Sample size determinations in original research protocols for randomised clinical trials submitted to UK research ethics committees: Review
To assess the completeness of reporting of sample size determinations in unpublished research protocols and to develop guidance for research ethics committees and for statisticians advising these committees. Review of original research protocols. Unpublished research protocols for phase IIb, III, and IV randomised clinical trials of investigational medicinal products submitted to research ethics committees in the United Kingdom during 1 January to 31 December 2009. Completeness of reporting of the sample size determination, including the justification of design assumptions, and disagreement between reported and recalculated sample size. 446 study protocols were reviewed. Of these, 190 (43%) justified the treatment effect and 213 (48%) justified the population variability or survival experience. Only 55 (12%) discussed the clinical importance of the treatment effect sought. Few protocols provided a reasoned explanation as to why the design assumptions were plausible for the planned study. Sensitivity analyses investigating how the sample size changed under different design assumptions were lacking; six (1%) protocols included a re-estimation of the sample size in the study design. Overall, 188 (42%) protocols reported all of the information to accurately recalculate the sample size; the assumed withdrawal or dropout rate was not given in 177 (40%) studies. Only 134 of the 446 (30%) sample size calculations could be accurately reproduced. Study size tended to be over-estimated rather than under-estimated. Studies with non-commercial sponsors justified the design assumptions used in the calculation more often than studies with commercial sponsors but less often reported all the components needed to reproduce the sample size calculation. Sample sizes for studies with non-commercial sponsors were less often reproduced. Most research protocols did not contain sufficient information to allow the sample size to be reproduced or the plausibility of the design assumptions to be assessed. Greater transparency in the reporting of the determination of the sample size and more focus on study design during the ethical review process would allow deficiencies to be resolved early, before the trial begins. Guidance for research ethics committees and statisticians advising these committees is needed.
Sample size determinations in original research
protocols for randomised clinical trials submitted to
UK research ethics committees: review
Timothy Clark research scientist, Ursula Berger senior statistician, Ulrich Mansmann director, and
chair of biostatistics and bioinformatics
Institut für Medizinische Informationsverarbeitung, Biometrie und Epidemiologie, Faculty of Medicine, Ludwig-Maximilians University, Munich,
Objectives To assess the completeness of reporting of sample size
determinations in unpublished research protocols and to develop
guidance for research ethics committees and for statisticians advising
Design Review of original research protocols.
Study selection Unpublished research protocols for phase IIb, III, and
IV randomised clinical trials of investigational medicinal products
submitted to research ethics committees in the United Kingdom during
1 January to 31 December 2009.
Main outcome measures Completeness of reporting of the sample size
determination, including the justification of design assumptions, and
disagreement between reported and recalculated sample size.
Results 446 study protocols were reviewed. Of these, 190 (43%) justified
the treatment effect and 213 (48%) justified the population variability or
survival experience. Only 55 (12%) discussed the clinical importance of
the treatment effect sought. Few protocols provided a reasoned
explanation as to why the design assumptions were plausible for the
planned study. Sensitivity analyses investigating how the sample size
changed under different design assumptions were lacking; six (1%)
protocols included a re-estimation of the sample size in the study design.
Overall, 188 (42%) protocols reported all of the information to accurately
recalculate the sample size; the assumed withdrawal or dropout rate
was not given in 177 (40%) studies. Only 134 of the 446 (30%) sample
size calculations could be accurately reproduced. Study size tended to
be over-estimated rather than under-estimated. Studies with
non-commercial sponsors justified the design assumptions used in the
calculation more often than studies with commercial sponsors but less
often reported all the components needed to reproduce the sample size
calculation. Sample sizes for studies with non-commercial sponsors
were less often reproduced.
Conclusions Most research protocols did not contain sufficient
information to allow the sample size to be reproduced or the plausibility
of the design assumptions to be assessed. Greater transparency in the
reporting of the determination of the sample size and more focus on
study design during the ethical review process would allow deficiencies
to be resolved early, before the trial begins. Guidance for research ethics
committees and statisticians advising these committees is needed.
The determination of sample size is central to the design of
randomised controlled trials.
