reported in randomised trials: comparison of publications
An-Wen Chan, clinical fellow,1Asbjørn Hro ´bjartsson, senior researcher,2Karsten J Jørgensen, researcher,2
Peter C Gøtzsche, director,2Douglas G Altman, director3
ObjectiveTo evaluatehow oftensamplesize calculations
and methods of statistical analysis are pre-specified or
changed in randomised trials.
Design Retrospective cohort study.
Data source Protocols and journal publications of
published randomised parallel group trials initially
Copenhagen and Frederiksberg, Denmark (n=70).
Main outcome measure Proportion of protocols and
publications that did not provide key information about
sample size calculations and statistical methods;
proportion of trials with discrepancies between
Results Only 11/62 trials described existing sample size
calculations fully and consistently in both the protocol
and the publication. The method of handling protocol
deviations was described in 37 protocols and 43
publications. The method of handling missing data was
described in 16 protocols and 49 publications. 39/49
protocols and 42/43 publications reported the statistical
test used to analyse primary outcome measures.
Unacknowledged discrepancies between protocols and
34 trials), methods of handling protocol deviations (19/
43) and missing data (39/49), primary outcome analyses
(25/42), subgroup analyses (25/25), and adjusted
analyses (23/28). Interim analyses were described in 13
protocols but mentioned in only five corresponding
Conclusion When reported in publications, sample size
calculations and statistical methods were often explicitly
discrepant with the protocol or not pre-specified. Such
amendments were rarely acknowledged in the trial
publication. The reliability of trial reports cannot be
assessed without having access to the full protocols.
Sample size calculations and data analyses have an
important impact on the planning, interpretation, and
conclusions of randomised trials. Statistical analyses
often involve several subjective decisions about which
data to include and which tests to use, producing
on the decisions taken.1-7Methods of analysis that are
chosen or altered after preliminary examination of the
data can introduce bias if a subset of favourable results
is then reported in the publication.
bias by documenting a pre-specified blueprint for
conducting and analysing a trial. Explicit descriptions
unacknowledged, potentially biased changes made
after reviewing the study results.8-10To evaluate the
completeness and consistency of reporting, we
and compared the sample size calculations and data
reported in the publications.
We included all published parallel group randomised
trials approved by the scientific-ethics committees for
Copenhagen and Frederiksberg, Denmark, from 1
January 1994 to 31 December 1995. We defined a
randomised trial as a research study that randomly
allocated human participants to healthcare inter-
ventions. We manually reviewed the committees’
files in duplicate to identify eligible studies as part of
a separate study of outcome reporting.9We confirmed
and searching PubMed, Embase, and the Cochrane
Controlled Trials Register.9
For each trial, we reviewed the protocol, statistical
appendices, amendments, and publications that
reported the primary outcome measures. Two
reviewers used electronic forms to independently
extract data relating to the design, sample size
calculation, and statistical analyses in duplicate; we
resolved disagreements by discussion. No reviewer
extracted data from both the protocol and publication
for the same trial.
The pre-specified primary outcomes of our study
werethe proportionof trialprotocolsandpublications
about sample size calculations and statistical methods
1Mayo Clinic, Rochester, USA
2Nordic Cochrane Centre,
3Centre for Statistics in Medicine,
University of Oxford, Oxford
Correspondence to: A-W Chan
Cite this as: BMJ 2008;337:a2299
BMJ | ONLINE FIRST | bmj.compage 1 of 8
the information presented in the protocol and the
between calculated sample sizes in the protocol and
publication to be a discrepancy, as well as any
qualitative or quantitative difference in other informa-
tion we examined.
From publications, we noted the achieved sample
size and any statements about early stopping or
whether analyses were pre-specified or amended.
From both protocols and publications, we categorised
the design framework of the trial as superiority, non-
inferiority, or equivalence (box 1). We also recorded
the fundamental components of sample size calcula-
tions (table 1), the basis on which the minimum
clinically important effect size (delta) and estimated
event rates were derived (for example, previous
literature, pilot data), and any reference to re-estima-
tion of sample size on the basis of an interim analysis.
we focused on the one for the primary outcome
We also documented how deviations from the
treatment protocol were handled in terms of both the
stated type of analysis (such as intention to treat) and
outcome measure of the trial (box 1), we recorded the
method of handling missing data and the type of
statistical test used. We recorded the factors and
outcome measures used in any subgroup analyses;
the covariates and outcome measures used in any
adjusted analyses; and the number of statistical
comparisons described or reported between rando-
mised groups, excluding baseline comparisons.
Finally, we recorded the use of interim analyses and
data monitoring boards.
