38 CLINICAL RESEARCHER – Vol1 No11 NOVEMBER 2001

Practical Issues in Trial Design

Why should patients in aclinical trial be randomized?The randomized controlled trial (RCT) isconsidered the gold standard for testing theefficacy of medical treatments. A fundamentalassumption that forms the basis of the RCTis that patients in different groups are similarfor characteristics such as age, gender, socialclass, time of year of presentation, countryof presentation and type of hospital. In alarge trial involving more than 1000 patients,these characteristics should be balancedacross each group so that any difference

seen between the groups at the end of thetrial is then due to the different treatmentstrategies, i.e. if patients do better in onegroup we can assume that this is due to thetreatment effect. This assumption is the basisof all comparative statistical tests performedin the trial. To achieve this balance werandomly assign the patients (hence the termrandomized in an RCT) to each treatmentstrategy so that, for example, men have anequal chance of being given treatment A or B,people aged over 60 have an equal chanceof being given treatment A or B, and so

on. Simple randomization is one way of performing this balancing function, but other methods are needed when the number of patients is small.

Minimizing biasA further requirement of randomization is that it must not be predictable by theperson assigning patients to the treatmentstrategies, otherwise there is a chance thatthe groups will contain bias. To prevent this,certain methods of ‘blinding’ or ‘masking’are used so that patients and staff (with theexception of the data and safety monitoringcommittee) are not aware whether treatmentA or B is the new treatment, or even whichgroup patients are in (active or placebo/standard treatment), until the end of thetrial. Physicians and study coordinatorsproviding the treatments to the patients use a randomization code to find out whichtreatment pack has been assigned to eachpatient (A or B), but the code provides noinformation about which treatment is which(active or placebo/standard treatment).Randomization must be protected by masking(methods of which will be discussed nextmonth) so that it remains unpredictable.

How should the randomizationcode be determined?A randomization code is a list of whichtreatment a subject should receive. It isusually determined by a statistician using

Randomization is the unpredictable allocation of a patient to a particulartreatment strategy in a clinical trial. When a large number of patients areinvolved, simple randomization will balance the groups in a trial for patientcharacteristics and other factors that might bias outcomes. The remainingdifferences in efficacy or safety outcomes between the groups can then beassumed to be due to the effects of the different treatment strategies.Randomization is therefore the cornerstone of a well-conducted clinical trial.

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Part 8: Methods of Randomization in Clinical Trials

Duolao Wang and Ameet Bakhai*, London School of Hygiene and Tropical Medicineand *Royal Brompton Hospital, London, UK

Dr Duolao Wang is a lecturer at the Medical Statistics Unit, LondonSchool of Hygiene and Tropical Medicine, London, UK, and a statisticalconsultant to the Clinical Trials and Evaluation Unit (CTEU) at theRoyal Brompton Hospital in London, UK. He has been a trial statisticianfor 20 clinical trials and has published extensively in other peer-reviewed journals. He is currently involved in the Wellcome-fundedproject ‘Developing methodology to take account of treatment changes in the analysis of randomized clinical trials’.

Dr Ameet Bakhai is a cardiology specialist registrar and seniorresearch fellow in the CTEU at the Royal Brompton Hospital inLondon, UK. He is currently evaluating the clinical and economicimpact of acute coronary syndromes and is director of an interventionalstudy looking at the use of specially coated stents in small coronaryarteries of subjects with coronary artery disease. His main interests lie in well-designed and carefully conducted registries and trials thatimprove the standards of care for all subjects.

CLINICAL RESEARCHER – Vol1 No11 NOVEMBER 2001 39

computer-generated random numbers or a random-number table. Some trials usemethods for assigning subjects according to date of birth (odd or even years), hospitalrecord number or date of screening for thestudy (odd or even days), but theserandomization methods have a level ofpredictability so strictly are not acceptablemethods of randomization.

Which are the commonrandomization methods?The generation of a randomization code can be achieved using one of a variety ofprocedures. Once a code and method ofallocation are decided on, their rules mustbe adhered to throughout the study. Commontypes of randomization methods are:

• Simple randomization• Permuted-block randomization• Stratified randomization• Minimization or adaptive randomizationA combination of these methods can

also be used, and other special methods doexist. Let us now discuss the more commonrandomization methods listed above.

