Methodological bias in cluster randomised trials

Article (PDF Available)inBMC Medical Research Methodology 5(1):10 · February 2005with18 Reads
DOI: 10.1186/1471-2288-5-10 · Source: PubMed
Cluster randomised trials can be susceptible to a range of methodological problems. These problems are not commonly recognised by many researchers. In this paper we discuss the issues that can lead to bias in cluster trials. We used a sample of cluster randomised trials from a recent review and from a systematic review of hip protectors. We compared the mean age of participants between intervention groups in a sample of 'good' cluster trials with a sample of potentially biased trials. We also compared the effect sizes, in a funnel plot, between hip protector trials that used individual randomisation compared with those that used cluster randomisation. There is a tendency for cluster trials, with evidence methodological biases, to also show an age imbalance between treatment groups. In a funnel plot we show that all cluster trials show a large positive effect of hip protectors whilst individually randomised trials show a range of positive and negative effects, suggesting that cluster trials may be producing a biased estimate of effect. Methodological biases in the design and execution of cluster randomised trials is frequent. Some of these biases associated with the use of cluster designs can be avoided through careful attention to the design of cluster trials. Firstly, if possible, individual allocation should be used. Secondly, if cluster allocation is required, then ideally participants should be identified before random allocation of the clusters. Third, if prior identification is not possible, then an independent recruiter should be used to recruit participants.
BioMed Central
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BMC Medical Research
Open Access
Research article
Methodological bias in cluster randomised trials
Seokyung Hahn
, Suezann Puffer
, David J Torgerson*
and Judith Watson
Medical Research Collaborating Center, Seoul National University College of Medicine, 2nd Floor Cancer Research Institute Building,
28 Yongon Dong, Chongno Gu, Seoul 110-744, Korea and
York Trials Unit, Department of Health Sciences, York YO10 5DD, UK
Email: Seokyung Hahn -; Suezann Puffer -; David J Torgerson* -;
Judith Watson -
* Corresponding author
Background: Cluster randomised trials can be susceptible to a range of methodological problems.
These problems are not commonly recognised by many researchers. In this paper we discuss the
issues that can lead to bias in cluster trials.
Methods: We used a sample of cluster randomised trials from a recent review and from a
systematic review of hip protectors. We compared the mean age of participants between
intervention groups in a sample of 'good' cluster trials with a sample of potentially biased trials. We
also compared the effect sizes, in a funnel plot, between hip protector trials that used individual
randomisation compared with those that used cluster randomisation.
Results: There is a tendency for cluster trials, with evidence methodological biases, to also show
an age imbalance between treatment groups. In a funnel plot we show that all cluster trials show a
large positive effect of hip protectors whilst individually randomised trials show a range of positive
and negative effects, suggesting that cluster trials may be producing a biased estimate of effect.
Conclusion: Methodological biases in the design and execution of cluster randomised trials is
frequent. Some of these biases associated with the use of cluster designs can be avoided through
careful attention to the design of cluster trials. Firstly, if possible, individual allocation should be
used. Secondly, if cluster allocation is required, then ideally participants should be identified before
random allocation of the clusters. Third, if prior identification is not possible, then an independent
recruiter should be used to recruit participants.
The randomised controlled trial (RCT) has a number of
important features that make it the 'gold-standard' evalu-
ation method. One of the most important aspects of ran-
dom allocation is that it eliminates selection bias.
Randomisation ensures that the two or more groups
formed are similar, except for chance differences, in all
aspects. Nevertheless unless trials are undertaken in a rig-
orous manner biases can be introduced that negate the
effect of random allocation. Indeed, a poorly conducted
RCT can be worse than a good observational study as the
latter is interpreted in the light of possible confounding
whereas the results of an RCT might be uncritically
Random allocation can take place either at the level of the
individual level or at a higher group or cluster level. In a
cluster randomised trial groups of people are allocated to
Published: 02 March 2005
BMC Medical Research Methodology 2005, 5:10 doi:10.1186/1471-2288-5-10
Received: 15 October 2004
Accepted: 02 March 2005
This article is available from:
© 2005 Hahn et al; licensee BioMed Central Ltd.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
BMC Medical Research Methodology 2005, 5:10
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receive an intervention or not. In some areas of evaluation
(e.g., education) the cluster is the natural method of allo-
cation. For example, a trial among school children may
well randomise by class or by school rather than by indi-
vidual child. Allocation by cluster may be preferable for a
number of reasons. There may be practical reasons: for
instance, teaching a novel curriculum will be easier to use
existing classes than form new ones through randomisa-
tion. There may be contamination issues. Individuals allo-
cated to a control treatment may inadvertently receive
some aspects of the intervention if they are in proximity to
the treated group.