We identified 70 parallel group randomised trials that
received ethics approval in 1994-5 and were subse-
quently published (table 2).9The median publication
industry. Most trials involved two study arms (n=47),
multiple centres (46), and some form of blinding (49).
(10th-90th centile range 13-324). The most common
specialty fields were endocrinology (n=11), anaesthe-
siology (5), cardiology (5), infectious diseases (5), and
Sixty nine trials were designed and reported as
superiority trials. One trial was stated to be an
equivalence trial in the protocol but reported as a
superioritytrial in thepublication; noexplanation was
given for the change.
Sample size calculation
Overall, only 11 trials fully and consistently reported
all of the requisite components of the sample size
calculation in both the protocol and the publication.
Completeness of reporting—An a priori sample size
calculation was reported for 62 trials; 28 were
described only in the protocol and 34 in both the
protocol and the publication. Thirty seven protocols
and 21 publications reported all of the components of
the samplesize calculation (figure).Individualcompo-
nents were reported in 74-100% of protocols and 48-
only the calculated sample size without any further
details about the calculation. Among trials that
reported an estimated minimum clinically important
effect size (delta), 20/53 protocols and 10/33 publica-
tions stated the basis on which the figure was derived.
Box 1 Definitions of collected data
Superiority trial—Explicitly described as a study designed to show a difference in effects
between interventions or not explicitly described as an equivalence or non-inferiority trial
interval is presented
neither inferior nor superior to another or an equivalence margin is specified
Handling of protocol deviations
Intention to treat analysis—All participants with available data are analysed in the original
group to which they were randomly assigned (as randomised), regardless of adherence to
the protocol. No data are excluded for reasons other than loss to follow-up
Per protocol analysis—Participants with available data are analysed as randomised
provided they meet some defined level of adherence to the protocol
As treated analysis—Participants are analysed in the group corresponding to the actual
intervention received (ignoring original randomisation)
Main outcome(s) of interest, in the following hierarchical order:
1. Explicitly defined as primary or main
2. Outcome used in the power calculation
3. Main outcome stated in thetrial objectives
Proportion of trials (%)
Reported in protocol
Reported in publication
>1 discrepancy between publication and
protocol for trials reporting relevant data
Reporting of sample size calculations and data analyses in
publications compared with protocols
page 2 of 8
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Comparison of calculated and actual sample sizes—Sixty
two trials provided a calculated sample size in the
size within 10% of the calculated figure from the
protocol; 22 trials randomised at least 10% fewer
participants than planned as a result of early stopping
(n=3), poor recruitment (2), and unspecified reasons
(17); and 10 trials randomised at least 10% more
participants than planned as a result of lower than
anticipated average age (1), a higher than expected
recruitment rate (1), and unspecified reasons (8). A
calculated sample size was as likely to be reported
with the actual sample size compared with no
discrepancy (11/32 v 14/30).
publications and the protocols for 34 trials described a
in at least one component of the published sample size
calculation when compared with the protocol for
18 trials (figure). Publications for eight trials reported
components that had not been pre-specified in the
protocol, and 16 had explicit discrepancies between
information contained in the publication and protocol
amendments to the original sample size calculation.
(figure). Overall, the primary method described
for handling protocol deviations in the publication
differed from that described in the protocol for
19/43 trials; table4 provides details. None of
these discrepancies was acknowledged in the journal
Thirty protocols and 33 publications used the term
“intention to treat” analysis and applied a variety of
definitions (table 5). Few of these protocols (n=7) and
publications (3) made it explicit whether study
participants were analysed in the group to which they
were originally randomised. Most protocols (22) and
publications (18) incorrectly excluded participants
from the intention to treat analysis for reasons other
than loss to follow-up (table 5).
only 16 protocols and 49 publications (figure).
Methods reported in publications differed from the
not pre-specified in the protocol (38/49). For one trial,
the protocol stipulated that missing data would be
counted as failures, whereas in the publication they
were excluded from the analysis.
Primary outcome analysis and overall number of tests
Fifty four trials designated at least one outcome
measure as primary in the protocol (n=49) or publica-
tion (43). The statistical method for analysing the
primary outcome measure was described in 39
that described the statistical test for primary outcome
measures differed from the protocol (figure, box 2).
The median number of between group statistical
tests defined in 44 protocols was 30 (10th-90th centile
range 8-218); the other 26 protocols contained
insufficient statistical detail. Publications for all 70
trials reported a median of 22 (8-71) tests. Half of the
protocols (n=36) and publications (34) did not define
whether hypothesis testing was one or two sided.