Simple randomizationThe most common form of randomization,referred to as simple or completerandomization, is a procedure that makeseach new treatment allocation withoutregard to those already made. The principleof this method for a trial with two treatmentscan be demonstrated by deciding treatmentassignment by tossing an unbiased coin, e.g.heads for treatment A and tails for treatmentB. When the next subject is to be assigned,previous allocations are not considered.This method is easy to implement and

unpredictable. However, as it is somewhatinconsiderate to previous allocations, it canoften produce small inequalities betweentreatment groups, e.g. if 200 women wereassigned to treatment A and 205 women totreatment B. In a large trial this makes onlya small difference, but in smaller trials at anearly clinical stage that involve only a fewdozen subjects, these inequalities couldhave a substantial impact.

ExampleConsider an example trial with 12 patients.While there is an equal chance of beingallocated treatment A or treatment B, thenumber of subjects randomly assigned toeach treatment ends up being 5 and 7,respectively (Table 1). This imbalance in the initial allocation results in significantdifficulties in the statistics and possibly a lower power for detecting differencesbetween the treatments. Therefore, in caseswhere there are few patients, there is aneed for other methods of randomization.

Block randomizationThe block randomization method, also knownas permuted-block randomization, is apopular method in clinical trials. A blockrandomization method can be used toperiodically enforce a balance in the numberof patients assigned to each treatment. Thesize of each block of allocations must be aninteger multiple of the number of treatmentgroups, so with two treatment strategies theblock size can be either 2, 4, 6, and so on.A block randomization can be implementedin three steps: Step 1: Choose the block size and the

number of blocks needed to cover the number of patients in the study

Step 2: List all possible permutations of treatments in a block

Step 3: Generate a randomization code for the order in which to select each block

ExampleConsider a clinical trial comparing treatmentsA and B in 24 patients. Here, we shouldchoose a block size of 4 because thesequence would become predictable withblocks of 2, and block sizes of 6 or aboveare too large for this small sample size.Using this size we must ensure that, afterevery fourth randomized subject, the numberof subjects in each arm is equal. Therefore,each block must contain two patients ontreatment A and two on treatment B.Step 1: Given a sample size of 24 and using

a block size of 4, we need six blocksStep 2: There are six possible permutations

that allow 2 As and 2 Bs in eachbox: AABB, ABAB, ABBA, BAAB,BABA and BBAA

Step 3: The randomization code for blockscan be generated by producing a random-number list forpermutations 1–6

Table 2 provides a listing of randompermutations of A and B for each subjectusing this method. Note that after everyfour patients there is a balance of subjects

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While simple randomization is unpredictable and easy to implement, it can oftenproduce small inequalitiesbetween treatment groups

Subject

123456789101112

Treatment

ABAABBBBAABB

Table 1. Example of simple randomization.

Block Permutation Subject Treatment

1 6 1 B2 B3 A4 A

2 4 5 B6 A7 A8 B

3 3 9 A10 B11 B12 A

4 1 13 A14 A15 B16 B

5 2 17 A18 B19 A20 B

6 5 21 B22 A23 B24 A

Table 2. Example of block randomization using a block size of 4.

between treatments A and B. If we needmore than six blocks (or have >24patients), we can continue sampling more of the six possible block permutations shownabove. The procedure is repeated until allpatients are randomized.

The balance forced by blocking isespecially important in long-term trials if:

• Recruitment is slow • The type of patients recruited in the

trial changes during enrollment period• The trial should be stopped early for

safety or efficacy reasons• Routine practice changes for patients

in both groups during the trialThe only disadvantage of blocking is that

every fourth patient, and occasionally everythird patient (when the sequence is AABB orBBAA), becomes predictable if the treatmentsare not masked and the previous allocationsof that block are known.

Stratified randomizationStratified randomization takes the balancecorrection suggested by blocking one stepfurther. Not only are the numbers withtreatments A and B balanced periodically,but a balance is also constantly maintainedfor a set of predetermined important factorsthat may impact on the prognosis of thepatient, such as age, gender, diabetes,severity of illness or geography. If prognosticfactors are not evenly distributed betweentreatment groups it can give the investigatorcause for concern, although statisticalmethods, such as the Cox regression model,are available that allow for such a lack of comparability.

Stratified randomization is implementedin three steps. We can illustrate theprocedures using the CF-WISE (Withdrawalof Inhaled Steroids Evaluation Study inPatients with Cystic Fibrosis) trial currentlybeing conducted at the Clinical Trials andEvaluation Unit of the Royal BromptonHospital, London, UK. The CF-WISE study

is a randomized placebo-controlled trialdesigned to test the feasibility and safety ofwithdrawing inhaled corticosteroids (ICS) in240 children and adults with cystic fibrosiswho are already taking ICS. The twotreatment strategies involve a return toeither ICS treatment after withdrawal (A)or to placebo (B). The primary endpoint isthe time to first respiratory exacerbation.ExampleStep 1: Choose the prognostic factors

that could impact on the primaryendpointExperience of earlier trials andliterature show that atopy, forcedexpiratory volume within 1 second(FEV1) and age are the mostimportant determinants of time to first respiratory exacerbation.