To have scientific validity a
clinical study must be appropriately designed to meet clearly
Clinical trials should provide precise
estimates of treatment effects, thus allowing healthcare
professionals to make informed decisions based on sound
Equally, trials should not be too large, as these may
expose some patients to unnecessary risks. An extensive
literature on sample size calculations in clinical research now
exists for a wide variety of data types and statistical tests.
International Conference on Harmonisation of technical
requirements for registration of pharmaceuticals for human use,
topic E9, sets down the requirements for sample size reporting
in research protocols for studies supporting the registration of
drugs for use in humans.
Although these standards primarily
concern commercial sponsors, the principles (box 1) have broad
application to all clinical trials. The consolidated standards of
reporting trials statement provides similar guidance for published
Surprisingly few evaluations have been made of the quality of
the sample size determination in randomised controlled trials.
Those that have been performed are mainly based on published
data owing to the difficulty in obtaining access to unpublished
Correspondence to: U Mansmann email@example.com
Extra material supplied by the author (see http://www.bmj.com/content/346/bmj.f1135?tab=related#webextra)
Filter criteria used to identify studies in research ethics database
Additional figures and tables
No commercial reuse: See rights and reprints http://www.bmj.com/permissions Subscribe: http://www.bmj.com/subscribe
BMJ 2013;346:f1135 doi: 10.1136/bmj.f1135 (Published 21 March 2013) Page 1 of 10
Box 1: Core components of the sample size determination (International Conference on Harmonisation topic E9)
For example, superiority, non-inferiority, equivalence
For example, parallel group, crossover, factorial
Clinically most relevant endpoints from the patients’ perspective
Statistical test procedure
For example, t test for continuous variables, χ
test for binary variables
Ratio of number of participants in each treatment arm
Treatment difference sought
Minimal effect that has clinical relevance or the anticipated effect of the new treatment, where this is larger
Other design assumptions
For example, variance, response rates, and event rates, used in the calculation
Type I error
Probability of erroneously rejecting the null hypothesis
Type II error
Probability of erroneously failing to reject the alternative hypothesis:
Expected rate of treatment withdrawals
Expected proportion of subjects with no post-randomisation information
Justification of treatment difference sought and other design assumptions
Investigation of how sample size changes under different assumptions (sensitivity analyses)
Other components depending on study design
Accrual and total study duration used to estimate the number of patients required in event driven studies
Adjustments for multiple testing—for example, multiple endpoints, multiple checks during interim monitoring
These reviews have several limitations.
Firstly, the reporting of the sample size determination in the
study publication is less detailed than in the research protocol.
Secondly, they are affected by publication bias. Thirdly, one
study showed that there are often discrepancies between the
research protocol and the publication.
conclusions about the quality of sample size determinations
should be based on a review of original research protocols.
Studies that are too large or too small have been branded as
2 15 16
The view that underpowered studies are in
themselves unethical has been challenged by some researchers,
who argue that this is too simplistic.
We believe that a study
must be judged on whether it is appropriately designed to answer
the research question posed, and the validity of the sample size
calculation is germane to this assessment. This is not merely a
matter of whether the sample size can be recalculated, since the
calculation can be correct mathematically but still be of poor
quality if the assumptions used have not been suitably researched
Greater transparency in the reporting of the
sample size determination and more focus on study design
during the ethical review process would allow deficiencies to
be resolved early, before the trial begins; once the trial starts it
is too late. We assessed the quality of sample size determinations
reported in research protocols with the aim of developing
guidance for research ethics committees.
We searched the research ethics database, a web based database
application for managing the administration of the ethical review
process in the United Kingdom, using filter criteria (see
supplementary file) to identify all validated applications for
randomised (phase IIb, III, and IV) clinical trials of
investigational medicinal products submitted to the National
Research Ethics Service for ethical review during 2009. We
designed these criteria to create a large database of recently
submitted protocols (2009 was the last complete year before
the project started in 2010) for randomised controlled trials.
Creation of the protocol database
Three researchers extracted the characteristics of the studies
(table 1⇓) from the research ethics database according to
prespecified rules and entered the data into the protocol database.
Two reviewers independently assessed each research protocol.