Interestingly, we found one neurology trial that used
and a one sided P value in another (P=0.028).
Table 2 |Characteristics of published parallel group
Characteristic No of trials (n=70)
No of study groups:
Blinded in some way 49
Industry and non-industry 11
Non-industry only 10
Table 1 |Reporting of sample size calculations in trial protocols and publications
Component of sample size calculation
No of trials reporting each component (n=62)*
Name of outcome measure5131 28
Minimum clinically important effect size (delta)533332
Estimated event rate in each study arm†20/2712/16 9/14
Standard deviation for delta‡ 18/249/147/12
Alpha (type 1 error rate) 50 3331
Power 5134 32
Calculated sample size 6230 30
All components reported3721 18
*Among trials reporting at least one component of sample size calculation in trial protocol.
†For trials reporting sample size calculations using binary outcome measures.
‡For trials reporting sample size calculations using continuous outcome measures.
BMJ | ONLINE FIRST | bmj.compage 3 of 8
Overall, 25 trials described subgroup analyses in the
protocol (n=13) orpublication (20). All had discrepan-
of the trials with protocol specified analyses reported
only some (n=7) or none (5) in the publication.
reported at least one that was not pre-specified in the
protocol. Protocols for 12 of these trials specified no
subgroup analyses, whereas seven specified some but
not all of the published analyses. Only seven publica-
tions explicitly stated whether the analyses were
defined a priori; four of these trials claimed that the
subgroup analyses were pre-specified even though
they did not appear in the protocol.
Overall, 28 trials described adjusted analyses in the
protocol (n=18) or publication (18). Of these, 23 had
discrepancies between the two documents (figure,
box 2). Twelve of the trials with protocol specified
analysis. Twelve of the trials with published adjusted
analyses used covariates that were not pre-specified in
the protocol. Ten of these trials did not mention any
adjusted analysis in the protocol, whereas two trials
the covariates were defined a priori.
Interim analyses and data monitoring boards
Interim analyses were described in 13 protocols, but
reported in only five corresponding publications. An
additional two trials reported interim analyses in the
there would be none. A data monitoring board was
described in 12 protocols but in only five of the
We identified a high frequency of unacknowledged
discrepancies and poor reporting of sample size
cohort of randomised trials. To our knowledge, this is
the largest review of sample size calculations and
statistical methods described in trial publications
compared with protocols. We reviewed key methodo-
sented or altered retrospectively. Ourbroad sample of
protocols is a key strength, as unrestricted access to
such documents is often very difficult to obtain.11
Previous comparisons have been limited to case
reports,6small samples,1213specific specialty fields,14
and specific journals.15Other reviews of reports
submitted to drug licensing agencies did not have
access to protocols.41617
One limitation is that our cohort may not reflect
can be done only several years after protocol submis-
sion to allow time for publication. Whether the
widespread adoption of CONSORT and other report-
ing guidelines for publications has improved the
quality of protocols or reduced the prevalence of
unacknowledged amendments in recent years is
unclear.18However, our results are consistent with
more recent examples of discrepancies.31213Further-
more, we previously found that the prevalence of
publication restrictions stated in industry initiated trial
protocols did not change between 1995 and 2004.19
scientific or ethical review as a result of varying
Box 2 Anonymised examples of unacknowledged
discrepancies in sample size calculations and statistical
analyses reported in publications compared with
Sample size calculation
Changed delta (1)
? Outcome: disease progression or death rate
? Protocol: delta 10%; event rates unspecified
? Publication: delta 6%; event rates 16% and 10%
Changed delta (2)
? Outcome: mean number of active joints
? Protocol: delta 2.5 joints
? Publication: delta 5 joints
Changed standard deviation
? Outcome: mean symptom score
? Protocol: 1.4
? Publication: 0.49
? Outcome: survival without disease progression
? Protocol: 90%
? Publication: 80%
Changed sample size estimate
? Outcome: thromboembolic complication rate
? Protocol: 2200
? Publication: 1500
Changed primary outcome analysis
? Outcome: global disease assessment
? Protocol: χ2test
? Publication: analysis of covariance
New subgroups added to publication
? Outcome: time to progression or death
? Protocol: baseline disease severity
? Publication: duration of previous treatment*, type of
previous treatment*, blood count*, disease severity
? Outcome: neurological score at six months
? Protocol: baseline neurological score, pupil reaction,
age, CT scan classification, shock, haemorrhage
? Publication: no adjusted analysis reported
*Described explicitly as pre-specified despite not
appearing in the protocol
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standards, even though this information has a role in
evaluating the validity of a study. However, this does
not explain the frequent discrepancies we found
between explicit descriptions in protocols and pub-
lications (box 2).
