Torgerson, D J

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This is a repository copy of Contamination in trials: is cluster randomisation the answer?.White Rose Research Online URL for this paper:https://eprints.whiterose.ac.uk/43/Article:Torgerson, D J orcid.org/0000-0002-1667-4275 (2001) Contamination in trials: is cluster randomisation the answer? British medical journal. pp. 355-357. ISSN 1756-1833 https://doi.org/10.1136/bmj.322.7282.355eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. Contamination in trials: is cluster randomisation theanswer?David J TorgersonMost randomised trials allocate individual participantsto different treatments. However, cluster randomisedtrials in which groups of subjects are allocated todifferent treatments are becoming increasingly popu-lar.1 Cluster randomisation is often advocated to mini-mise treatment “contamination” between interventionand control participants. For example, in a trial ofdietary change, people in the control group mightlearn about the experimental diet and adopt itthemselves.Contamination of control participants has tworelated effects. It reduces the point estimate of an inter-vention’s effectiveness and this apparent reduction maylead to a type II error—that is, rejection of an effectiveintervention as ineffective because the observed effectsize was neither statistically nor clinically significant.Although the threat of contamination is an issue insome controlled trials, it may be not be of much practi-cal importance in many. Trialists should use individualrandomisation if possible because of the drawbacks ofcluster allocation. Cluster trials are associated withproblems of recruitment bias and the need for largersamples than would be required in similar, individuallyrandomised trials. In recruitment bias, different sorts ofparticipants are selected into the various arms of thetrial, thereby defeating the objective of randomisation,while a larger sample size may increase the cost of atrial, its length, or its complexity. This paper describesthe difficulties of cluster trials and argues that theproblem of contamination can often be dealt with byindividual randomisation.Sample sizeMembers of clusters cannot be treated as independent,and the effect of this on outcomes leads to a need toincrease the sample size.1 2 This problem can also bedescribed as follows: for any given sample size, the cor-relation between cluster members will reduce the over-all power of the study. The difficulty is well known andmuch has been published recently on sample size andanalytical issues.1–4Selection bias in cluster trialsThe randomised trial is the ideal study design in evalu-ative research because of its ability to deal with knownand unknown confounding factors. If randomisation issuccessful, these factors should be balanced across thetreatment groups. Balance in cluster trials can beachieved through randomisation across the trial armsat the cluster level if there are sufficient clusters. How-ever, simple randomisation of clusters, even withrelatively large numbers, can still result in animbalance. For instance, in a randomised trial of breastscreening there was an imbalance in socioeconomicgroups between the two study arms even though 87clusters (general practices) and 50 000 women wereincluded.5 This imbalance would have been extremelyunlikely had the trial used individual randomisation.Cluster trials generally use the postrandomisedconsent method of trial design, which is similar in con-cept to Zelen’s method in individually randomiseddesigns.6 Participants are not asked for their consent torandomisation; they are usually asked for consent totreatment (although this is not always done in clustertrials) and are asked whether they consent to inclusionin the study analysis. When cluster trials are analysed atthe individual level using this method, balance betweenthe randomised groups can only be guaranteed if oneof two conditions are fulfilled: all members of the clus-ter must be included in the trial, or a random sample ofparticipants must be included in the trial’s analysis. Thelatter approach may be used to increase the statisticalpower of the study for a given sample size by increasingthe number of clusters rather than the total number ofpatients.4 For instance, Kerse et al took a random sam-ple of patients from each cluster rather than allrandomised individuals.7 Neither of these conditionshas been met in recently published cluster trials. Oftenparticipants are asked after randomisation whetherthey will participate in the trial in terms of providingdata for follow up. If a significant proportion refuses,there is a possibility of selection bias.Observable characteristicsAn example of selection bias was seen in a recent trialof counselling to reduce the risk of cardiovascular dis-ease.8 Participants were allowed the choice