The researchers met regularly to discuss and agree on the final
data to be entered into the database.
To verify the data sources we checked that the information in
the research ethics database was consistent with the research
protocol on file at the research ethics committee office.
The database was analysed using SPSS Version 19. We describe
the results using frequency tables with percentages, cross
tabulations, relative risks with 95% confidence interval, and
box and Bland-Altman plots.
No commercial reuse: See rights and reprints http://www.bmj.com/permissions Subscribe: http://www.bmj.com/subscribe
BMJ 2013;346:f1135 doi: 10.1136/bmj.f1135 (Published 21 March 2013) Page 2 of 10
Assessing the sample size determination
We assessed sample size determination based on three factors:
the reporting of how the sample size was determined, the
reporting of and justification for the design assumptions, and
recalculation of the original sample size determination.
Reporting of sample size determination
We reviewed each protocol to determine the presence or absence
of the core sample size components. Reporting of additional
information such as adjustment for multiple testing (for example,
multiple endpoints, multiple checks during interim monitoring)
required for the sample size calculation was also documented.
We did not assess the appropriateness of the proposed methods
Reporting and justifying design assumptions
Each design assumption was categorised (box 2). We also
documented the reporting of sensitivity analyses and
consideration of an adaptive design. We did not independently
assess the appropriateness of the design assumptions.
Recalculation of original sample size
The three researchers who created the protocol database
recalculated the original sample size according to prespecified
rules. Two independent reviewers carried out each recalculation;
the researchers met regularly to discuss and agree the final data
to be entered into the database. Any outstanding questions were
referred to a fourth reviewer for resolution (n=65).
If the sample size determination stated that a specific statistical
software had been used (for example, nQuery Advisor, East,
PASS) or referenced a specific publication, then we used the
same software or published methodology to recalculate the
sample size. If the protocol stated that the sample size was based
on a more complex method of analysis, such as analysis of
covariance then we used PASS 11 or nQuery 6.01. Otherwise
we used standard formulas for normal, binary, or survival data.
Missing information was imputed in four ways. Firstly, if the
withdrawal rate was not specified we recalculated the sample
size using the variables given. This recalculated sample size
was then compared with the sample size reported in the protocol.
Secondly, if the type I error or type II error (power of a trial is
1−probability of a type II error) was not specified, we
recalculated the sample size using a two sided 5% type I error
or a 20% type II error. Thirdly, when adjustments for multiple
testing were not reported we assumed no adjustment had been
applied. Finally, if the sample size was based on a more complex
method of analysis, but insufficient information was reported
to allow the sample size to be recalculated for the planned
method, we used standard formulas to recalculate the sample
We defined two populations for analysis: protocols where
missing information was imputed and protocols that reported
all core components and any additional information such as
adjustments for multiple testing required to accurately
recalculate the sample size (complete reporting).
If the ratio of the number of evaluable patients or events reported
in the protocol to that calculated fell within the range 0.95 to
1.05, then we reproduced the sample size, since a difference of
5% or less either way represented an inconsequential reduction
or increase in power (approximately 2% for normal, binary, or
A total of 929 research protocols were identified by the initial
search. Of these, 446 met the inclusion criteria (see
supplementary figure 5). Table 2⇓ lists the main characteristics
of the 446 research protocols (also see supplementary table 5).
The most common therapeutic areas were oncology (94; 21%)
and endocrinology (49; 11%). Most studies were sponsored by
industry (314; 70%), were in phase III (251; 56%), had a parallel
group design (319; 72%), and had superiority of the test over
control medicinal product as the primary objective (375; 84%).
Six (1%) protocols included sample size re-estimation in the
Reporting of sample size components
The individual core components of the sample size were
generally reported in the 446 protocols, with the exception of
withdrawals (269; 60%, fig 1⇓) (also see supplementary table
6). Of the 446 protocols, 240 (54%) reported all the core
components; withdrawal rate was the only element missing in
143 out of 206 (69%) protocols that did not report all core
When we considered protocols that reported all core components
and additional information such as adjustments for multiple
testing to accurately recalculate the sample size (complete
reporting) then the number reduced to 188 protocols (42%).