Step 2: Determine the number of strata for each factorWhen several prognostic factorsare chosen, a stratum forrandomization is formed byselecting one subgroup for eachfactor (continuous variables suchas age are split into meaningfulcategorical ranges). The totalnumber of strata is therefore theproduct of the number ofsubgroups in each factor. Table 3describes the strata for stratifiedrandomization in the CF-WISEstudy. In this example, the totalnumber of strata is 2 (atopy) × 3(FEV1) × 2 (age) = 12.

Step 3: Generate randomization codesThis is done by generating arandomization list for eachstratum and then combining allthe lists. Within each stratum, therandomization process itself couldbe simple randomization, but inpractice most clinical trials use ablocked randomization method. Inour example, three blocks of size4 are shown for stratum 1. Thekey with this method is to choosethe most important prognosticfactors and keep the number ofstrata to a minimum so thatrandomization using blocksremains unpredictable.

MinimizationMinimization—also called an adaptiverandomization procedure—takes theapproach of assigning subjects to treatmentsin order to minimize the differences betweenthe treatment groups on selected prognosticfactors. This method starts with a simplerandomization method (the first of ourexamples) for the first several subjects,and then adjusts the chance of allocating a new patient to a particular treatmentbased on existing imbalances in thoseprognostic factors.

Using minimization with the CF-WISEstudy as an example, if treatment A hasmore atopy-positive patients than atopy-negative patients, then the allocationscheme is such that the next few atopy-

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Stratified randomization not only balances patientnumbers but also maintains an even distribution ofprognostic factors across the arms of a trial

Stratum Atopy FEV1 Age Randomization

1 Positive 40–60% <17 ABAB, BABA, AABB...

2 Positive 40–60% ≥17

3 Positive 61–80% <17

4 Positive 61–80% ≥17

5 Positive 81–100% <17

6 Positive 81–100% ≥17

7 Negative 40–60% <17

8 Negative 40–60% ≥17

9 Negative 61–80% <17

10 Negative 61–80% ≥17

11 Negative 81–100% <17

12 Negative 81–100% ≥17

CF-WISE = Withdrawal of Inhaled Steroids Evaluation Study in Patients with Cystic Fibrosis

Table 3. Strata definitions for the CF-WISE study.

40 CLINICAL RESEARCHER – Vol1 No11 NOVEMBER 2001

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positive patients are more likely to berandomized to treatment B. This method is employed in situations involving manyprognostic factors, and patient allocation is then based on the aim of balancing the subtotals for each level of each factor.

ExampleTable 4 shows a hypothetical distribution of 100 patients according to treatment andthree prognostic factors in the CF-WISEstudy. Consider that the next patient is atopypositive, has an FEV1 <60% and is aged15 years old. To find the number of similarpatients already assigned to each treatmentarm, the patients in the correspondingthree rows of Table 4 are added:

Sum for A = 22 + 19 + 25 = 66Sum for B = 21 + 18 + 26 = 65Minimization requires that the patient

be given the treatment with the smallestmarginal total, which in this case istreatment B. If the sums for A and B are equal, then simple randomizationwould be used to assign the treatment.

Although this method is mathematicallyuncomplicated, it has not been widely used because of the practical difficultiesassociated with implementing it. However,with increasing use of computers and,more recently, interactive voice-responsesystems, this method is gaining popularity,particularly in large trials, thereby removingthe need for pre-specified randomization lists.

Concluding remarksSeveral commonly used methods ofrandomization have been described here,but there are many others. Whichevermethod is used, the purpose of randomizationremains the same: to validate the assumptionthat the differences seen in the outcomes arelikely due to differences in the treatments.

AcknowledgementWe would like to thank Dr Belinda Lees(CTEU) and the CF-WISE team for materialfrom the CF-WISE clinical study and foreditorial suggestions.

Next month:Methods of masking

Further reading

Pocock SJ. Clinical Trials: A PracticalApproach. New York: John Wiley, 1983.

Chow SC, Liu JP. Design and Analysis of Clinical Trials: Concepts andMethodologies. New York: John Wiley,1998.

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Factor Level Treatment A Treatment B Subtotal Total

Atopy Positive 22 21 43Negative 28 29 57 100

FEV1 40–60% 19 18 3761–80% 20 21 4181–100% 11 11 22 100

Age <17 25 26 51≥17 25 24 49 100

FEV1 = forced expiratory volume within 1 second

Table 4. Treatment assignments based on three prognostic factors for 100 patients.

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