Study parameters
Enter the expected values: the number of volunteers and the power curve update instantly. Your data stay in your browser.
Power at different numbers of volunteers
How the number of volunteers grows with variability (other parameters as entered)
| CV | In analysis | With allowance |
|---|---|---|
| 10 % | 12 | 14 |
| 15 % | 12 | 14 |
| 20 % | 20 | 24 |
| 25 % | 28 | 32 |
| 30 % | 40 | 46 |
| 35 % | 52 | 58 |
| 40 % | 66 | 74 |
| 50 % | 98 | 110 |
| 60 % | 134 | 150 |
Where the interval lies relative to the limits
The EAEU Bioequivalence Rules require at least 12 subjects in the analysis (clause 26).
What the calculator does. The standard design is a randomised two-period, two-sequence crossover study with a single dose (clause 15 of the EAEU Bioequivalence Rules). The analysis uses log-transformed AUC or Cmax, and the conclusion rests on the 90 % confidence interval (two one-sided tests at α = 0.05). Power is calculated exactly, without a normal approximation. At least 12 subjects must be included in the analysis (clause 26 of the Rules).
What it does not do. The calculation is indicative and does not replace the sample-size justification in the protocol. For highly variable drugs, parallel and replicate designs the calculation is different; a biostatistician does it against your protocol.
How to use the calculator
Enter the expected values on the first tab:
- Intra-subject CV — the variability of the measure within the same person. The higher it is, the more volunteers are needed.
- Expected T/R ratio — how far, in your expectation, the test product differs from the reference on average. The further it is from 100 %, the more volunteers are needed.
- Power — how reliably the study should demonstrate equivalence. 80 % or 90 % is usual.
- Dropout allowance — how many people to enrol on top of the number needed in the analysis.
- Equivalence limits — the standard 80.00–125.00 % or the narrow 90.00–111.11 % for drugs with a narrow therapeutic range (clause 104 of the Rules); the conditions of use are set by the protocol.
The second tab works the other way round: it shows the 90 % confidence interval a study result gives and whether it fits within the equivalence limits.
How many volunteers are needed in the analysis
Indicative values for a standard 2×2 crossover study, limits of 80.00–125.00 % and a 5 % significance level:
| CV | T/R 100 %, power 80 % | T/R 95 %, power 80 % | T/R 90 %, power 80 % | T/R 95 %, power 90 % |
|---|---|---|---|---|
| 10 % | 12 | 12 | 12 | 12 |
| 15 % | 12 | 12 | 22 | 16 |
| 20 % | 16 | 20 | 38 | 26 |
| 25 % | 24 | 28 | 56 | 38 |
| 30 % | 32 | 40 | 80 | 52 |
| 35 % | 42 | 52 | 106 | 70 |
| 40 % | 54 | 66 | 134 | 88 |
| 50 % | 80 | 98 | 202 | 132 |
| 60 % | 108 | 134 | 276 | 182 |
The value 12 is the lower limit set by the Rules: at low variability the calculated number is smaller, but at least 12 subjects must be included in the analysis. A dropout allowance is added to these numbers, and the total is made even so that the sequences stay equal.
The main lesson of the table. The number of volunteers grows faster than variability. If the real ratio of the products is worse than expected (90 % instead of 95 %), twice as many volunteers are needed. So assumptions about CV and T/R are best taken from data, not padded by eye.
How to read the result
- Volunteers in the analysis — the smallest number at which power is not below the target. The calculation steps through even numbers: the two sequences have equal numbers of volunteers.
- Enrol with allowance — the number after allowing for dropouts, rounded up to an even number.
- Power at this number — the actual power. It is slightly above the target because the number of volunteers is a whole, even number.
- The chart shows how power grows with the number of volunteers and where your value sits. Adding a few people beyond the threshold gains less and less.
