EAEU GCP Rules require power-based justification of subject numbers, and EEC Recommendation No. 19 shows how to calculate it
The sponsor of a clinical trial (CT) specifies the planned number of subjects in the protocol and justifies it with a calculation. The Good Clinical Practice (GCP) Rules of the Eurasian Economic Union (EAEU), hereinafter the GCP Rules, require this: explanations or calculations for the statistical power of the trial are needed (power is the probability of detecting a real effect).
The protocol is part of the set of documents submitted with the application for authorization to conduct a CT. It is received by the expert institution (the organization to which the Ministry of Health of the Russian Federation, hereinafter the Russian Ministry of Health, assigns the review of documents) and by the ethics council (the body that assesses the ethical soundness of the trial). Under the Federal Law «On the Circulation of Medicines» (hereinafter Law No. 61-FZ), the ground for refusing authorization is an opinion of the expert panel or the ethics council that the trial cannot be conducted.
If the documents lack information, the Russian Ministry of Health sends a request and suspends the time limit for deciding whether to conduct the reviews until the applicant responds. After authorization is granted, the protocol can be changed by notifying the Russian Ministry of Health, which decides within 28 business days. The law provides no fine for an unjustified sample size: the Code of the Russian Federation on Administrative Offenses (hereinafter the CAO RF) has no article on liability for violations in the conduct of clinical trials of medicinal products.
The sample size calculation is set out in the Guideline on the Application of Biostatistics Principles in Clinical Trials of Medicinal Products (hereinafter the Guideline), approved by Recommendation No. 19 of the Board of the Eurasian Economic Commission (EEC) of 3 November 2020. The Guideline is addressed to sponsors and to experts who assess the evidence of a product’s efficacy and safety.
What the GCP Rules require and what the Guideline recommends
The mandatory minimum is set by EEC Council Decision No. 79 of 3 November 2016 «On Approval of the Rules of Good Clinical Practice of the Eurasian Economic Union». The GCP Rules apply as amended by EEC Council Decision No. 63 of 1 August 2025, applicable from 10 March 2026.
The statistical part of the protocol consists of seven elements:
statistical analysis methods and the timing of each planned interim analysis
the planned number of subjects (in a multicenter trial, for each center) and the justification of the sample size
the significance level applied
criteria for stopping the trial
procedures for handling missing data, data not subject to analysis and falsified data
procedures for reporting deviations from the original statistical plan
selection of subjects for analysis
The GCP Rules contain no calculation method. The principles of calculation are set out in the Guideline, and the Board recommends that member states apply it six months after its publication on the official website of the Union. The Recommendation was published on 6 November 2020, so the six months ended on 6 May 2021.
The Guideline is advisory, so the statistics section of the GCP Rules remains mandatory. The Guideline contains no specific statistical procedures. Practical steps to implement its principles remain the sponsor’s responsibility, and the calculation method, together with the estimates of all values, is recorded in the protocol.
The sponsor must involve a biostatistician under the GCP Rules themselves. Qualified persons, including biostatisticians, take part at all stages of the trial: in developing the protocol and the statistical analysis plan, and in preparing the interim and final reports. The Guideline expresses the same idea through the role of the trial statistician, who approves the protocol and amendments and ensures that they cover all significant statistical aspects.
What the calculation consists of under the Guideline
The sample size is determined from the primary variable unless a different approach is justified. If the number of subjects is calculated from safety requirements or from an important secondary objective, that basis must be stated and justified. Such a trial may need more subjects than a calculation based on the primary efficacy question.
The principles of the Guideline apply first of all to late-stage trials, many of which are confirmatory. In a confirmatory trial, a hypothesis formulated in advance is tested when the trial is completed. The sample size in such a trial must be sufficient for a clear and unambiguous answer to each clinical question on efficacy or safety. It is also necessary to explain why the results are generalized to the target population, and this may affect the number and type of centers.
Exploratory trials are planned more flexibly. Their objectives are not always limited to testing predefined hypotheses, and they do not formally confirm efficacy. If one trial has both a confirmatory and an exploratory part, the protocol must clearly separate them.