Allocation by cluster has some important statistical issues
that have been addressed 65 years ago in the educational
trial literature [1] and subsequently widely in medical sta-
tistics [2]. In brief, analysis of cluster trials needs to take
into account the clustered nature of the data otherwise the
risk of a Type I error (i.e., erroneously concluding there
was a statistically significant difference) increases. How-
ever, more seriously in our view is the potential of cluster
trials producing a biased estimate of treatment effect.
Randomisation should eliminate selection bias. Selection
bias can be reintroduced within any trial if there is high
loss to follow-up or failure to use intention to treat analy-
sis. In cluster trials selection bias can also be introduced
through participant recruitment. Because cluster trials
often recruit their participants after the clusters have been
randomly allocated this can lead to selection effects[3,4].
There are a number of potential reasons for this.
Foreknowledge of allocation
If the person recruiting participants has both knowledge
of the clinical characteristics of the participants and of the
allocation schedule biased recruitment can occur. Subver-
sion, within individually randomised trials, can occur by
recruiting participants with poor prognostic characteris-
tics so that they are more likely to enter the 'unfavoured'
group [5,6]. Evidence for the biasing effects of allocation
foreknowledge has been shown on treatment effect sizes
[7,8]. Consequently a rigorously designed individually
randomised trial ought to conceal the allocation schedule
from the people who are recruiting participants.
Cluster randomised trials often do not, or cannot, conceal
treatment allocation. For example, a trial was undertaken
to reduce violence among children randomised by school
[9]. After allocation the children were recruited into the
study and the intervention was delivered. The allocation
could not be concealed from the teachers researchers or
children. This has two potentially unfortunate conse-
quences. Awareness of the allocation can lead to biased
recruitment in cluster trials [10]. Alternatively, or in addi-
tion, participants can differentially refuse consent to par-
ticipate in the trial and this could be another source of
selection bias. For example, in a cluster trial evaluating the
use of advanced end of life directives among residents of
nursing homes there was a differential in participant rates
of 83% among people in the intervention homes com-
pared with 92% in the control arm [11]. Such differential
participation rate can lead to selection bias.
Treatment effects on recruitment
Recruitment of participants with different clinical charac-
teristics is not necessarily a sign of subversion it could be
simply a consequence of the cluster level intervention. For
example, in an evaluation of an educational package for
the treatment of back pain primary care physicians were
trained in 'evidence based' management of back pain
[12]. This training was associated with an increased
recruitment rate among practices allocated to training
compared with no training. Because training involved rec-
ognition and diagnosis of back pain with hindsight we
should not be unsurprised that differential recruitment
would occur in this instance.
As well as having more potential, than individually ran-
domised trials, for the introduction of selection bias.
Cluster randomised trials also may be at more risk of dilu-
tion bias. Because consent for treatment is often not
obtained until after randomisation more participants,
than in an individually randomised study, may refuse
treatment and this will consequently dilute any treatment
effects. For example, Kendrick and colleagues in a cluster
randomised trial to prevent accidental injuries among
young children found that only 75% of the group allo-
cated to the experimental group actually received the
intervention [13].
Whatever the underlying reasons for differences in recruit-
ment the consequences are potentially the same: selection
bias has been introduced. Figure 1 shows the potential
sources of bias that can occur after cluster randomisation.
With the introduction of selection bias trial results are
unreliable. In this paper we examine some evidence for
this phenomenon and make recommendations on how to
design this problem out of future cluster trials.
Evidence for recruitment bias among individual trials
A recent review identified a sample of 36 cluster ran-
domised trials from three major general medical journals,
between 1997 and 2002 [4]. This review identified all
cluster randomised trials published in three major medi-
cal journals over a period of five years. In this review 15 of
the trials could have experienced bias in their recruitment
of participants. Of these 15 trials seven showed some evi-
dence in the published papers of consenting differential
numbers of participants or excluding participants in a
selective fashion. One of the remaining 8 trials, whilst
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having no evidence of bias in the original published paper
was later subsequently found to have experienced recruit-
ment bias [10]. Therefore, 25% of cluster trials published
in major clinical journals suffered potential selection bias.