of acceptingthe intervention and providing data on outcomes. Par-ticipation in the control arm was more desirable thanparticipation in the intervention, as a result of whichnearly twice as many subjects were recruited ascontrols. Moreover, the participants in the interventiongroup had some observable characteristics, such as alower prevalence of smoking, which put them at alower risk of coronary heart disease than the controlgroup. Thus, the modest effect associated with theA statisticalappendix appearson the BMJ’swebsiteSummary pointsCluster trials are often used to prevent“contamination” between intervention andcontrol groupsCluster trials are usually very much larger thanindividually randomised trials and can besusceptible to recruitment biasThe problem of contamination can often beovercome by increasing the sample sizeIn terms of total sample size, cluster trials are onlymore efficient where contamination exceeds 30%Education and debateCentre for HealthEconomics,University of York,York YO10 5DDDavid J Torgersonsenior research fellowdjt6@york.ac.ukBMJ 2001;322:355–7355BMJ VOLUME 322 10 FEBRUARY 2001 bmj.comintervention could have been due to the recruitment ofdifferent types of participant rather than the interven-tion. Similarly, in a cluster trial of diabetes care theintervention clusters identified about 25% moreeligible patients than the control clusters, although thetotal size of the list of patients was slightly greater in thecontrol clusters.9Unobserved characteristicsEven when recruitment between the intervention andcontrol clusters is similar and the observed baselinecharacteristics between allocation groups seem bal-anced, if not all the members of the cluster or arandom sample of them are included in the analysis,the trial may still be unbalanced because of unobservedcharacteristics. For example, in a trial of a behaviouralintervention to prevent violence in schools, thenumber of pupils in the two groups was similar, butonly 66% of children—those whose parents hadreturned consent forms—were included in the study.10However, the intervention was still delivered tochildren whose parents had not returned consentforms. Although the trial recorded a creditable 82%follow up, this represented only 54% of the entire ran-domised sample. In contrast, a trial of accident preven-tion in children included all relevant members of thecluster in the analysis (children aged 3-12 months) andmanaged to collect and analyse outcome data on morethan 92%, thus reassuring us that little, if any, selectionbias had taken place.11Reduced power: Zelen’s methodWhen Zelen’s method is used in an individuallyrandomised trial there is usually a loss of statisticalpower because there is incomplete penetration of theintervention. Thus, uptake of a new treatment that isless than 100% will lead to a dilution of the effect oftreatment and will reduce the measurable effect size.12Because cluster trials also use Zelen’s method, this dilu-tion of effect applies to them too. For example, in acluster trial of injury prevention in young children theintervention was not delivered to about 25% of parentsin the experimental arm.11 This problem is not gener-ally recognised in estimating the sample size for clustertrials, and if it is taken into account it will lead to a gen-eral increase in sample sizes. Thus, some cluster trialsnot only need to account for the clustering effects onstatistical power, they also need to boost sample sizesbecause of the dilution effect.Dealing with contaminationBefore considering cluster randomisation as a way ofaddressing contamination we need to be certain thatcontamination is a real rather than a theoretical possi-bility. Are patients who are receiving counselling reallygoing to pass on the intervention in such a way as toalter behaviour in the control arm of a trial? This thesiscould be tested empirically by undertaking a pilot trialusing individual randomisation with contamination ofthe control group as the outcome. However, even ifcontamination were a problem and a sizeableproportion of the control group was affected,individual randomisation might still be best.As an example, consider a trial of counselling topromote healthy behaviour in adults at high risk ofcardiovascular disease.8 To detect a 9% reduction insmoking prevalence from 50% to 41% with 90% powerat a significance value of 5%, a total of 1282participants would have been needed. However,because the trialists elected to use a cluster design asample of 2000 was required. The trialists could havechosen individual randomisation with a sample size of2000 and utilised the extra power of this increasedsample to cope with any contamination. Thus, a sampleof 2000 would have been able to detect a 7% differencein smoking prevalence with 90% power and 5% signifi-cance, allowing for up to a 20% contamination of thecontrol