Reporting design assumptions
Less than half of the 446 protocols (190; 43%) reported the data
on which the treatment difference (or margin) was based. Of
the 190 protocols that did report the basis of the treatment
difference, 92 (48%) cited previous studies with the product or
a product in the same class and 38 (20%) cited a literature search
(fig 2⇓ and supplementary table 7). In only four (2%) protocols
was the estimated treatment difference based on a meta-analysis.
Reporting the basis for the treatment difference was lowest in
studies on oncology (28/94; 30%) and cardiovascular disease
(12/36; 33%) and highest in those on pain and anaesthesia
(16/27; 59%) (see supplementary table 8).
Overall, 55 out of 446 (12%) protocols reported both the basis
of the treatment effect and its clinical importance, 135 (30%)
protocols reported the basis only, and 256 (57%) reported
neither. Limited information on the nature of the data
underpinning the treatment effect was usually given, and just
13 (3%) protocols gave a reasoned explanation why the value
chosen was plausible for the planned study.
The same pattern was observed with population variability or
survival, with less than half (213/446; 48%) of the protocols
reporting the basis of the variable used in the calculation (fig 2
and supplementary table 9). Previous studies, a literature search,
or both, were again most commonly cited. The variability or
survival estimate was based on a meta-analysis in only two of
the 213 (1%) protocols. Again, limited information was usually
given, and just 17 (4%) protocols explained the plausibility of
the value chosen.
Only 11 out of the 446 (3%) protocols reported analyses
investigating the sensitivity of the sample size to deviations
from the assumptions used in the calculation.
Reporting of strategies to control type I (false
positive) and type II (false negative) error
Adjustments for multiple comparisons (81/144; 56%) or interim
analyses (56/95; 59%) were reported in just over half of the
research protocols with these design features (see supplementary
No commercial reuse: See rights and reprints http://www.bmj.com/permissions Subscribe: http://www.bmj.com/subscribe
BMJ 2013;346:f1135 doi: 10.1136/bmj.f1135 (Published 21 March 2013) Page 3 of 10
Box 2: Categorisation of design assumptions
Variable with no justification
Variable and data on which assumption based (the “basis”)
Details of the data underpinning the variable—for example, previous studies with the new drug or products in the same therapeutic
class, physician survey, meta-analysis, literature search given
Treatment difference and data on which assumption based and discussion of its clinical importance
Required more than a simple statement that the “treatment difference was clinically important”. Reference to a specific study or studies
in which the clinically relevant difference has been determined, or a detailed clinical discussion of why the investigators considered the
difference sought to be meaningful
Variable and data on which assumption based and a reasoned explanation for choice
Required a discussion of the data underpinning the variable and an explanation why the value used in the sample size calculation was
plausible for the planned study
table 10). The potential for increasing the type II error was not
considered in any study with multiple comparisons. If all
co-primary variables must be significant to declare success then
the type II error rate can be inflated, resulting in reduction in
the overall study power.
Recalculation of the original sample size
If all protocols were considered using the rules for imputing
missing information then 262 of out 446 (59%) sample size
determinations could be reproduced, with 51 (11%)
under-estimated and 103 (23%) over-estimated. Thirty (7%) of
the original sample size calculations could not be recalculated
(see supplementary table 11). Figure 3⇓ shows a box plot of the
relative differences between the reported and recalculated sample
A total of 134 of the 188 (71%) sample size calculations from
protocols with complete reporting could be reproduced, with
20 (11%) under-estimated and 34 (18%) over-estimated,
respectively. The reproducibility of the sample size increased
with more comprehensive reporting, primarily withdrawal rates
and adjustments for multiple testing. None the less, both
analyses showed a tendency for over-estimation, and in total
only 134 of the 446 (30%) original sample size calculations
could be accurately reproduced.
Supplementary figure 6 shows a Bland-Altman plot comparing
reported and calculated sample sizes.