On the other hand a review of 152 cluster trials under-
taken in primary care found that only 8 (5%) were found
were the authors reported differential recruitment [14].
However, unlike Puffer and colleagues each trial was not
carefully scrutinised to ascertain whether or not there was
a problem of biased recruitment (Eldridge, personal
Although Puffer and colleagues noted that some trials had
significant differences in recruitment and retention rates
between groups they did not investigate whether or not
this had an impact on important treatment covariates. To
assess whether observed differences in recruitment could
have had an effect on important predictors of outcome we
examined the age differences between treatment groups.
We chose age for two reasons: first, it is a commonly
reported baseline characteristic and, second, is the most
likely common confounder across different disease
groups. Nevertheless, we acknowledge that biased recruit-
ment may not manifest itself in terms of age differences
[12]. From the 36 trials we identified 14 that reported,
either directly or indirectly, the mean age and standard
deviation of the treatment groups. Of the 14 trials that
were included nine stated they had taken clustering into
account in their sample size calculation, two had not and
the remaining three it was not clear whether they had
adjusted their sample size. We then grouped the 14 trials
according to whether Puffer et al considered there was evi-
dence for differential recruitment. Eight out of the 14
Sources of bias in cluster trialsFigure 1
Sources of bias in cluster trials
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trials had been regarded as potentially biased. In Figure 2
we plot the standardised mean age differences between
treatment groups (ie., age difference divided by the
pooled within group standard deviation). Negative age
differences were all converted to positive differences as we
were uninterested in the direction of the bias.
As can be seen in Figure 2 the age difference between treat-
ment groups tend to be larger in the potentially biased
group. The mean age difference was greater than 10% of
their standard deviation in 3 out of the 8 potentially
biased trials. The pooled standardised mean difference in
the biased group was also twice as large as that in the non-
biased group. A test for the difference using a meta-regres-
sion resulted in a non-significant p-value of 0.15; there-
fore, the difference observed in this instance was not
conclusive. Age imbalances for any single trial could be
due to chance as it is more difficult to achieve balance in
cluster randomised trials compared with individually ran-
domised trials due to the smaller number of allocated
units. On the other hand, cluster trials, like individually
randomised trials should be balanced across all cluster tri-
als if there was no bias present.
In Figure 3 we plot the standardised mean age differences
by whether or not the trial showed a statistically signifi-
cant effect. The significance was determined as p-value <
0.05. In all 14 trials the analysis took the clustering effect
into account through various methods The figure suggests
that significant trial results were associated more often
with potentially biased recruitment with larger baseline
differences in age, even though a formal test for interac-
tion did not show a statistical significance (p-value 0.3) as
this was not adequately powered.
Evidence for bias from a systematic review
Cluster randomised trials often answer different questions
to individually randomised trials or cannot use individual
allocation. Therefore, it is difficult to make a direct com-
parison between individual and cluster randomised trials
in terms of the likely differences in effect sizes within the
same subject area. However, within the area of hip protec-
tion for fracture prevention there are trials using both
individual and cluster allocation. The most recent
Cochrane review of hip protectors has identified 13 RCTs
of hip protectors with hip fracture outcomes [15]. In addi-
tion, there is a large individually randomised trial that has
not yet been included in the review (i.e., 14 in total) [16].
In figure 4 the effect sizes from these trials are plotted
against their sample size. The sample sizes were adjusted
for the design effect for the cluster trials and therefore the
sample sizes for these trials are the effective sample sizes
(sample size divided by the design effect). One out of the
five cluster randomised trials reported their design effect,
from which we estimated an intra-cluster correlation coef-
ficient (ICC) and applied this to the other four studies, as
they are all similar trials, to calculate a correction factor.
As the figure shows the resulting funnel plot indicates lit-
tle evidence of effect from individually randomised trials.
In contrast, all of the cluster trials show a substantial ben-
efit when using the cluster design. This suggestion of bias
could be as a result of publication bias. On the other
hand, there are a number of alternative explanations.