group. Furthermore, this estimate of the allow-able contamination assumes that the effectiveness ofthe intervention through contamination is as powerfulas if it had been delivered by healthcare professionals.However, if we assume that it was only half as effective,contamination could be much greater. Indeed, ifcontamination in this particular trial had beentheoretical, the non-significant effect size noted in thetrial would have been significant if individual randomi-sation had been used.Effects of contamination on sample sizeThe probable scale of contamination will clearly differwith the intervention, and I am not aware of any pub-lished estimates in trials that might have used a clusterdesign to avoid contamination. However, a review ofZelen’s method in cancer trials that did not use clusterrandomisation showed that the mean proportion ofpatients who crossed from one treatment to another,which is analogous to contamination, was 18% (range10%-36%).12 The tables show the impact that differentintracluster correlation coefficients and contaminationrates have on estimates of sample size or contamina-tion. Around 30% contamination can be sustainedbefore the sample size has to be doubled to take intoaccount the reduced effect size from such contamina-tion. However, use of cluster randomisation rapidlyleads to a doubling of the sample size. Even if the intra-cluster coefficient of correlation is very low, the clustersare small, and there are relatively high levels ofcontamination, individual randomisation can stillresult in a smaller sample size.Reduced effect sizeAlthough some contamination can be dealt with byincreasing the sample size, a trial might still show a sta-tistically significant effect but one that is too small to beof clinical relevance. Trials are rarely powered on thebasis of a minimum clinical significance. Rather, theyare powered on the likely effect that other trials havedetected or on the basis of observational work or onlogistical factors. Thus, the reduced effect size causedTable 1 Numbers of participants required in an individually randomised trial to detect adifference between two groups where the true effect size is 25%Contamination (%)0 5 10 15 20 25 30Sample size 116 126 144 164 182 200 236Contamination effect 1 1.09 1.24 1.41 1.58 1.72 2.03Education and debate356 BMJ VOLUME 322 10 FEBRUARY 2001 bmj.comby contamination could be used to calculate samplesizes.DiscussionOften a cluster design is the correct design for a trial.For instance, a randomised trial of training teachers topromote smoking cessation demanded a cluster designas it would not have been practical to randomisechildren to different teachers.13 In these instances onemust be aware of the potential problems of selectionbias creeping into the study. However, there isuncertainty with many trials. Thus, recent cluster trialswhich probably could have used an individuallyrandomised design include a vitamin A supplementa-tion study,14 an accident prevention trial,11 and alifestyle behaviour changes study.8 Because of theproblems outlined in this paper, trialists ought to con-sider very carefully the cluster approach to trial design.Substantial contamination can be tolerated within theusual individual randomised trial before a clusterdesign is better in terms of total sample size.I thank Hazel Inskip, the BMJ ’s referee, for helpful comments onthe original manuscript.Competing interests: None declared.1 Campbell MK, Grimshaw JM. Cluster randomised trials: time forimprovement. BMJ 1998;317:1171-2.2 Kerry SM, Bland M. The intracluster correlation coefficient in cluster ran-domisation. BMJ 1998;316:1455-60.3 Ukoumunne OC, Gulliford MC, Chinn S, Sterne J, Burney P, Donner A.Evaluations of health care interventions at area and organisation level. In:Black N, Brazier J, Fitzpatrick R, Reeve B, eds. Health services research meth-ods: a guide to best practice. London: BMJ Publishing, 1998.4 Campbell MK, Grimshaw J, Steen N. Sample size calculations for clusterrandomised trials. J Health Services Res Policy 2000;5:12-6.5 Alexander FE, Anderson TJ, Brown HK, Forrest APM, Hepburn W, Kirk-patrick AE, et al. 14 years of follow-up from the Edinburgh randomisedtrial of breast-cancer screening. Lancet 1999;353:1903-8.6 Zelen M. A new design for randomized clinical trials. N Engl J Med1979;300:1242-5.7 Kerse NM, Flicker L, Jolley D, Arroll B, Young D. Improving the healthbehaviours of elderly people: randomised controlled trial of a generalpractice education programme. BMJ 1999;319:683-7.8 Steptoe A, Doherty S, Rink E, Kerry S, Kendrick T, Hilton S. Behaviouralcounselling in general practice for the promotion of healthy behaviouramong adults at increased risk of coronary heart disease: randomisedtrial. BMJ 1999;319:943-8.9 Kinmouth AL, Woodcock A, Griffin S, Spiegal N, Campbell MJ.Randomised controlled trial of patient centred