RandomizationinClinicalTrialsVersion1.0May2011

1. SimpleRandomization2. Blockrandomization3. Minimizationmethod

Stratification

RELATEDISSUES

1. AccidentalBias2. SelectionBias3. PrognosticFactors4. Randomselection5. Randomallocation

TwoIndependentGroups

Research isoften conductedusing experimentation involving themanipulationof a least

onefactor.Commonlyusedexperimentaldesigns includetheexperimentaldesignsforthe

twogroupproblem forsuperiority (i.e. isonetreatmentsuperiortoanotheronaprimary

outcome?),fornoninferiority(isanewtreatmentnoworsethananexistingtreatmentona

particularoutcome?),orforequivalence(aretwo interventionsessentially identicaltoone

anotheronaprimaryoutcome?).Strongconclusionsmaybedrawnfromsuchendeavours

providing the design is sufficiently powered and providing there are no threats to the

validity of conclusions. The use of randomization in experimental work contributes to

establishingthevalidityofinferences.

The following notes relate to the experimental comparison of two treatments with

participants randomized tooneof two treatments;suchdesignscanviewedasbeingRCT

designs[RCT===RandomizedControlTrialifonetreatmentisacontrolormoregenerally

RCT===RandomizedClinicalTrial].

SimpleRandomSamplesandRandomAllocation

Simplerandomselectionandrandomallocationarenotthesame.Randomselectionisthe

processofdrawinga sample fromapopulationwhereby the sampleparticipantsarenot

known inadvanced.ASimpleRandomSampleofsizek isasampledeterminedbychance

wherebyeachindividualinthepopulationhasthesameequalprobabilityofbeingselected

andeachpossiblesubsetofsizekinthepopulationhasthesamechanceofbeingselected.

Itishopedthatasimplerandomsamplewillgiveasamplethatisarguablyrepresentativeof

the population, and in doing so helpwith the external validity or generalizability of the

results.

RandomAllocation

Random allocation is a procedure in which identified sample participants are randomly

assignedtoatreatmentandeachparticipanthasthesameprobabilityofbeingassignedto

anyparticulartreatment.IfthedesignisbasedonNparticipantsand aretobeassigned1n

1 Randomization

to Treatment 1 then all possible samples of size have the same probability of being

assignedtoTreatment1.

1n

Example Purely forsimplicityofexpositionsuppose thereareN=4participants [Angela,

Ben,Colin,Dee],twoofwhomaretobeassignedtoTreatment1andtwotoTreatment2.

ThepossiblegroupsthatcouldbeassignedtoTreatment1are;1.[Angela,Ben],2.[Angela,

Colin],3.[Angela,Dee],4.[Ben,Colin],5.[Ben,Dee],6.[Colin,Dee].Rollingafairsixsided

diewouldbeonewayofperformingtherandomallocation.Forinstance,ifthedielandson

thenumber3 thenAngelaandDeewouldbeassigned toTreatment1andBenandColin

wouldbeassignedtoTreatment2.

The above is theway amethodologistwould consider random allocation. However the

abovedoeshaveitspracticaldrawbacks.ForinstancesupposeweconsideracaseofN=60

participantsand30aretobeassignedtoTreatment1andtheother30toTreatment2.For

theseparametersthereare155,117,520possibledifferentsamplesofsize30whichcould

assigned toTreatment1. Who in their rightmindwouldwriteout the listofallpossible

155,117,520combinations? Findingadiewith155,117,520sidesmightbedifficulttoo![A

computercouldbeusedtorandomlygenerateanumberfromtheintegers1to155,117,520

toselectasample.]

As described, random allocation can have practical problems but logically equivalent

pragmatic solutions exist (e.g. names in a hat with the first drawn out allocated to

Treatment1andtheremaindertoTreatment2).

1n

WhyRandomlyAllocate

Suppose two treatments, Treatment A and Treatment B are to be compared. Further

suppose the sample forTreatmentAareallmenand the sample forTreatmentBareall

female.Ifatanalysisadifferenceintheprimaryoutcomebetweenthetwogroupsisfound,

couldwe thenemphaticallyattribute thisdifferenceasa treatmenteffect? Clearlyunder

thisdesigntheanswertothatquestionwouldbeNo.Underthisdesignitcouldbeargued

that the effectmight be due to Sex, or to Treatment, or in fact bothmight affect the

2 Randomization

outcomeandtheiruniqueeffectscannotbedetermined.Inthisdesign,SexandTreatment

arecompletelyconfoundedandtheirseparateeffectscannotbeidentified.Inthisdesignan

argument foracausal effectdue to treatmentwouldnot standclose scrutinybecausea

plausiblealternativeexplanationforanydifferenceisevident.