Standardised mean differences of patient ageFigure 2
Standardised mean differences of patient age
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First, the cluster trials might have been undertaken in a
different setting than the individually randomised trials
and this might account for the observed differences in
effect. Second, the intervention (hip protection) may
work better using a clustered design. Third, there might be
treatment contamination in the individually randomised
trials: biasing the treatment effect towards the null.
Fourth, the observed differences may be due to poor
implementation of cluster trial methodology, which
biases the results of those trials towards the positive.
There is a tendency for the cluster trials to be largely
undertaken among residents of nursing homes compared
with individually randomised trials – although one of the
largest individually randomised trial was in a nursing
home setting. It is possible that compliance might have
been better in a nursing home setting and this could
account for the difference in effect. However, the compli-
ance rates were not that different from those trials using
individually randomisation.
The second reason that hip protection might work in a
clustered design might be that the intervention is deliv-
ered as a 'package' of care and their use alerts the clinical
staff responsible (e.g., nursing home staff) to the dangers
of falls and this encourages other anti-fracture
It is possible that in the individually randomised trials the
control group could have been 'contaminated' by access-
ing hip protection by, for example, buying the product
themselves. In a large individually randomised trial we
undertook of hip protectors [16] some participants in the
control arm did purchase hip protectors; however, the
prevalence of this was very low.
An alternative explanation of the difference was poor
implementation of the cluster trial methodology: includ-
ing selective recruitment, differential loss to follow-up
and failure to use intention to treat analysis. For example,
the largest cluster randomised trial had a 30% difference
Standardised mean difference by bias group and treatment significanceFigure 3
Standardised mean difference by bias group and treatment significance
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in the population that were included in the trial after ran-
dom allocation [17].
Preventing biased recruitment
In order for cluster randomised trials to provide unbiased
evidence for treatments we must design out any sources of
recruitment bias. In this section we will consider design
suggestions that should minimise this threat.
Use individual allocation
Often cluster randomisation is used to overcome the per-
ceived threat of contamination between the treatment
groups. Although in many instances this threat is real in
some cases there may be little contamination. Indeed,
even if there are quite high contamination rates (e.g.,
20%) it may still be more efficient in sample size terms to
randomise more patients in an individual trial and accept
a diluted effect size [3]. Therefore, one solution to avoid-
ing biased recruitment is to avoid using cluster trial meth-
ods if at all possible.
Prior identification of participants
In some instances it may be possible to identify partici-
pants before cluster allocation. For example, if we con-
sider a school based evaluation of a health promotion
curriculum. Children within schools or intact classes can
be identified before the cluster allocation. Children and
their parents can be asked to participate in the study and
are presented with the alternatives under consideration.
Once consent has been obtained to take part in the study
then the schools or classes are randomised to the different
Independent recruitment
Evaluation of an intervention for incidence disease cases
means prior identification is not possible. For example,
consider a trial of educating primary care physicians for
the treatment of acute shoulder pain. Because the condi-
tion has an incident nature it is necessary to recruit partic-
ipants in a prospective manner. Should the primary care
physician undertake this then selection bias is likely to
Funnel plot of individually and cluster randomised trialsFigure 4
Funnel plot of individually and cluster randomised trials
BMC Medical Research Methodology 2005, 5:10
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ensue. Therefore, to reduce this possibility an 'independ-
ent' person needs to recruit participants. Consider a recent
example of such an approach. In a trial of educating GPs
for the identification and treatment of depression in pri-
mary care trial participants were recruited by practice
receptionists. Because the receptionists from both inter-
vention and control practices had been exposed to the
same amount of trial training then the potential for selec-
tion bias is reduced, although never eliminated [18].
The use of cluster randomised trials has significantly
increased in medical research in recent years [19]. Despite
Lindquist outlining an appropriate approach to the anal-
ysis of cluster trials in 1940 [1] – many fail to undertake
the analysis taking the clustering effect into account. Con-
sequently the attention of many medical statisticians has
been directed at the appropriate analysis and sample size
issues with less attention to more serious problems with
the design of cluster trials. Whilst inappropriate analysis
will give misleading precision (i.e., smaller confidence
intervals and lower p values) it will rarely change the
point estimate of a treatment effect. In contrast, bias can
give a misleading effect size estimate.
Cluster randomised trials are potentially more susceptible
to some forms of bias than individually randomised trials.