care of diabetes in generalpractice: impact on current wellbeing and future disease risk. BMJ1998;317:1202-8.10 Grossman DC, Neckerman HJ, Koepsell TD, Liu PY, Asher KN, Beland K,et al. Effectiveness of a violence prevention curriculum among children inelementary school: a randomised trial. JAMA 1997;277:1605-11.11 Kendrick D, Marsh P, Fielding K, Miller P. Preventing injuries in children:cluster randomised controlled trial in primary care. BMJ 1999;318:980-3.12 Altman DG, Whitehead J, Parmar MKB, Stenning SP, Fayers PM, MachinD. Randomised consent designs in cancer clinical trials. Eur J Cancer1995;31A:1934-44.13 Aveyard P, Cheng KK, Almond J, Sherratt E, Lancashire R, Lawrence T, etal. Cluster randomised controlled trial of expert system based on thetranstheoretical (“stages of change”) model for smoking prevention andcessation in schools. BMJ 1999;319:948-53.14 West KP, Katz J, LeClerq SC, Pradham EK, Sherestha SR, Connor PB, etal. Double blind, cluster randomised trial of low dose supplementationwith vitamin A or â carotene on mortality related to pregnancy in Nepal.BMJ 1999;318:570-5.(Accepted 24 July 2000)Table 2 Numbers of participants required in a cluster trial to detect a differencebetween two groups where the true effect size is 25%Cluster sizeIntracluster correlation coefficient 1 10 20 30 40 50 1000.01:Sample size 116 126 139 150 161 173 231Design effect 1 1.09 1.20 1.29 1.39 1.49 1.990.02:Sample size 116 137 160 184 207 230 346Design effect 1 1.18 1.38 1.59 1.78 1.98 2.980.03Sample size 116 148 182 218 252 287 461Design effect 1 1.27 1.57 1.88 2.17 2.47 3.97A memorable patientA life saving procedureA 34 year old temple priest from the Maharashtra district ofcentral India was on his way home from a pilgrimage to a templein northern India. He had been suffering from diarrhoea andvomiting for the past 12 hours. He thought he would cope with ituntil he arrived home and saw his doctor. But he was wrong. Hewas fast losing body water and getting colder. I know because Iwas travelling in the same train, in the same compartment. Hewas weak and could barely open his eyes. His pulse was weak,thready, and rapid, his extremities were cold and he wasperspiring. I told his wife that he needed at least two lines in hisarms and lots of fluids.I requested the ticket checker to bring an emergency kit, butwhen I opened it I found it did not have intravenous fluids. All Icould do was to give him an injection to keep up his bloodpressure. The next stop was three and a half hours away, and thatwas too long for him. I discussed this again with his wife, and bynow everybody in the compartment was involved. A unanimousdecision was made to pull the chain and stop the train at somestation on the way.But then came the next problem. All the chains turned out tobe jammed. It was a real surprise and nobody knew what to donext. There was no way of communication between the ticketchecker and the driver.I then suggested that when the train slowed down at somestation on the way we should drop a note carrying a message forthe station master to alert the master at the next station to haltour train there. We wrapped the note round a five rupee coin andthrew it near enough for the signalman to notice. It worked. Thetrain was stopped at the next station and the priest was lifted awayto hospital, while his wife kept on thanking me.I felt frustrated at not being of much help to him, and angry atthe rail authorities for their negligence. Also I thought I wouldnever be able to find out how the priest was.Surprisingly, his wife had checked on the list of passengers andfound my address, because when I reached home I found a letterof thanks from the priest. He had made an uneventful recoveryafter two days in hospital. After that he kept writing to mebecause he thought I had helped save his life—not because of theinjection but because I had come up with the idea of stopping thetrain. Recently he has invited me to his elder daughter’s wedding.Kalpesh Shah clinical observer, IpswichWe welcome articles of up to 600 words on topics such asA memorable patient, A paper that changed my practice, My mostunfortunate mistake, or any other piece conveying instruction,pathos, or humour. If possible the article should be supplied on adisk. Permission is needed from the patient or a relative if anidentifiable patient is referred to. We also welcome contributionsfor “Endpieces,” consisting of quotations of up to 80 words (butmost are considerably shorter) from any source, ancient ormodern, which have appealed to the reader.Education and debate357BMJ VOLUME 322 10 FEBRUARY 2001 bmj.com

Contamination in trials: is cluster randomisation the answer?

D. J Torgerson

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Contamination in trials: is cluster randomisation the answer?

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