Sample-Size-Calculations

[e-mail]:c319–c323DOI:10.1159/000322830SampleSizeCalculationsMarlies Noordzij aFriedo W. Dekker bCarmine Zoccali cKitty J. Jager aa ERA-EDTARegistry,DepartmentofMedicalInformatics,AcademicMedicalCenter,UniversityofAmsterdam,Amsterdam,andb DepartmentofClinicalEpidemiology,LeidenUniversityMedicalCentre,Leiden,TheNetherlands;c CNR-IBIM,ClinicalEpidemiologyandPathophysiologyofRenalDiseasesandHypertension,RenalandTransplantationUnit,OspedaliRiuniti,ReggioCalabria,Italysamplesizecalculationsistodeterminethenumberofparticipantsrequiredtodetectaclinicallyrelevanttreat-menteffect.Optimizingthesamplesizeisextremelyim-portant.Ifthesamplesizeistoosmall,onemaynotbeabletodetectanimportanteffect,whileasamplethatistoolargemaybeawasteoftimeandmoney.Determiningthesamplesizeisoneofthefirststepsinthedesignofatrial,andmethodstocalculatethesamplesizeareex-plainedinseveralconventionalstatisticaltextbooks[1,2].However,itisdifficultforinvestigatorstodecidewhichmethodtouse,becausetherearemanydifferentformulasavailable,dependingonthestudydesignandthetypeofoutcomestudied.Furthermore,thesecalculationsaresensitivetoerrors,becausesmalldifferencesinselectedparameterscanleadtolargedifferencesinsamplesize.Inthispaper,weexplainthebasicprinciplesofsamplesizecalculationsbasedonanexampledescribingahypothet-icalrandomizedcontrolledtrial(RCT)ontheeffectoferythropoietin(EPO)treatmentonanaemiaindialysispatients.TheBasicPrinciplesofClinicalStudies:AnExampleSupposeonewishestostudytheeffectofEPOtreat-mentonhaemoglobinlevelsinanaemicdialysispatients(haemoglobin!13g/dlinmenand!12g/dlinwomen)[3].ThesepatientsarerandomizedtoreceiveeitherEPOKeyWordsSamplesizePowerStudydesignEpidemiologyStatisticsNephrologyAbstractThesamplesizeisthenumberofpatientsorotherexperi-mentalunitsthatneedtobeincludedinastudytoanswertheresearchquestion.Pre-studycalculationofthesamplesizeisimportant;ifasamplesizeistoosmall,onewillnotbeabletodetectaneffect,whileasamplethatistoolargemaybeawasteoftimeandmoney.Methodstocalculatethesam-plesizeareexplainedinstatisticaltextbooks,butbecausetherearemanydifferentformulasavailable,itcanbedifficultforinvestigatorstodecidewhichmethodtouse.Moreover,thesecalculationsarepronetoerrors,becausesmallchang-esintheselectedparameterscanleadtolargedifferencesinthesamplesize.Thispaperexplainsthebasicprinciplesofsamplesizecalculationsanddemonstrateshowtoperformsuchacalculationforasimplestudydesign.Copyright©2011S.KargerAG,BaselIntroductionThesamplesizeisthenumberofpatientsorotherex-perimentalunitsthatshouldbeincludedinastudytobeabletoanswertheresearchquestion.ThemainaimofPublishedonline:February3,2011MarliesNoordzij,PhDERA-EDTARegistry,DepartmentofMedicalInformaticsAcademicMedicalCenter,UniversityofAmsterdam,POBox22700NL–1100DEAmsterdam(TheNetherlands)Tel.[phone],Fax[phone],E-Mailm.noordzij @ amc.uva.nl©2011S.KargerAG,Basel1660–2110/11/1184–0319$38.00/0Accessibleonlineat::UniversityofWesternOntario198.143.60.65-8/30/20153:13:56AMNoordzij /Dekker /Zoccali /Jager NephronClinPract2011;118:c319–c323c320orplacebotreatment.Theprimaryoutcomeofthisstudyisacontinuousone,namelyhaemoglobinlevel.Aftertheinterventionperiod,haemoglobinlevelsinthetreatedandplacebogroupsarecompared.Ofcourse,wehopetofindastatisticallysignificantdifferenceinhaemoglobinlevelbetweenthegrouptreatedwithEPOandtheplacebogroup.Intuitively,weexpectthatthemorepatientsweincludeinourstudy,themoresignificantourdifferencewillbe.TodeterminehowmanypatientsweactuallyneedtoincludeinourRCTtodetectaclinicallyrelevanteffectofEPO,weneedtoperformasamplesizecalculationorestimation.Inthecaseofasimplestudydesign,suchasourRCTonEPOtreatment,agraphicalmethodcanbeusedtoes-timatethesamplesizerequiredforthestudy.Figure1showsanexampleofanomogramforsamplesizeestima-tionaspublishedbyAltman[4].Fromthisnomogram,wecanreadthatweneedafewparameterstoestimatetherequiredsamplesize,i.e.thestandardizeddifferenceinastudy,thepowerandthesignificancelevel.Tobeabletousesuchanomogramoranothermethodforsamplesizecalculation,itishelpfultohavesomeun-derstandingofthebasicprinciplesofclinicalstudies.Whenperformingaclinicalstudy,aninvestigatorusuallytriestodeterminewhethertheoutcomesintwogroupsaredifferentfromeachother.Inmostcases,individualstreat-edwithacertaindrugorotherhealthinterventionarecomparedwithuntreatedindividuals.Ingeneral,the‘trueeffect’ofatreatmentisthedifferenceinaspecificoutcomevariable,inourexamplehaemoglobinlevel,betweentreatedanduntreatedindividualsinthepopulation.How-ever,inclinicalresearch,effectsareusuallystudiedinastudysampleinsteadofinthewholepopulationandasaresulttwofundamentalerrorscanoccur,whicharecalledtypeIandtypeIIerrors.ThevaluesofthesetypeIandtypeIIerrorsareimportantcomponentsinsamplesizecalculations.Inaddition,itisnecessarytohavesomeideaoftheresultsexpectedinastudytobeabletocalculatethesamplesize.Thesecomponentsofsamplesizecalculationsaredescribedbelowandaresummarizedintable