Biased recruitment can be a problem in some cluster ran-
domised trials. One symptom of biased recruitment is dif-
ferential recruitment rates. However, one trial noted
significant selection bias even when there were similar
recruitment rates [10]. Therefore, even when recruitment
rates appear similar between treatment arms selection bias
can be introduced. We have examined the issue of bias in
cluster trials by comparing a sample of trials against simi-
lar individually randomised studies from a review of hip
protectors. This suggested a difference in effect size that
was dependent upon the type of study design. However,
the sample size was small and there are alternative
explanations to the apparent differences in effect sizes: not
least the explanation of chance. We have also looked at
baseline differences in ages of people in cluster trials that
appeared to be free of bias with those that seem to have
had bias introduced due to poor methodological applica-
tion of design. There was a difference in age imbalance,
which was suggestive of an interaction with statistical sig-
nificance of trial results although a formal statistical test
failed to show a significance of the difference. Our sample
size was relatively small and we could have missed a sta-
tistically significant difference through lack of statistical
power. Nevertheless, this paper does raise concerns about
the design of cluster trials and signals that such trials
should be used with caution.
If there are important confounding variables, stratifica-
tion, matching or regression models for clustered data are
required. Studies with evidence of biased recruitment
might try methods of analysis that allow for observed con-
founding. For example, if there were imbalances in
patient or cluster level covariates between the randomised
groups multi-level or hierarchical models explicitly model
the treatment effect adjusting for the confounding, pro-
vided that there is a fairly large number of clusters. How-
ever, even the most sophisticated statistical analysis
cannot adjust for the unmeasured or unknown con-
founder, which is one of the main reasons we undertake
random allocation. Therefore, it is crucial that we avoid
the introduction of bias into our cluster designs.
Future cluster randomised trials should endeavour to
either identify participants before randomisation or use
an independent person, preferably blind to allocation, to
recruit participants. Furthermore, cluster randomised tri-
als ought to be undertaken such that loss to follow-up is
similar between groups and intention to treat is always
Competing interests
The author(s) declare that they have no competing
Authors' contributions
SH undertook the statistical analysis and wrote sections
about statistical methods and implications. SP wrote the
first draft and contributed to the original data collection.
DT had the original idea of the paper and undertook revi-
sions to the original draft. SW contributed to the original
review and collected additional data for the paper. All
authors contributed to commenting on drafts of the
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Pre-publication history
The pre-publication history for this paper can be accessed
    • "However, given that adherence rates based on prescription records frequently overestimate adherence [32], and as the INCA device is designed to assess actual adherence (defined as the number of doses taken correctly at the correct time), we feel that this is justified. As with other cluster randomised trials where allocation concealment is not possible there is a risk of selection bias [33, 34] both from the pharmacist and participant perspective. To minimise such bias pharmacists in each individual site are trained to recognise the importance of unbiased recruitment and recruitment to each site is monitored by the lead pharmacist researcher so that potential bias can be identified and addressed through further counselling and/or training as required. "
    [Show abstract] [Hide abstract] ABSTRACT: Background Poor adherence to inhaled medication may lead to inadequate symptom control in patients with respiratory disease. In practice it can be difficult to identify poor adherence. We designed an acoustic recording device, the INCA® (INhaler Compliance Assessment) device, which, when attached to an inhaler, identifies and records the time and technique of inhaler use, thereby providing objective longitudinal data on an individual’s adherence to inhaled medication. This study will test the hypothesis that providing objective, personalised, visual feedback on adherence to patients in combination with a tailored educational intervention in a community pharmacy setting, improves adherence more effectively than education alone. Methods/design The study is a prospective, cluster randomised, parallel-group, multi-site study conducted over 6 months. The study is designed to compare current best practice in care (i.e. routine inhaler technique training) with the use of the INCA® device for respiratory patients in a community pharmacy setting. Pharmacies are the unit of randomisation and on enrolment to the study they will be allocated by the lead researcher to one of the three study groups (intervention, comparator or control groups) using a computer-generated list of random numbers. Given the nature of the intervention neither pharmacists nor participants can be blinded. The intervention group will receive feedback from the acoustic recording device on inhaler technique and adherence three times over a 6-month period along with inhaler technique training at each of these times. The comparator group will also receive training in inhaler use three times over the 6-month study period but no feedback on their habitual performance. The control group will receive usual care (i.e. the safe supply of medicines and advice on their use). The primary outcome is the rate of participant adherence to their inhaled medication, defined as the proportion of correctly taken doses of medication at the correct time relative to the prescribed interval. Secondary outcomes include exacerbation rates and quality of life measures. Differences in the timing and technique of inhaler use as altered by the interventions will also be assessed. Data will be analysed on an intention-to-treat and a per-protocol basis. Sample size has been calculated with reference to comparisons to be made between the intervention and comparator clusters and indicates 75 participants per cluster. With an estimated 10 % loss to follow-up we will be able to show a 20 % difference between the population means of the intervention and comparator groups with a power of 0.8. The Type I error probability associated with the test of the null hypothesis is 0.05. Discussion This clinical trial will establish whether providing personalised feedback to individuals on their inhaler use improves adherence. It may also be possible to enhance the role of pharmacists in clinical care by identifying patients in whom alteration of either therapy or inhaler device is appropriate. Registration NCT02203266. Electronic supplementary material The online version of this article (doi:10.1186/s13063-016-1362-9) contains supplementary material, which is available to authorized users.