How the calculation works
The calculator computes the power of the two one-sided tests procedure for log-transformed AUC or Cmax. This is the same as checking whether the 90 % confidence interval of the ratio of the products lies within the equivalence limits. Power is calculated exactly, by integrating over the distribution of the variability estimate rather than using a normal approximation (the method was described by Diletti, Hauschke and Steinijans, 1991). The calculation has been checked against an independent simulation: over a hundred thousand virtual studies for each of the control sets of parameters give the same power to within a tenth of a percentage point.
What the calculator does not cover
- Other designs. For parallel-group, replicate (three- and four-period, clause 110 of the Rules) and adaptive studies the calculation is different.
- Highly variable drugs and widened limits. The rules and the protocol define the requirements and the calculation for them; the calculation is usually done by simulation.
- Several measures at once. Equivalence is assessed on AUC and Cmax together. A practical guide is to take the larger of the two CVs.
- Unbalanced sequences and protocol deviations. They reduce power compared with the calculated value.
What next
If you need a calculation for your product and protocol, send a synopsis or protocol: we will assess feasibility, including a realistic number of volunteers and recruitment timelines, and prepare a proposal for the bioequivalence study.
Sources
- Rules for Conducting Bioequivalence Studies of Medicinal Products within the EAEU — Decision of the EEC Council of 3 November 2016 No. 85 (as amended): clause 15 — the standard design (a randomised two-period, two-sequence crossover study with a single dose); clause 26 — the number of subjects is justified by a sample-size calculation, and at least 12 are included in the analysis; clauses 81, 87 and 88 — the criterion (the 90 % confidence interval, limits of 80.00–125.00 %) and log transformation; clause 104 — the narrow limits.
- Diletti E., Hauschke D., Steinijans V. W. Sample size determination for bioequivalence assessment by means of confidence intervals. Int J Clin Pharmacol Ther Toxicol. 1991; 29(1): 1–8.
Questions and answers
How many volunteers does a bioequivalence study need?
It depends on the intra-subject variability of the measure (CV), the expected ratio of the products, the required power and the equivalence limits. With a CV of 20 % and an expected ratio of 95 %, a standard crossover study needs 20 volunteers in the analysis; 40 at a CV of 30 %; 66 at 40 %. At least 12 subjects must be included in the analysis (clause 26 of the EAEU Rules).
What is intra-subject CV and where do I get it?
It is the variability of a measure (AUC or Cmax) within the same person on repeated dosing, expressed as a percentage. It is taken from published studies of the active substance, from a pilot study or from data on the reference product. If both measures are known, use the one with the higher variability.
Why allow for dropouts?
Some volunteers may leave before the end or be withdrawn under the protocol. If fewer people reach the analysis than were calculated, power falls. So more people are enrolled than are needed in the analysis; the size of the allowance is set by the protocol.
How does 80 % power differ from 90 %?
Power is the probability that the study shows bioequivalence if the true ratio of the products and the variability are as you assumed in the calculation. At 80 % there is about a one-in-five chance of failing to confirm equivalence; at 90 % about one in ten. Higher power needs more volunteers: 52 instead of 40 at a CV of 30 % and a ratio of 95 %.
Does the calculator replace the calculation in the protocol?
No. It is a planning guide. For highly variable drugs, drugs with a narrow therapeutic range, and parallel and replicate designs the calculation is different. The sample-size justification in the protocol is done by a biostatistician against your data.
See also
Bioequivalence studies in Moscow
A bioequivalence study shows that a generic medicine reaches the bloodstream in the same way as the reference medicine. Bessalar Clinic conducts such studies in healthy volunteers in its in-patient unit and processes samples on site.
Learn moreWhat is bioequivalence? Cmax, AUC and Tmax in plain language
Bioequivalence is the similarity in how two medicines with the same active substance enter the bloodstream. It is tested in volunteers by comparing concentration–time curves using Cmax and AUC.
Learn more
Feasibility assessment of a clinical study
A feasibility assessment is a review of the protocol before a study starts. It shows whether the study can be run at the site within the required timelines and with the required number of participants. The clinic carries out this assessment for sponsors and contract research organisations (CROs).
Learn more