With the usual calculation method, seven parameters must be described:
the primary variable (the main outcome measure used to calculate the sample size)
the statistical test
the null hypothesis (there is no difference between the interventions)
the alternative (working) hypothesis for the chosen dose, with the difference between interventions that is to be detected or rejected
the probability of wrongly rejecting the null hypothesis (Type I error, false positive)
the probability of wrongly failing to reject the null hypothesis (Type II error, false negative)
the approach to subjects excluded from the trial and to protocol violations
The calculation method is recorded in the protocol together with the estimates of all values used: variance, mean values, response rates, event rates and the target difference, and the basis for those estimates. In confirmatory trials, assumptions as a rule rest on published data or the results of earlier studies. The target difference may reflect the minimal clinically significant effect, or the expected effect of the new intervention if it is larger than the effect of the standard one.
Type I error is traditionally set at 5% or lower, and an adjustment is introduced for multiple comparisons. Type II error is traditionally 10 or 20%. This corresponds to a power (the probability of detecting a real effect) of 90% and 80%, and sponsors are advised to keep this error as low as possible, especially in trials that are difficult or impossible to repeat. The Guideline sets no lower limit for power, and values that differ from the traditional ones are acceptable and sometimes preferable.
The provisions of the Guideline mainly concern frequentist methods. A Bayesian approach is also allowed if the grounds for using it are clearly defined and the results and conclusions are sufficiently robust.
Table 1. Requirements of the GCP Rules and recommendations of the Guideline for sample size calculation
| Element | GCP Rules (Decision No. 79) | Guideline (Recommendation No. 19) |
|---|---|---|
| Number of subjects | Planned number, for each center in a multicenter trial | The calculation method and the estimates of all values are recorded in the protocol |
| Justification | Explanations or calculations for statistical power and clinical justification | Basis of the estimates: publications or earlier studies |
| Type I error | State the significance level applied | Traditionally 5% or lower, with an adjustment for multiplicity |
| Type II error | Through statistical power | Traditionally 10 or 20%, keep as low as possible |
| Sensitivity of the calculation | Not mentioned in the statistics section | Examine deviations from the assumptions and report a range of sample sizes |
| Dropouts and protocol violations | Procedures for handling data, selection of subjects for analysis | The approach is part of the calculation, and for the full analysis set the effect may need to be reduced |
| Involvement of a biostatistician | The sponsor involves biostatisticians from protocol development to the reports | The statistician approves the protocol and amendments |
| Recalculation during the trial | Deviations from the statistical plan are described and justified | Recalculation on blinded data (without revealing who is in which group) is possible and is formalized by a protocol amendment |
How to calculate sample size for means and proportions
The Guideline contains no formulas, so standard ones are used. To compare means in two parallel groups, the number of subjects per group is calculated as follows:
n = 2 × (Z(1−α/2) + Z(1−β))² × σ² / Δ²
Here Z is a quantile of the normal distribution, σ² is the variance and Δ is the target difference of means. The formula gives an approximation based on the normal distribution. A calculation based on the t-distribution gives one more subject for the example below, 92 and 123 subjects per group at 80% and 90% power, so the protocol states which method was used.
In the example, the primary variable, the change in systolic blood pressure, has a standard deviation of 12 mmHg, the target difference is 5 mmHg and the two-sided α is 5%. At 80% power, 91 subjects per group are needed, and at 90% power 122, so the sample grows by about one third. If α is reduced from 5 to 1%, 135 subjects per group are needed at 80% power.
To halve the width of a confidence interval, the sample must be increased four times. With a 2 to 1 allocation of groups, the total sample size for comparing means under the same assumptions grows by 12.5% by the standard formula.
For proportions the formula is different, and the result depends on both expected proportions:
n = (Z(1−α/2) + Z(1−β))² × [p1(1−p1) + p2(1−p2)] / (p1 − p2)²
A response is expected in 50% of subjects in the drug group and 34% in the placebo group. At α of 5% and 80% power, 146 subjects per group are needed, and at 90% power 195.
The Guideline suggests checking how the calculation responds to deviations from the assumptions and reporting a range of sample sizes. For the example with means, this range is shown in Table 2.
Table 2. Subjects per group at 80% power and two-sided α of 5%, by standard deviation σ and difference Δ
| Standard deviation σ | Δ = 4 mmHg | Δ = 5 mmHg | Δ = 6 mmHg |
|---|---|---|---|
| 10 | 99 | 63 | 44 |
| 12 | 142 | 91 | 63 |
| 14 | 193 | 124 | 86 |
Between the mildest combination of assumptions (σ 10, Δ 6) and the harshest (σ 14, Δ 4), the sample differs from 44 to 193 subjects per group, which is more than fourfold. If variability was taken from a single publication and is actually higher (14 instead of 12), then at a difference of 5 mmHg the sample grows from 91 to 124 subjects per group.
