent outcomes by showing that the estimated treatment difference remains entirely within pre-specified equivalence margins.
Mathematical Formulae
Primary Formula
Equivalence criterion:
L < (?? ? ??) < U
where:
- L = lower equivalence margin
- U = upper equivalence margin
- ?? = mean outcome for Treatment 1
- ?? = mean outcome for Treatment 2
Equivalence is concluded when the confidence interval for (?? ? ??) lies completely within (L, U).
Supporting Formulae
Two One-Sided Tests (TOST):
H??: ?? ? ?? � L
H??: ?? ? ?? � U
Equivalence is demonstrated only if both null hypotheses are rejected.
Confidence interval:
CI = (??? ? ???) � t ? SE(??? ? ???)
Related Mathematical Methods
- Two One-Sided Tests (TOST)
- Confidence Interval Estimation
- Hypothesis Testing
- Intention-to-Treat Analysis
- Per-Protocol Analysis
- Analysis of Variance
- Linear Regression
Example
A trial compares a biosimilar with its reference biologic using an equivalence margin of �5 percentage points for treatment response. The estimated difference in response rates is 1.2%, with a 95% confidence interval of ?2.4% to 4.1%.
Because the entire confidence interval lies within the equivalence interval of ?5% to +5%, the biosimilar is concluded to be therapeutically equivalent to the reference product. The estimated treatment effect may subsequently be incorporated into a cost-minimisation or cost-effectiveness analysis.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| CONFIDENCE.T | =CONFIDENCE.T(0.05,SD,N) | Calculate the confidence interval half-width for the treatment difference. |
| AVERAGE | =AVERAGE(B2:B201)-AVERAGE(C2:C201) | Estimate the mean treatment difference. |
| IF | =IF(AND(LowerCI>LowerMargin,UpperCI<UpperMargin),"Equivalent","Not Equivalent") | Determine whether equivalence has been demonstrated. |
| T.TEST | =T.TEST(B2:B201,C2:C201,2,2) | Perform supporting statistical comparisons. |
| STDEV.S | =STDEV.S(B2:B201) | Estimate variability for confidence interval calculations. |
VBA (Optional)
VBA can automate equivalence testing by calculating confidence intervals, evaluating equivalence margins and generating regulatory trial summary reports.
Sources
- Piaggio G, Elbourne DR, Altman DG, Pocock SJ, Evans SJW. Reporting of Noninferiority and Equivalence Randomized Trials: Extension of the CONSORT Statement.
- Chow SC, Shao J, Wang H. Sample Size Calculations in Clinical Research.
- FDA. Statistical Approaches to Establishing Bioequivalence.
- EMA. Guideline on the Investigation of Bioequivalence.
- Friedman LM, Furberg CD, DeMets DL, Reboussin DM, Granger CB. Fundamentals of Clinical Trials.
- NICE. Health Technology Evaluation Manual.
Related Concepts (2)
Library
Publications
1
Economic Evaluation in Clinical Trials — Glick, Doshi, Sonnad & Polsky, 2nd Edition ed., 2015 (Oxford University Press)
Practical guidance on conducting cost-effectiveness analyses alongside controlled trials, covering trial design, measurement of costs and quality-adjusted life years, handling censored and missing data, and reporting stochastic uncertainty. Volume 4 in the Handbooks in Health Economic Evaluation series.
BookView source →
Frequently Asked Questions (6)
What is an equivalence trial?
A trial designed to show a new treatment's effect is neither substantially better nor worse than an existing treatment, within a set margin.
Source: Piaggio et al. 2006
Why can an equivalence trial not simply look for no significant difference?
Finding no statistically significant difference between two treatments does not prove them equivalent, because a small or imprecise trial can fail to detect a difference that is really there. An equivalence trial instead sets a margin, the largest difference considered unimportant, and is designed to show, with adequate power, that the true difference falls within that margin in both directions. Only demonstrating the difference is confined within the margin establishes equivalence. Absence of a significant difference is not the same as evidence of equivalence. Piaggio and colleagues (2012) explain this.
Source: Piaggio et al. 2012
How does an equivalence trial work?
An equivalence trial works by defining in advance an equivalence margin, the largest difference in effect considered clinically unimportant in either direction, and then testing whether the confidence interval for the difference between the new and existing treatments falls entirely within that margin. If it does, the treatments are concluded to be equivalent within the margin. This differs from a superiority trial, which seeks to show a difference. The margin must be justified as clinically negligible, since the conclusion of equivalence depends on the difference being confined within it.
Source: Piaggio et al. 2006
How does an equivalence trial differ from a non-inferiority trial?
An equivalence trial aims to show that a new treatment is neither substantially better nor worse than the comparator, so it uses a margin in both directions, whereas a non-inferiority trial aims only to show that the new treatment is not substantially worse, using a margin in one direction and allowing the new treatment to be better. So equivalence is two-sided and non-inferiority one-sided. Non-inferiority trials are common when a new treatment is expected to be similar but offers other advantages, while equivalence trials require the effect to be close in both directions.
Source: Piaggio et al. 2006
Why is the equivalence margin important?
The equivalence margin is important because it defines how large a difference in effect is considered clinically unimportant, and the conclusion of equivalence depends entirely on the difference falling within it, so the margin must be justified as representing a clinically negligible difference. Too wide a margin could allow a meaningfully worse treatment to be called equivalent, while too narrow a margin makes equivalence hard to demonstrate. Because the margin determines the validity and meaning of the equivalence conclusion, it is specified in advance with clinical and statistical justification.
Source: Piaggio et al. 2006
What are the challenges of equivalence trials?
The challenges of equivalence trials include justifying and setting an appropriate equivalence margin, which is critical and requires clinical judgement; the need for adequate sample size and trial quality, since poor conduct can spuriously make treatments look similar; and the risk that a trial not designed rigorously could wrongly conclude equivalence. The analysis and interpretation differ from superiority trials, requiring care. These challenges mean equivalence trials are designed with a well-justified margin, adequate power, and rigorous conduct, and reported transparently, so that a conclusion of equivalence is credible and meaningful.
Source: Piaggio et al. 2006
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 13 Nov 2025
Content version: 1.0.0
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- Persistent URI
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- Term code
- HE-ES-CTM-032
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