Common Mistake in Adjusting Sample Size for Anticipated Dropouts

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WHITEPAPER

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CommonMistakeinAdjustingSampleSize

forAnticipatedDropoutsinClinicalTrials

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Mr.PrasanthS,Ms.RajaniVandDr.A.K.Mathai

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CommonMistakeinAdjustingSampleSize

forAntici

atedDro

outsinClinicalTrials

ay by day the clinical trial field is expanding li ke anything. New molecules are needs to be

experimented in human beings and the existing drugs are needs to be monitored for long term

safety.ThusPhaseItoIVclinicaltrialactivitiesareincreasingexponentially allovertheworld.However,it

isdifficulttoworkwithlargepopulationsandhenceresearchersworkwithrepresentativesamplesofthe

patientpopul a tion.Estimationofsamplesizeiscriticalinplanningclinicaltrialbecausethisisusuallythe

mostimportantfactordeterminingthetimeandcostofthestudy.Inmostofthestudies,thesamplesize

calculations are based on the primary research question/objective that the investigator wants to do

research.The samplesize calculationmust betaken intoaccount ofall availabledata,cost ofthe study,

supportfacilities, andethicsofsubjecting patients to research.Basicelementsconsidered forestimating

sample size include level of significance, power of the study, clinically meaningful difference, and the

variabilityorstandarddeviationandofcoursetheavailabilityofpatients.

The initial sample size es timated in the study need to be increased in accordance with the expected

responserate,losstofollowup,lackofcompliance,andanyotherpredictedreasonsforlossofsubjects.

Previousstudiesinthesamepopulationwillgiveanestimateoftheexpectednumberofsubjectsdropped 

outattheendofthestudy.Adverseeventsduetostudytreatment,followuplength,lackofefficacyetc.

will influence the dropout rate. The final number arrived should be increased to include a margin for

requiredsamplesizetoaccommodatethedropoutrate,sothatthenumberneededforevaluationremains

same after expected loss of study subjects. While reviewing some protocols, authors found that

researchers are using different methods for adjusting the sample size for dropout rate. The objective of

thispaperis todemonstratethecorrectprocedureforadjustingthesamplesizefordropoutrateinclinical

trial.

CommonMistakeinAdjustingforDropout

Researchers are often doing mistake while adjusting the dropout rate in sample size calculation. They

simplyaddapercentageofthenumbertotheestimatednumberofsamplesizeasanadjustedsamplesize

fordropout.Forexample,Nisthefinaladjustedsamplesizeandnisthecalculate dsamplesizeandz%is

the expected dropout rate, then the adjusted sample size, N = n+ (n*z/100), which is not the correct

adjustmentprocedure.Thecorrectprocedureistodividethenumber(n)by1minusthedropoutrateto

gettheadjustedsamplesize(N).i.e.,N=n/(1‐(z/100)).

Illustration

Suppose the researcher wants to compare the effectiveness of two drugs A and B. He is expecting that

bothdrugsarealmostequallyefficacious.Heisalsoexpecting95%success rateinbothdruggroups.So

this study becomes anequivalence trial. Further he is expecting an equivalence margin of 10%. His past

experience showsthat about20% dropoutsare expected in thisproposed trial. By assuming5% level of

significanceand80%powerofthetest,wecanestimatethesamplesizebyusingthefollowingformula

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CommonMistakeinAdjustingSampleSize

forAntici

atedDro

outsinClinicalTrials

()

(

)

()

εδ

−

2211

)1(1

βα

−+−+ ppppZZ

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Where,

=ExpectedsuccessrateinDrugA(95%)

=ExpectedsuccessrateinDrugB(95%)

ε=Expecteddifferenceinsuccessratebetweentwostudygroups(P

‐P

)

δ=Equivalencelimit(10%)

α=Levelofsignificance(5%)

=1.64

1‐β=Powerofthestudy(80%)

β/2

=1.28

()()

(

)

()

|0|10.0 −

)95.01(95.095.0195.028.164.1 −+−+

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=82

Thus82subjectsarerequiredforthepresentstudywithoutconsidering thedropoutrateineachtreatment

group.Nextstepistoadjustthedropoutrateof20%.

821−0.2=102.5=103ineachgroup.Thusatotalof206subjectsarerequiredtoconductaclinicaltrial(103

intreatmentgroupand103incontrolgroup).

Ifwefollowtheincorrectmethodasmentionedabove,theadjustedsamplesizeinonegroup=

20100) =98.4=99.Thuswerequire about 198subjectsfortheproposedstudy.However,  thismethodof

adjustmentisinappropriate.Thusthere isadifference of8patients betweentwo procedures.Thus, this

typeofadjustmentinsamplesizeestimationgivesalwaysunderestimatedsamplesize.

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CommonMistakeinAdjustingSampleSize

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outsinClinicalTrials

ConclusionandRecommendation

Aswithotherbasicelementsofsamplesizecalculations,theproportionofeligiblesubjectswhowillrefuse

to participate or provide inadequate information or who will be dropout from the study due to lack of

efficacy and AEs will beunknownat thebeginning ofthe study. However,a goodestimateor a brilliant

guesswouldoftenbepossibleusinginformationfromsimilar studiesincomparablepopulationsorfroman

appropriatepilotstudy.Itisparticularlyimportanttoaccountfordropoutswhenplanningaclinicaltrial.

Alsoresearchersmustawareaboutthecorrectmethodofadjustingthedropoutratewhileestimatingthe

samplesize.Thus,awellplannedandwelldesignedclinicaltrialwouldgivebetterresults.

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