Commercial versus non-commercial sponsors
The reporting of the core components of the sample size
determination did not differ noticeably between studies with
commercial and non-commercial sponsors (fig 4⇓ and
supplementary table 12). Studies with non-commercial sponsors
were more likely than those with commercial sponsors to report
the basis for design assumptions (relative risk 1.69, 95%
confidence interval 1.38 to 2.08 for treatment difference and
1.29, 1.07 to 1.56 for variance and survival). Conversely, studies
with non-commercial sponsors were less likely than those with
commercial sponsors to report adjustments for multiple
comparisons (0.26, 0.13 to 0.50) and interim analyses (0.54,
0.31 to 0.93) and provide complete reporting (0.60, 0.45 to
0.81); the sample size calculation from protocols of studies with
non-commercial sponsors was also less likely to be reproduced
(0.72, 0.59 to 0.88).
Our review suggests that the reporting of the sample size
determination in the research protocol often lacks essential
information. Treatment difference and type I error were usually
given, but withdrawal rates and adjustments for multiple testing
were often missing. Only 188 of 446 (42%) protocols contained
sufficient information to accurately recalculate the sample size.
More than half of the research protocols provided no justification
for the assumptions used in the sample size calculation. When
a justification was given, it generally lacked detail. Sensitivity
analyses, which can help investigators understand the reliability
of the variables used in the sample size calculation and whether
sample size re-estimation should be included in the study design,
were rarely reported.
Imputing missing information resulted in 262 out of 446 (59%)
reproduced sample sizes. This increased to 134 out of 188 (71%)
when only complete reports were considered. Overall, only 134
of the 446 (30%) sample size calculations could be accurately
reproduced. Study size tended to be over-estimated rather than
Our research, the first extensive review of unpublished research
protocols, raises several problems with the statistical planning
of randomised controlled trials, in particular the limited
consideration afforded to the choice of design assumptions.
Sample size determinations are highly sensitive to changes in
design assumptions, which behoves sponsors to be rigorous
when estimating these variables.
Moreover, if the degree of
uncertainty is high then design assumptions should be checked
during the course of the trial.
Limitations of this review
We only reviewed the research protocol submitted to the
research ethics committee and had no access to any other
documents. Moreover, our review was completely independent
of the ethical review process. The protocols were submitted in
2009 to the UK National Research Ethics Service and reflect
clinical research practice at that time. None the less, the sample
is relatively recent and many sponsors planned to include sites
both within and outside the United Kingdom, so we believe our
findings can be generalised to other countries and regions for
commercial studies where global regulatory requirements exist.
For non-commercial studies, the quality of reporting depends
on the investigators experience. We did not verify the
appropriateness of the design assumptions used in the sample
size determination in this research project.
Implications of the findings
In many instances the validity of the sample size determination
and by extension the scientific validity of the study—one of the
main aspects of the ethical review process—could not be
The available evidence suggests that key sample size
assumptions are not determined in a rigorous manner. This may
explain why large differences have been observed between
design assumptions and observed data.
BMJ 2013;346:f1135 doi: 10.1136/bmj.f1135 (Published 21 March 2013) Page 4 of 10
sizes tended to be over-estimated, which is a concern given the
challenges of recruiting to randomised controlled trials.
methodologies to check assumptions and re-estimate sample
size during the study are often not applied, despite the fact that
these methods are encouraged by regulatory authorities.
Investigators should be rigorous in the determination of design
assumptions. There is no “one size fits all” approach. Sufficient
information should be reported to allow the sample size to be
reproduced and show that there is solid reasoning behind the
assumptions used in the calculation (box 3).
We would also ask the suppliers of software used to calculate
sample size to consider including the withdrawal and dropout
rate in the package to ensure that this is taken into account and
reported in the research protocol.
A poorly designed trial cannot be saved once it is completed.
Greater transparency in the reporting of sample size
determinations in research protocols would facilitate the early
detection of deficiencies in the study design. Moreover, better
justification of the design assumptions in the research protocol
would facilitate the overall ethical review process.
Despite calls for a different approach to sample size
determination, we believe that there is no substitute for spending
time designing the study and giving due consideration to the
risks and how these can be tackled.
Wherever the responsibility for scientific and statistical review
lies, we believe clear guidance on the sample size determination
should be provided and followed. Individuals with appropriate
statistical expertise should also play a central role in the ethical
review of research protocols.