We found that sample size calculations and impor-
tant aspects of statistical analysis methods were often
incompletely described in protocols and publications.
When reported in the publication, they were discre-
pant with the protocol for 44-100% of trials. The 70
unacknowledged changes to primary outcome mea-
sures in more than half of 102 trials,9so we are not
of study conduct.
Because the choice of parameters for sample size
calculations and statistical analyses is based on some-
what subjective judgments, specifying them a priori in
order to avoid selective reporting or revisions on the
basis of the data is important. This includes defining
each component of the sample size calculation20; the
analysis plan for primary outcome measures8; the
primary population for analysis21; and subgroup,2223
a favourable subset of analyses done can lead to
inaccurate interpretation of results, similar to selective
publication or selective outcome reporting.2526
Even when analysis plans are reported, concerns
may exist that published plans were constructed after
exploration of the data. Accurate reporting of sample
size calculations and data analysis methods is impor-
tant not only for the sake of transparency but also
because the choice of methods and the reasons for
protocols is thus needed to reliably appraise trial
publications. Several journals have recognised this
principle and require submission of protocols with
specification, where published information about the
sample size calculation or data analysis methods did
not appear in the protocol; and unacknowledged
amendments, where published information differed
from the protocol. Whereas the first type of discre-
pancy could be explained by varying standards in
protocol content, the second represents an explicit
publication of the trial. Retrospective amendments to
methods of statistical analysis can sometimes be
justifiable before unblinding of the trial, but no good
reason exists to misrepresent the pre-trial sample size
calculation or misleadingly describe the methods as
pre-specified when the protocol suggests otherwise.
committees and explicitly acknowledged in the pub-
Sample size calculations
Although good reasons exist for reporting sample size
calculations in publications,2031previous reviews of
publications have found poor reporting of sample size
Table 4 |Discrepancies in primary method of handling protocol deviations, as reported in
publications compared with protocols
Discrepancy and No
Primary method(s) described
Not pre-specified in protocol*—11:
4 None Per protocol
1 None ITT and per protocol
1 None ITT and as treated
Added new method in publication†—3:
2 Per protocol ITT and per protocol
1ITT ITT and on treatment analysis
Omitted protocol-specified method†—2ITT and per protocolPer protocol
1 Per protocol ITT
1As treated ITT
1 ITT Per protocol
ITT=intention to treat.
*Among 43 trials that described methods of handling protocol deviations in publication. †Among 32 trials that
described methods of handling protocol deviations in both publication and protocol.
Table 3 |Discrepancies in sample size calculations reported in trial publications compared with protocols
Component of sample size calculation
No of trials with discrepancy
Total Not pre-specified* Different from protocol description
Outcome measure (n=31)†734
Estimated delta (n=33)† 1266: 3 larger in protocol; 3 larger in article
Estimated event rates (n=16)‡330
Estimated standard deviation (n=14)§
52 3: 2 larger in protocol; 1 larger in article
Power (n=34)†927: 5 larger in protocol; 2 larger in article
Calculated sample size (n=30)†808¶: 7 larger in protocol; 1 larger in article
Any component (n=34)**188 16
*Reported in publication but not mentioned in protocol.
†Among trials reporting component in publication.
‡Among trials reporting event rates for binary outcome measures in publication.
§Among trials reporting standard deviations for continuous outcome measures in publication.
¶Greater than 10% difference in calculated sample size.
**Among trials reporting any component in publication.
BMJ | ONLINE FIRST | bmj.compage 5 of 8
calculations and their underlying assumptions.1432-36
These reviews involved specific specialty fields or
journals, and only one had access to trial protocols.14
Inadequate reporting and unacknowledged changes
in sample size calculations can introduce bias and lead
to misinterpretation of trial results. For example,
favourable results could be highlighted by changing
to calculate sample size,9or by modifying the pre-
specified minimum clinically important effect size
(delta), which helps to determine whether one study
intervention can be declared superior or equivalent to
another.631In addition, publications of studies with
poor recruitment might report a modified sample size
size had originally been planned. Although methods
for valid changes to sample size parameters mid-trial
study in our sample.