If the primary variable is related to survival, the calculation is built on the required number of events, and additional assumptions are needed to arrive at the final number of subjects. The outcome itself must be carefully specified. Mortality cannot be chosen as the primary variable without additional conditions. It is assessed by the proportion of survivors at fixed time points or by the distribution of survival time over a set period.
A crossover design (each subject receives the interventions in turn) reduces the number of subjects for a given power, sometimes considerably. The price is the risk of a carryover effect between periods, so it is suitable only for a chronic stable disease and with sufficient washout periods (breaks in which the effect of the previous intervention wears off) between interventions. In a factorial design (combinations of several interventions are tested in one trial), the test for interaction may lack power if the sample was calculated for the main effects.
If a trial has several primary variables, the calculation depends on whether the effect must be confirmed for one of them or for all. When the aim is to confirm the effect for all variables, no adjustment for Type I error is required. At the same time, the effect of multiplicity on Type II error and on the sample size is analyzed in detail. Categorizing a continuous variable loses information and reduces power, and this is built into the calculation.
In a multicenter trial, the usual calculations assume that the differences between interventions in different centers estimate the same value. For this reason, the protocol must be common to all centers, and procedures must be standardized as far as possible.
What changes for equivalence and non-inferiority
Superiority over placebo or an active control is one of the most convincing ways to establish efficacy, and the sample for it is calculated with the same formulas. For equivalence and non-inferiority, the calculation starts from a margin that is set in the protocol.
The margin is set as the largest clinically acceptable difference, and it must be smaller than the difference shown by the active comparator in superiority trials. For equivalence, both margins are specified and a two-sided confidence interval is used. For non-inferiority, the lower margin and a one-sided interval are enough. The sample size calculation must rely on the same methods.
If the power of an equivalence trial was estimated at a true difference of zero, but in fact the difference is not zero, the sample will be too small. The same is true for non-inferiority when the effect of the investigational product is weaker than the effect of the active control. The clinically acceptable difference may be smaller than the clinically significant difference from superiority trials, and its choice needs separate justification.
A conclusion of equivalence based on a non-significant result of testing the null hypothesis of no difference is unacceptable. Such trials are non-conservative by nature. Flaws in planning and conduct shift the result in favor of equivalence, and protocol violations and losses to follow-up should be as few as possible.
Adjustments for dropouts, the analysis set and enrollment
How many subjects should be randomized if some will drop out? The formula gives the number of subjects whose data will enter the primary analysis, so more must be randomized. If the proportion of dropouts is d, the final number is calculated as follows:
N = n / (1 − d)
For 91 subjects per group with 10% dropout, 102 must be randomized, with 15% 108, with 20% 114. The Guideline gives no dropout percentage. The approach to excluded subjects and protocol violations is described in the calculation itself.
The analysis set also affects the final number. The primary analysis may be run on the full analysis set (the intention-to-treat principle, where practically all randomized subjects are included). In that case the effect estimate may have to be reduced compared with the per-protocol set (it includes only subjects who followed the protocol sufficiently). Such an analysis includes the data of subjects who left early and of subjects with low adherence, and the effect is diluted. The assumptions about variability may also need to be revised.
In trials with long enrollment, the enrollment rate is monitored during the trial. If it is markedly below the planned rate, the causes are identified and measures are taken to preserve power.
The result of the calculation can be set out in the protocol as follows (using the example in this article):
The sample size was calculated for the primary variable, the change in systolic blood pressure by week 12. A standard deviation of 12 mmHg was assumed (source: publication, reference), the target difference is 5 mmHg (minimal clinically significant effect, justification), the two-sided significance level is 5% and the power is 80%. This requires 91 subjects per group. Allowing for expected dropout of 15%, 108 subjects per group will be randomized, 216 in total. The sensitivity of the calculation to deviations from the assumptions is shown in Table 2, and the range of sample sizes is from 44 to 193 subjects per group.
Sample size recalculation and interim analyses
What to do if the assumptions of the calculation are not confirmed? In long trials they can be checked during the trial. A check on blinded data sometimes shows that the pooled variance, the event rate or the survival rate differ from the expected ones. The sample may then be recalculated if the recalculation is justified and recorded in a protocol amendment and in the CT report.
The justification explains how blinding is preserved and how the recalculation affects Type I error and the width of confidence intervals, if it does. The potential need to revise the sample is provided for in the protocol in all applicable situations.