Improving the review process
to place more focus on study design was the aim of the National
Research Ethics Service at the start of this project and we
propose to use the results of our research to develop guidance,
working with the ethics service and others interested in this
We thank the National Research Ethics Service for its support; IBE
research assistants Mathias Heibeck and Linda Hayanga for their
contribution to this project; and Michael Campbell, Sir Iain Chalmers,
Douglas Altman, Gary Collins, and Hugh Davies for their comments on
Contributors: UM had full access to all of the study data and takes
responsibility for the integrity of the data and the accuracy of the data
analyses. He is guarantor. TC and UM conceived and designed the
study. TC, Mathias Heibeck, and Linda Hayanga collected the data. TC
and UB carried out the statistical analyses. TC, Mathias Heibeck, Linda
Hayanga, and UM recalculated the sample sizes. TC, UM, and UB
interpreted the data. TC drafted the manuscript. UM and UB critically
reviewed the manuscript. The views expressed in the paper are those
of the authors and do not necessarily reflect the views of the National
Research Ethics Service, which became a part of the Health Research
Authority in December 2011.
Funding: This study received no funding.
Competing interests: All authors have completed the ICMJE uniform
disclosure form at www.icmje.org/coi_disclosure.pdf (available on
request from the corresponding author) and declare that: TC received
support for travel from the National Research Ethics Service and has
worked as a consultant for the clinical research organisation ICON in
the previous three years; they have no other relationships or activities
that could appear to have influenced the submitted work.
Ethical approval: Not required.
Data sharing: No additional data available.
1 ICH harmonised tripartite guideline. Statistical principles for clinical trials E9. Current Step
4 version dated 5 February 1998.
2 Emanuel EJ, Wendler D, Grady C. What makes clinical research ethical? JAMA
3 Victor N. Prüfung der wissenschaftlichen Qualität und biometriespezifischer Anforderungen
durch die Ethikkommissionen? Medizinrecht 1999;9:408-12.
4 Julious SA. Sample sizes for clinical trials. Chapman and Hall, 2009.
5 Chow SC, Shao J, Wang H. Sample size calculations in clinical research. Chapman and
6 Machin D, Campbell M, Tan SB, Tan SH. Sample size tables for clinical studies, 3rd ed.
7 Julious SA. Tutorial in biostatistics: sample sizes for clinical trials with normal data. Stat
8 Julious SA, Campbell MJ, Altman DG. Estimating sample sizes for continuous, binary
and ordinal outcomes in paired comparisons: practical hints. J Biopharm Stat
9 Campbell MJ, Julious SA, Altman DG. Estimating sample sizes for binary, ordered
categorical, and continuous outcomes in two group comparisons. BMJ 1995;311:1145-8.
10 Altman DG, Schulz KF, Moher D, Egger M, Davidoff F, Elbourne D, et al. The revised
CONSORT statement for reporting randomized trials: explanation and elaboration. Ann
Intern Med 2001;134:663-94.
11 Moher D, Schulz KF, Altman DG. The CONSORT statement: revised recommendations
for improving the quality of reports of parallel group randomised trials. Lancet
12 Chan AW, Upshur R, Singh JA, Ghersi D, Chapuis F, Altman DG. Research protocols:
waiving confidentiality for the greater good. BMJ 2006;332:1086-9.
13 Charles P, Giraudeau B, Dechartres A, Baron G, Ravaud P. Reporting of sample size
calculation in randomised controlled trials: review. BMJ 2009;338:b1732.
14 Chan AW, Hrobjartsson A, Jorgensen KJ, Gotzsche PE, Altman DG. Discrepancies in
sample size calculations and data analyses reported in randomised trials: comparison of
publications with protocols. BMJ 2008;337:a2299.
15 Altman DG. Statistics and ethics in medical research III: how large a sample? BMJ
16 Halpern SD, Karlawish JHT, Berlin JA. The continuing unethical conduct of underpowered
clinical trials. JAMA 2002;288:358-62.
17 Schulz KF, Grimes DA. Sample size calculations in randomised trials: mandatory and
mystical. Lancet 2005;365:1348-53.