In any practical situation the participants will have some (identifiable or unidentifiable)

characteristics thatmay be related to the outcome under investigation. A clustering of

thesecharacteristicswithanyonetreatmentcouldcauseasystematiceffect(asystematic

bias)betweenthegroupswhich isquitedistinct fromanytreatmenteffect (i.e.wewould

have a confounding effect). In the long run, random allocation will equalise individual

differences between treatment groups and in doing sowill remove extraneous bias and

allow the treatment effect to be established uncontaminated by other potentially

competing explanations. In any one experiment it is hoped that random allocationwill

minimisetheeffectofpossibleconfounders,reducingextraneoussystematicbias,leadingto

afaircomparisonbetweentreatmentsbyreducingthepossibilityofpartialconfoundingand

hencehelpingtoruleoutotherpotentialcompetingcausalexplanations.

Thedatageneratedunderanexperimentaldesignwill,mostlikely,beassessedusingformal

statisticalmethods.Thetheoryunderpinningpermutationtestsandrandomisationtestsis

based on the assumption of random allocation. Accordingly valid and defendable data

analysisplansmaybedevisedifrandomallocationisused.

SimpleRandomization

Themostcommonlyencounteredsituationinpracticeisatwotreatmentcomparisonwitha

predeterminedoverallsamplesizeNwithapredeterminedsamplesizeof forTreatment

1andsize forTreatment2( + =N).AtotalofNopaqueenvelopes, containingan

identifierforTreatment1and containinganidentifierforTreatment2,maybeshuffled.

Theorderoftheshuffledenvelopesdeterminestheallocationofparticipantstotreatments.

This process is relatively simple to organise, preserves the predetermined design

parameters,andcanbereadilyextendedtosituationswheremultipletreatmentsaretobe

compared.

1n

1n2n 1n

2n

2n

3 Randomization

SimpleSequentialRandomization

Acommonlyencounteredsituation isatwogroupcomparisonwheresamplesizes and

are required to be equal or approximately equal. In a two group trial, the process is

analogous to the tossofa coin such thateachparticipanthasanequalprobability tobe

allocated to either of the treatments. When the sample size is relatively large, simple

randomization is expected to produce approximately equally sized treatment groups

however this isnotguaranteedand thegeneral recommendation is toonly consider this

approachwhereoverallsamplesizeis200orabove.

1n

2n

PossibleProblemswithSimpleRandomization

Simple randomization reduces bias by equalising some factors that have not been

accounted for in theexperimentaldesigne.g.agroupofpeoplewithahealth condition,

different from the disease under study,which is suspected to affect treatment efficacy.

Anotherexample is thata factor suchasbiological sex couldbean importantprognostic

factor. Chance imbalances or accidental bias, with respect to this factor may occur if

biologicalsexisnottakenintoaccountduringthetreatmentallocationprocess.Anexample

ofaperfect randomizationwith respect togenderasan importantprognostic factor isas

showninFigure1.Figure2depictsanexamplewherethereisaccidentalbiaswithrespect

tobiologicalsex.

4 Randomization

30%

20%

30%

20% Treatment/Males

Treatment/Females

Control/Females

Control/Males

Figure1:Noaccidentalbias:perfectbalancewithrespecttoSex

10%

40%

30%

20%

Treatment/Males

Treatment/Females

Control/Females

Control/Males

Figure2:Accidentalbias:imbalancewithrespecttoSex

5 Randomization

Itmaybearguedthatrandomization istoo importanttobe lefttochance! Inthesecases

some practitioners may argue for a blocked randomization scheme, or a stratified

randomizationscheme,oronewhichdeliberatelyminimisesdifferencesbetweengroupson

keypredeterminedprognosticfactors.

BlockRandomization

Blockrandomization iscommonlyused inthetwotreatmentsituationwheresamplesizes

for the two treatments are to be equal or approximately equal. The process involves

recruitingparticipantsinshortblocksandensuringthathalfoftheparticipantswithineach

blockareallocatedtotreatmentAandtheotherhalftoB.Withineachblock,however

theorderofpatientsisrandom.