Revising the sample by comparing the groups requires unblinded access to the data and counts as an interim analysis. It needs a statistical plan in the protocol (or in an amendment before the first analysis), an amendment before unblinded access to the data, and control of the overall Type I error.
In a group sequential design (with interim analyses after which the trial can be stopped early), the exact sample size cannot be fixed in advance, because it depends on the stopping rules and on the true difference between interventions. The protocol states the expected and maximum sample sizes and the schedule of interim analyses or the principles for drawing it up, for example an alpha-spending function (a rule by which the permitted Type I error is distributed among the interim analyses).
An interim analysis is conducted confidentially. Trial site staff and sponsor staff, other than those who perform it, remain blinded, and investigators are told only of the decision to continue or stop the trial or to change procedures. In many trials, especially those with a major effect on public health, an independent data monitoring committee monitors the comparisons of efficacy and safety, and its responsibilities are described in the protocol. A poorly planned interim analysis is best avoided because it may discredit the results of the trial.
Changing the inclusion criteria during the trial can also affect the calculation. A protocol amendment must describe the statistical consequences, including an adjustment of the sample size because of a different event rate.
Bioequivalence and sample size
Bioequivalence studies fall under equivalence. They are governed by separate Rules for Conducting Bioequivalence Studies of Medicinal Products within the Eurasian Economic Union, approved by EEC Council Decision No. 85 of 3 November 2016 (hereinafter the BE Rules). The BE Rules apply mainly to immediate-release solid oral forms and to the comparison of chemical compounds.
The BE Rules give no formulas and set two conditions: the sample size must be based on a proper calculation, and the number of subjects included in the analysis may not be less than 12. The standard design is a randomized two-period crossover study with two sequences and a single dose.
Bioequivalence is confirmed if the 90% confidence interval of the ratio of geometric means of AUC (area under the concentration-time curve) and Cmax (maximum concentration) lies within the limits of 80.00 to 125.00%. A separate sample size calculation for tmax (time to reach Cmax) is usually not made.
The minimum is 12 subjects, and the loss of each of them reduces power. If, after subjects with a non-zero baseline concentration (more than 5% of Cmax) are excluded, fewer than 12 remain in the analysis, continuing the study is considered unacceptable. «Standby» subjects, who go through the procedures separately from the main sample in order to replace dropouts, may not be included. A reserve is built into the number to be randomized using the same formula N = n / (1 − d).
A product is considered highly variable if within-subject variability exceeds 30%, and a replicate crossover design with 3 or 4 periods is recommended for it. The limits for Cmax may be widened to 69.84 to 143.19% if the variability of Cmax of the reference product in the study itself exceeded 30% and the possibility of widening is stated in the protocol in advance. For AUC the limits remain 80.00 to 125.00% at any variability. For products with a narrow therapeutic range, the limits narrow to 90.00 to 111.11% for AUC and Cmax. The narrower the limits, the more subjects are needed under the same assumptions.
A two-stage design makes it possible to add subjects to the group if bioequivalence was not confirmed at the first stage. The overall probability of Type I error must be preserved, and the stopping rules must be defined before the trial begins. The first analysis can be treated as an interim one, and both analyses are conducted at adjusted significance levels. Confidence intervals are constructed with a probability of at least 90%, for example 94.12%. The design itself is described in the protocol in advance.
If bioequivalence cannot be confirmed from concentrations, the studies move to pharmacodynamic or clinical ones, and the sample grows quickly there. Under the BE Rules, pharmacodynamic studies may need a large number of patients because of high variability and the placebo effect, and a third, placebo group is also recommended. In clinical equivalence trials, 95% intervals are used instead of 90% ones, and the number of patients is usually much larger than in a bioequivalence study.
For the bioassay of vasoconstriction by topical corticosteroids, 40 to 60 subjects suitable for assessment are included in the pivotal study. For topical products applied to the skin, the number of subjects must be based on a calculation and be at least 12.
Trial authorization and protocol amendments in Russia
In Russia, clinical trials of medicinal products are conducted under the GCP Rules and on the basis of an authorization from the authorized federal executive authority. The decision to issue the authorization is taken by the Russian Ministry of Health under the Procedure for Maintaining the Register of Issued Authorizations for Clinical Trials of Medicinal Products for Medical Use, approved by Order of the Russian Ministry of Health of 23 December 2024 No. 708n (hereinafter Order No. 708n). The authority issues the authorization based on the results of the expert review of documents and the ethical review.