18 Bacchetti P, Wolf LE, Segal MR, McCulloch CE. Ethics and sample size. Am J Epidemiol
19 Chalmers I. Cardiotocography v Doppler auscultation: all unbiased comparative studies
should be published. BMJ 2002;324:483-5.
20 Scharf HP, Mansmann U, Streitberger K, Witte S, Krämer J, Maier C, et al. Acupuncture
and knee osteoarthritis: a three-armed randomized trial. Ann Intern Med 2006;145:12-20.
21 Wood L, Egger M, Gluud LL, Schulz KF, Juni P, Altman DG, et al. Empirical evidence of
bias in treatment effect estimates in controlled trials with different interventions and
outcomes: meta-epidemiological study. BMJ 2008;336:601-5.
22 Julious SA, McIntyre NE. Sample sizes for trials involving multiple correlated must-win
comparisons. Pharm Stat 2012;11:177-85.
23 Senn SJ. Statistical issues in drug development. Wiley, 2007:198-9.
24 Bacchetti P. Current sample size conventions: flaws, harms, and alternatives. BMC Med
25 Kieser M, Wassmer G. On the use of the upper confidence limit for the variance from a
pilot sample for sample size determination. Biom J 1996;38:941-9.
26 Julious SA. Designing clinical trials with uncertain estimates of variability. J Pharm Stat
27 Djulbegovic B, Kumar A, Magazin A, Schroen A, Soares H, Hozo I, et al. Optimism bias
leads to inconclusive results—an empirical study. J Clin Epidemiol 2011;64:583-93.
28 McDonald AM, Knight RC, Campbell MK, Entwistle VA, Grant AM, Cook JA, et. al. What
influences recruitment to randomised controlled trials? A review of trials funded by two
UK funding agencies. Trials 2006;7:9.
29 FDA draft guidance for industry, adaptive design clinical trials for drugs and biologics.
FDA, Feb 2010.
30 Kieser M, Friede T. Simple procedures for blinded sample size adjustment that do not
affect the type I error rate. Stat Med 2003;22:3571-81.
31 Savulescu J, Chalmers I, Blunt J. Are research ethics committees behaving unethically?
Some suggestions for improving performance and accountability. BMJ 1996;313:1390-3.
32 Norman G, Monteiro S, Salama S. Sample size calculations: should the emperor’s clothes
be off the peg or made to measure? BMJ 2012;345:e5278.
33 Williamson P, Hutton JL, Bliss J, Blunt J, Campbell MJ, Nicholson R. Statistical review
by research ethics committees. J R Stat Soc Ser A 2000;163:5-13.
Accepted: 31 January 2013
Cite this as: BMJ 2013;346:f1135
This is an open-access article distributed under the terms of the Creative Commons
Attribution Non-commercial License, which permits use, distribution, and reproduction in
any medium, provided the original work is properly cited, the use is non commercial and
is otherwise in compliance with the license. See: http://creativecommons.org/licenses/by-
nc/2.0/ and http://creativecommons.org/licenses/by-nc/2.0/legalcode.
BMJ 2013;346:f1135 doi: 10.1136/bmj.f1135 (Published 21 March 2013) Page 5 of 10
Box 3: Recommended information to be reported in research protocols
All components necessary to reproduce the sample size, in particular withdrawal or dropout rate and adjustments for multiple comparisons
or interim analyses
Confidence interval for variables used in the calculation
A concise summary of the data from which variable estimates are derived. If the variable is based on previous studies then give details
of the study design, clinical phase, study population, relevant outcome measures, relevant results, and study size, ideally in a table
Discussion of the clinical importance of the treatment effect
A reasoned explanation of why the treatment difference and other design assumptions are plausible for the planned study, taking into
• All existing data, for example, previous clinical studies, relevant clinical pharmacology (dose effect relation, etc) and non-clinical data
• How any differences between the previous studies and the one planned impact on the design assumptions
• How robust the sample size and/or statistical power is to different assumptions (sensitivity analysis). If the variable estimates are
considered unreliable then re-estimation of the sample size could be considered
What is already known on this topic
Sample size determination is an accepted and important part of the planning process for randomised controlled trials
Sample size reporting in publications is often lacking essential information
What this study adds
Sample size reporting in original research protocols is often incomplete and in many instances the reliability of the design assumptions
and hence the validity of the sample size determination cannot be judged
The ethical review process should place greater focus on study design
Withdrawal and dropout rate are frequently not reported and therefore suppliers of sample size software could include this variable in
the package to improve reporting
Table 1| Study characteristics entered into research protocol database
Study identifier or research ethics committee reference number
Commercial or non-commercial sponsor
Therapeutic area and disease category
Standard drug treatments for medical condition. Was there an accepted “standard treatment” for the medical condition at the time the study was being designed?