Although results for primary outcome measures are
profile, we found that the analysis method for primary
or altered in the publication. Such unacknowledged
changes compound previously identified discrepan-
cies in primary outcome measures.910
The recommended primary analysis population for
superiority trials is defined by the intention to treat
principle, whereby data from all trial participants are
analysed according to their randomly allocated study
arm, irrespective of the degree of compliance or
crossover to other interventions.38Missing data from
losses to follow-up can be handled with various
statistical methods that can each produce different
found that a high proportion of publications provide
deviations or missing data.4041In addition, a compar-
ison of publications with protocols of cancer trials
often than was reported in the publications.14
retrospective choices of analysis populations in almost
half of the publications in our cohort. This creates the
potential for preferential reporting of per protocol
analyses over less favourable intention to treat
analyses.45The definition of the term intention to
treat was also highly variable and often inaccurately
applied in our cohort, as has been found in other
reviews.40-42To avoid ambiguity, the study arm in
which participants are analysed and the criteria for
excluding participants from analyses should be expli-
citly defined in the protocol and publication.8
or to include particular covariates in adjusted analyses
may be influenced by extensive exploratory analyses
of the data.22Subgroup analyses in publications are
clarity about whether they were pre-specified.132743-45
Although exploratory analyses should be identified as
such, we found that assertions about analyses being
pre-specified were often misleading when compared
with protocols. In addition, most interim analyses
described in protocols were not mentioned in the
publication, which deprives readers of important
information about the decisions to stop or continue a
trial as planned.24
Our findings support the need to improve the content
of trial protocols and encourage transparent reporting
of amendments in publications through research
training. In collaboration with journal editors, trialists,
methodologists, and ethicists, we have launched the
initiative to establish evidence based recommenda-
tions for the key content of trial protocols.46Public
availability of trial protocols and submissions to
regulatory agencies is also necessary to ensure trans-
parent reporting of study methods.16174748Prospective
trial registration is an effective means of ensuring
public access to protocol information, although a
limited amount of methodological information is
currently recorded on registries.49-51
To improve the reliability of published results,
tions and full analysis plans before the trial is started
and should then analyse the results with fidelity to the
study protocol or describe major amendments in the
publication.8As the guardians of clinical research
before study inception, scientific and ethical review
committees can help to ensure that statistical analysis
plans are well documented in protocols. Only with
fully transparent reporting of trial methods and public
access to protocols can the results be properly
appraised, interpreted, and applied to care of patients.
Table 5 |Definitions of “intention to treat” analysis used in protocols and publications
Protocols (n=30) Publications (n=33)
Group assignment for analysis
According to original randomisation:5 20
Assumed on basis of participant flow diagram08
Assumed on basis of same participant
numbers at baseline and in results
According to intervention actually received*20
No description 23 13
Exclusion of participants from analysis
Exclude losses to follow-up only4 13
Exclude data from participants owing to†: 22 18
Inadequate adherence to treatment19 12
Other protocol violations65
Adverse events or lack of efficacy101
Unclear reasons for exclusion42
*Regardless of original randomised group assignment.
†Some trials had multiple reasons for exclusion.
page 6 of 8
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Contributors:All authors contributed to the study design, data collection,
data interpretation, and drafting of the manuscript. A-WC also did the
statistical analyses and is the guarantor.
Funding sources: None.
Competinginterests:A-WC chairs and AH, DGA, and PCG are members of
the steering committee for the SPIRIT (standard protocol items for
randomised trials) initiative, a project that aims to define key protocol
content for randomised trials.
Ethicalapproval:The scientific-ethics committees for Copenhagen and
Frederiksberg granted unrestricted access to trial protocols. The research
did not undergo the usual ethical review process, as patients’ data were
Provenanceandpeerreview:Not commissioned; externally peer
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WHAT IS ALREADY KNOWN ON THIS TOPIC
The results and conclusions of randomised trials are influenced by the choice of statistical
analysis methods and individual components of sample size calculations
If these methodological choices are defined or altered after examination of the data, the
potential for biased reporting of favourable results is substantial
WHAT THIS STUDY ADDS
Trial protocols and publications are often missing important methodological information
about sample size calculations and statistical analysis methods
When described,methodological information in journal publicationsisoften discrepant with
information in trial protocols
BMJ | ONLINE FIRST | bmj.com page 7 of 8
45 Assmann SF, PocockSJ, EnosLE, Kasten LE. Subgroup analysis and
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randomised trials. German J Evid Quality Health Care (suppl)
analysis?J Clin Epidemiol 2003;56:44-51.
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database. PLoS Med2004;1:e60.
Clinical trial registration—looking back and moving ahead. N Engl J
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registration: transparency isthe watchword. Lancet
51 Krlez ˇa-Jeric K, ChanAW, Dickersin K, Sim I, Grimshaw J, Gluud C.
Principlesfor international registration of protocol informationand
results from humantrials of health related interventions: Ottawa
statement (part 1). BMJ 2005;330:956-8.
Accepted: 10 September 2008
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