    Full-text · Article · Dec 2016
    • "Alternatives of randomisation on a patient level are cluster randomisation or a step-wedge design . A difficulty of cluster randomisation is the need for comparable clusters [48], which is not possible for this study on the hospital level as patient characteristics differ between hospitals. Likewise, a difficulty of a stepwedge design is the need for a larger sample size, starting with all clusters (i.e. "
    [Show abstract] [Hide abstract] ABSTRACT: Background Although the importance of work for patients with cancer is nowadays more acknowledged both in the literature as well as in cancer survivorship care, effective interventions targeting the return to work of these patients are still scarce. Therefore, we developed a nurse-led, stepped-care, e-health intervention aimed at enhancing the return to work of patients with cancer. The objective of this study is to describe the content of the intervention and the study design used to evaluate the feasibility and (cost) effectiveness of the intervention. Methods We designed a multi-centre randomised controlled trial with a follow-up of 12 months. Patients who have paid employment at the time of diagnosis, are on sick leave and are between 18–62 years old will be eligible to participate. After patients have signed the informed consent form and filled in the baseline questionnaire, they are randomly allocated to either the nurse-led, stepped-care, e-health intervention called Cancer@Work, or care as usual. The primary outcome is sustainable return to work. Secondary outcomes are sick leave days, work ability, work functioning, quality of life, quality of working life and time from initial sick leave to full return to work without extensive need for recovery. The feasibility of the Cancer@Work intervention and direct and indirect costs will be determined. Outcomes will be assessed by questionnaires at 3, 6, 9 and 12 months of follow-up. DiscussionThe results of this study will provide new insights into the feasibility and (cost) effectiveness of Cancer@Work, a nurse-led, stepped-care, e-health intervention for cancer patients aimed at enhancing their return to work. If proven effective, the intention is to implement the Cancer@Work intervention in usual psycho-oncological care. Trial registrationNTR (Netherlands Trial Registry): NTR5190. Registered on 18 June 2015.
    Article · Dec 2016
    • "This may challenge the balance between groups in terms of baseline covariates. Indeed, clusters are sometimes randomized before the identification and recruitment of participants, which may jeopardize allocation concealment2345. In their review, Puffer et al. [6] showed that 39 % of the selected CRTs were at risk of confounding bias on individual characteristics . "
    [Show abstract] [Hide abstract] ABSTRACT: Background: Despite randomization, baseline imbalance and confounding bias may occur in cluster randomized trials (CRTs). Covariate imbalance may jeopardize the validity of statistical inferences if they occur on prognostic factors. Thus, the diagnosis of a such imbalance is essential to adjust statistical analysis if required. Methods: We developed a tool based on the c-statistic of the propensity score (PS) model to detect global baseline covariate imbalance in CRTs and assess the risk of confounding bias. We performed a simulation study to assess the performance of the proposed tool and applied this method to analyze the data from 2 published CRTs. Results: The proposed method had good performance for large sample sizes (n =500 per arm) and when the number of unbalanced covariates was not too small as compared with the total number of baseline covariates (≥40 % of unbalanced covariates). We also provide a strategy for pre selection of the covariates needed to be included in the PS model to enhance imbalance detection. Conclusion: The proposed tool could be useful in deciding whether covariate adjustment is required before performing statistical analyses of CRTs.
    Full-text · Article · Dec 2016
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