Clinical phase: IIb, III, or IV
Primary outcome variables
Form of primary outcome variables (continuous, binary, time to event) and test procedure
Objectively assessed outcome—that is, one that is not influenced by investigators’ judgment (for example, all cause mortality and recognised laboratory variables)
Study blinding such as open label, partial blind, or double-blind
Comparators such as placebo and active-control
Study design, such as parallel group, crossover, group sequential
Study objective: superiority, non-inferiority, or therapeutic equivalence
Treatment difference sought (or margin). Data on which assumption was based; why plausible for planned study
Clinical importance of the treatment difference discussed
Standard deviation of treatment difference (or margin) or hazard rates, median survival, event rate, or responder rate in each study arm. Data on which assumption
was based; why plausible for the planned study
Type I error: one sided or two sided test
Type II error (power of a trial is 1−probability of a type II error)
Sample size: evaluable number of patients required for analysis or in the case of an event driven study, the number of events. The evaluable number of patients
required for analysis (obtained from the sample size calculation before adjusting for withdrawals). If only the total number of subjects to be enrolled was reported
then the number of evaluable patients was calculated using the assumed withdrawal rate. If the research protocol only reported one value for the sample size with
no information on assumed withdrawals then this figure was entered into the database
Withdrawal or dropout rate
Interim analysis and strategy to control type I error
BMJ 2013;346:f1135 doi: 10.1136/bmj.f1135 (Published 21 March 2013) Page 6 of 10
Multiple comparisons and strategy to control type I error
Additional information: additional variables needed to perform sample size calculations for specific statistical tests—for example, analysis of covariance, negative
binomial model, non-parametric tests; and sensitivity analyses
BMJ 2013;346:f1135 doi: 10.1136/bmj.f1135 (Published 21 March 2013) Page 7 of 10
Table 2| Main characteristics of the 446 research protocols
No (%) of protocols (n=446)Study characteristics
38 (9)Infectious disease
36 (8)Cardiovascular disease
35 (8)Central nervous system
34 (8)Respiratory system
34 (8)Musculoskeletal system
27 (6)Pain and anaesthesia
99 (22)Other therapeutic areas (each <5%)
102 (23)Phase IIb
5 (1)Phase II/III
251 (56)Phase III
88 (20)Phase IV
319 (72)Parallel group
88 (20)Group sequential
58 (13)Non-inferiority and equivalence
11 (2)Superiority and non-inferiority
2 (0.4)Not stated
BMJ 2013;346:f1135 doi: 10.1136/bmj.f1135 (Published 21 March 2013) Page 8 of 10
Fig 1 Reporting of core sample size components
Fig 2 Reporting the design assumptions
Fig 3 Difference between reported and calculated sample size. *Ratio of number of evaluable patients or events reported
in protocol to that calculated. †All calculations (n=416) with missing data imputed. Observations below 2.5th (0.61) or above
the 97.5th (1.74) centile are excluded. Minimum and maximum values (not shown) observed were 0.12 and 5.21, respectively.
‡Complete reporting (n=188): no data imputation. Minimum and maximum values (not shown) observed were 0.32 and
2.45, respectively. Central boxes span 25th (1.00 for both plots) and 75th (1.05 and 1.03, respectively) centiles, the
interquartile range. Horizontal line within box represents median (1.01 in both plots)
BMJ 2013;346:f1135 doi: 10.1136/bmj.f1135 (Published 21 March 2013) Page 9 of 10