Conceptually there are an infinite number of possible block sizes. Supposewe consider

blocks of size four. There are six different ways that four patients can be split evenly

betweentwotreatments:

1.AABB,2.ABAB3.ABBA,4.BAAB,5.BABA,6.BBAA

Thenextstepistoselectrandomlyamongstthesesixdifferentblocksforeachgroupoffour

participants thatare recruited.The random selection canbedoneusinga listof random

numbers generated using statistical software e.g. SPSS, Excel, Minitab, Stata, SAS. An

exampleofsucharandomnumbersequenceisasshown;

9795270571964604603256331708242973...

Since there areonly sixdifferentblocks, allnumbersoutside the rangeof1 to6 canbe

droppedtohave;

52516464632563312423...

6 Randomization

Blocks are selected according to the above sequence. For example the first eighteen

subjectswouldbeallocatedtotreatmentsasfollows:

5 2 5 1 6

BABA ABAB BABA AABB BB

In the example, one group has two more participants than the other; but this small

differencemaynotnecessarilybeof great consequence. Inblock randomization there is

almostperfectmatchingofthesizeofgroupswithoutdepartingtoofarfromtheprincipleof

purely random selection. Note however this procedure is not the same as simple

randomization e.g. the first fourparticipants cannotbe all allocated to TreatmentA and

henceallpossiblecombinationsofassignmentarenotpossible.Notethatsimplesequential

randomizationisthesameasblockrandomizationwithblocksofsize1.

Stratification

Astratificationfactorisacategorical(ordiscretizedcontinuous)covariatewhichdividesthe

patientpopulationaccordingtoitslevelse.g.

sex,2levels:Male,Female

age,3levels:

Minimization

Usingthismethod,thefirstpatientistrulyrandomlyallocated;foreachsubsequentpatient,

the treatmentallocation is identified,whichminimizes the imbalancebetween groups at

thattime.Forexample,considerasituationwherethereare3stratificationfactors;sex(2

levels),age (3 levels),anddiseasestage (3 levels).Supposethereare50patientsenrolled

andthe51stpatientismale,age63,andstageIIIdisease.

TreatmentA TreatmentB

Sex Male 16 14

Female 10 10

Age

Therearetwopossiblecriteria:

Countonlythedirection(sign)ofthedifferenceineachcategory.TreatmentAisahead

intwocategoriesoutofthree,soassignthenextpatienttoTreatmentB

Addthetotaloverallcategories(26Asvs24Bs).SinceTreatmentA isahead,assignthe

nextpatienttoTreatmentB

Thesetwocriteriawillusuallyagree,butnotalways

Bothcriteriawillleadtoreasonablebalance

Whenthereisatie,usesimplerandomization

Balancebymarginsdoesnotguaranteeoveralltreatmentbalance,orbalancewithin

stratumcells

ProblemsandAdditionalBenefitsofRandomization

With some methods of allocation an imbalance due to the foreknowledge of the next

treatment allocation between the treatment groups with respect to an important

prognostic factor may also occur i.e. when an investigator is able to predict the next

subjects group assignment by examining which group has been assigned the fewest

patients up to that point. This is known as selection bias and occurs very oftenwhen

randomization is poorly implemented e.g. Preprinted list of random numbers can be

consultedbyanexperimenter beforenextpatientcomes in,orenvelopescanbeopened

beforenextpatientcomesin,oranexperimentercanpredictthenextallocationwithstatic

methodse.g.thelasttreatmentineachblockinblockrandomisation.

A practical issue in experimentation is allocation concealment, which refers to the

precautionstakentoensurethatthegroupassignmentofpatients isnotrevealedpriorto

definitively allocating them to their respective groups. In other words, allocation

concealment shields thosewho admitparticipants to a trial from knowing theupcoming

9 Randomization

10 Randomization

assignmentsandcanbeachievedbycodingthetreatmentsandnotusingtheirrealnames.

Thisiscalledmaskingandisdifferentfromblinding:

Masking or allocation concealment seeks to prevent selection bias, protects assignment

sequencebeforeanduntilallocation,andcanalwaysbesuccessfullyimplemented.

Incontrast,blindingseekstopreventsamplingbias,protectssequenceafterallocation,and

cannot always be successfully implemented. For example, it is impossible to implement

blindinginasituationwherethetreatmentisasurgicalprocedure.

Ingeneralsimplerandomallocation,aswellashavingverydesirabletheoreticalproperties

from a statistical perspective, often permits the implementation of very desirable

methodologyincludingmaskingandcangreatlyhelpwithpreservingtheoverallconclusions

fromexperimentalresearch.