The expert institution and the ethics council prepare their opinions within 25 business days. The decision to refuse authorization and the opinions of the experts or the ethics council can be appealed.
Before the reviews, the authority checks the completeness and reliability of the documents. If information is missing, it sends the applicant a request for the missing information. The applicant responds within 90 business days, and for that time the time limit for deciding whether to conduct the reviews is suspended. The grounds for refusing to conduct the reviews are: the documents were submitted incompletely, the request was not answered on time, or the documents lack the exhaustive list of necessary information.
A copy of the compulsory insurance contract, which states the maximum number of patients in the trial, is attached to the application. A patient’s participation in the trial is not permitted without such a contract.
After authorization is granted, the protocol can be changed by notifying the Russian Ministry of Health in the form it has established. The Ministry decides to make the changes or to refuse within 28 business days. To assess the validity of the changes, it may involve experts of the ethics council and of the expert institution.
The number of patients taking part in the trial is stated in the authorization itself under the Administrative Regulation of the Ministry of Health of the Russian Federation for issuing authorization to conduct a clinical trial of a medicinal product, approved by Order of the Russian Ministry of Health of 19 January 2018 No. 20n (hereinafter Order No. 20n), and is part of the register entry for it under Order No. 708n. Changes to the entry are made at the same time as changes to the authorization. The data in the authorization are updated at the applicant’s request with a reasoned justification and supporting documents, and the Ministry makes the changes or refuses within 28 business days.
If the supervisory authority in healthcare finds violations of the GCP Rules that affect the completeness or reliability of the trial, it suspends the trial and issues an order to the medical organization. If the violations are not eliminated on time, the trial is terminated, and the conclusion is sent for a decision on cancelling the authorization.
The CAO RF has no article on violations in the conduct of clinical trials of medicinal products, including liability for an unjustified sample size.
What to do
Check the statistical section of the protocol against the GCP Rules. Check that it contains all seven elements and that the number of subjects is given for each center if the trial is multicenter. Make sure the biostatistician took part in the work on the protocol from the start.
Name the source of each assumption. For the standard deviation, the response or event rate and the target difference, give a publication or an earlier study and explain the clinical significance of the difference.
Calculate the range of sample sizes. Build a table for several values of variability and difference, as in Table 2, and attach it to the justification before the protocol is finalized.
Build in an adjustment for dropouts. Define the analysis set before the calculation and recalculate the sample size with the formula N = n / (1 − d). Check the final number against the maximum number of patients in the compulsory insurance contract and against the number of patients in the authorization. For a bioequivalence study, check that at least 12 subjects will remain in the analysis after the expected exclusions.
Set the rules for recalculation and interim analyses. If a blinded recalculation of the sample or early stopping is possible, describe it in the protocol in advance: the schedule, the alpha-spending function, the measures to preserve blinding. Report any change to the protocol after authorization to the Russian Ministry of Health.
Regulatory framework:
1. Recommendation of the Board of the EEC of 3 November 2020 No. 19 «On the Guideline on the Application of Biostatistics Principles in Clinical Trials of Medicinal Products»
2. Decision of the EEC Council of 3 November 2016 No. 79 «On Approval of the Rules of Good Clinical Practice of the Eurasian Economic Union» (as amended by Decision of the EEC Council of 1 August 2025 No. 63, applicable from 10 March 2026)
3. Decision of the EEC Council of 3 November 2016 No. 85 «On Approval of the Rules for Conducting Bioequivalence Studies of Medicinal Products within the Eurasian Economic Union» (as amended by Decision of the EEC Council of 12 April 2024 No. 30, in force from 13 June 2024)
4. Federal Law of 12 April 2010 No. 61-FZ «On the Circulation of Medicines» (version of 4 August 2026, applicable from 1 September 2026)
5. Code of the Russian Federation on Administrative Offenses of 30 December 2001 No. 195-FZ (version of 4 August 2026)
6. Order of the Russian Ministry of Health of 23 December 2024 No. 708n «On Approval of the Procedure for Maintaining the Register of Issued Authorizations for Clinical Trials of Medicinal Products for Medical Use»
7. Order of the Russian Ministry of Health of 19 January 2018 No. 20n «On Approval of the Administrative Regulation of the Ministry of Health of the Russian Federation for the Provision of the State Service of Issuing Authorization to Conduct a Clinical Trial of a Medicinal Product for Medical Use» (version of 24 October 2019, applicable from 7 March 2020)