sample size in health sciences - basics and selected examples
TRANSCRIPT
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Sample size estimation: Basics & selected examples Dr. S. A. Rizwan, M.D.
Public Health SpecialistSBCM, Joint Program – Riyadh
Ministry of Health, Kingdom of Saudi Arabia
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Learningobjectives
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• Importanceofsamplesizeestimation• Basicconceptsinsamplesizecalculation• Howdoessamplesizerelatetostudyresults• Samplesizecalculationinspecificsituations
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Booksandsoftware
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• Books• Samplesizedeterminationinhealthstudies- apracticalmanual(Lwanga &Lemeshow)
• SampleSizeCalculationsinClinicalResearch(Shein-ChungChow,HanshengWang,JunShao)
• Software• Epitools,onlinecalculators,Statcal inEpi Info,Gpower• PASS,nmaster,Statsdirect,Stata• Manyothers
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Obligatoryopeningjoke!
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RethinkingAesop’sfables…
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Let’splayagame!
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Samplesize:Basicconcepts
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Prerequisitesforthisclass
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• Understandingofthefollowingbasicconcepts• Typesofstudydesigns• Measuresofassociation• Mean/SD• Proportion• Standarderror• Hypothesistestingandtypes• Confidenceintervals
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Somerelatedterms
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• Significancelevel• Power• Effectsize• Variability• Precision
Con.level Zα95% 1.96(2sided)95% 1.64(1sided)99% 2.57(2sided)99% 2.32(1sided)Power Zβ90% 1.28285% 1.03780% 0.84275% 0.67570% 0.524
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Samplesize&statisticalinference
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• Twomethodsofstatisticalinference• Hypothesistesting• Confidenceintervalestimation
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Twoaspectsofagoodsample
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• Thesamplesize• Ifadequate,thengoodinternalvalidity
• Thesamplingmethod• Ifrepresentative,thengoodexternalvalidity
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Whycalculatesamplesize?
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• Statingtheassumptionsandparametersbeforestartofthestudyincreasesthevalidityofstatisticalconclusionsmadeafterthestudy
• Post-hocanalysisandresultsareconsideredmerelyexploratory
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Thoughtexercise
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• IamapplyingforajobandintheresumeIhavestatedthatmytypingspeedisveryfast.
• Myfriendisapplyingforthesamejobandinhisresumehestatedthathistypingspeedwas60words/min.
Whichcandidateareyoumorelikelytoassessinavalidmanner?
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Whycalculatesamplesize?(contd.)
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• Fundsandtimeconstraints
• Reallynotnecessarytostudytheentirepopulation(ethicalproblem!)
• Smallsamplesunabletodetectclinicallyrelevantdifferences
• Ifastudywithsmallsamplefindsnon-significantresults– whatdoesitmean?
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Thoughtexercise
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• Study 1: A study was conducted for an anti-hypertensive drug on 10,000 people whichshowed a statistically significant fall in BP of1mm Hg over 3 months
• Study 2: It was found that there was 30%reduction in mortality due to propranolol amongMI patients. But that was not significant. 66cases and 64 controls were studied
Stateyourcommentoneachoftheabovescenario.
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Thoughtexercise
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Then,howlargeshouldSSbe?
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• Neither too small nor too large
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Samplesizeestimatedforprimaryobjective
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• Samplesizeiscalculatedfor‘primaryoutcomevariable’
• Ifthereare>1primaryoutcomessamplesizecalculatedforeachoutcomeandlargestchosen
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Commonscenariosforsamplesize
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• 100sofscenariosforcalculationsamplesize
• Descriptive:• Proportion,mean/SD
• Analytical:• Twoproportions,2means/SD• Also,riskdiff,OR&RR,incidencedensity
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Uncommonscenariosforsamplesize
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• Survival• Regression• Correlation• Qualityassurance• Diagnosticteststudies• Andmanymore
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Furtherconsiderationsforsamplesize
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• Studydesign• Clusterdesign• Crossover• Matched/paired• Typeofhypothesis(inequality,equivalence,non-inferiority&superiority)
• Fixedfollowupduration• Ratioofcontrolstocases
• HypothesistestingorCIestimation?
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HowtoapproachaSSproblem?
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1. Converttheresearchquestionintoastatisticalproblemstatement2. Determineformulaorsoftwarecommand&determineinputsneeded3. Selectthesourcesfortheinputs4. Substitutethevaluesintheformulaorenterinthesoftware5. Factorinnon-response/drop-outrate
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HowtoapproachaSSproblem?
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• First:Converttheresearchquestionintoastatisticalproblemstatement
• Foreg.,• ToestimatethemeanbirthweightofneonatesborntomotherswithanaemiaintheeasternsectorofRiyadh
• Estimationofasinglemeanwithstatedprecision
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HowtoapproachaSSproblem?
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• Second:Findouttheformulaorthesoftwarecommandappropriateforthisproblem
• Foreg.,• Estimationofasinglemeanwithstatedprecision
N=(Zα2 *S2)/L2
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HowtoapproachaSSproblem?
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• Second:anddeterminetheingredientsyourequiretoinputintheformula• Exp.proportion,incidence• Exp.SD• Exp.RRorOR• Power,precision• Confidencelevel• Others(DE,ICC,COV,clustersize)
• Foreg.,• EstimateofSD,alfa &precision
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HowtoapproachaSSproblem?
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• Third:Selectingthesourcesfortheinputs
• Matchthelocationascloseaspossible• Matchthestudypopulationascloseaspossible• Matchthestudysettingascloseaspossible• Matchthestatisticascloseaspossible• Orconductapilotstudy
• Foreg.,• OthersectorinRiyadh->someothercityinKSA->Middleeast->anydevelopingcountry->anywhere
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HowtoapproachaSSproblem?
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• Third(contd.):Whatsourcestouse?
• Fromwhere• PublishedLiterature• Pilotstudy• Expertsinthefield• Educatedguess(gutfeeling)
Itbegsthequestionthatifwealreadyknowtheseinputsthenwhyconductthestudyinthefirstplace!
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HowtoapproachaSSproblem?
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• Third(Contd.):eg., anappropriatesource
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HowtoapproachaSSproblem?
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• Fourth:Substitutethevaluesintheformulaorenterinthesoftware
N=(Zα2 *S2)/L2
N=(1.96*1.96*600*600)/100*100N=138.2N=Roundedto140
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HowtoapproachaSSproblem?
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• Fifth:Factorinnon-response/drop-outrate
• Finalsamplesize= !"#$%&()*&+,$&-.&/0&($12(&0".&
• Foreg.,• Foranon-responserateof20%• Finalsamplesize=140/0.80=175
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Samplesize:Someselectedscenarios
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Samplesizeinspecificsituations
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Authors Originalresearchquestion Simplifiedproblemstatement
1.Dr. Nariman Whatistheproportion ofpatientswhoquitsmoking inatobaccocessationprogram?
Estimationofasingleproportionforaspecialgroup
2.Dr. GhadeerWhatistheincidenceofDMinobesehypertensivesandwhatistheincidenceofDMinnon-obesehypertensiveduringafiveyearfollow-upperiod?
Comparisonofincidenceratesintwogroupsinacohortstudy
3.Dr. Rahma
Whatistheproportion ofLBWneonatesborn tosicklecellmothersandwhatistheproportion ofLBWneonatesborn tonormalmothers inacohortofmothers?
Comparisonoftwoproportionsinacohortstudy
4.Dr. Abrar
Whatistheproportion of ILIabsentstudentsinthehandwashingschoolsandwhatistheproportion ofILIabsentstudents inthecontrolschools?Hereschoolsaretheunitsofrandomisation
Comparisonoftwoproportionsina2groupclusterRCT
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Scenario1:Estimatingasingleproportion
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Scenario1– Step1
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• Whatistheproportionofpatientswhoquitsmokinginatobaccocessationprogram?
• Specifically,whatistheproportionofpatientswithDMandHTNwhoquitsmokinginatobaccocessationprogram?
• Itisacross-sectionalstudybasedonsecondarydataanalysis
• Estimatingasingleproportion
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Scenario1– Step2
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• SSformulaforestimationadifferencebetweentwoproportionsincohortstudy• Inputsrequiredareexpectedproportionofquitting,precision&confidencelevel
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Scenario1– Step3
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• Athoroughliteraturereviewandpreliminarydataanalysisshowedawidevariationintheexpectedproportion– from10%to50%
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Scenario1– Step4
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• Substitutingthevaluesforanumberofscenariosinthesoftware
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Scenario1– Step5
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• Theconceptofdropoutsorlosstofollow-upinnotapplicable inthiscasebecauseitissecondarydataanalysis
• Sothesamplesizeshouldbe>400andbutneednotbe>3500
• Finaldecisionwilldependonfeasibility
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Scenario2:Comparisonofincidenceratesinatwogroupcohortstudy
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Scenario2– Step1
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• Hypothesis:theriskofdeveloping(incidence)DMwillbehigherinobesehypertensivepatientsascomparedtonon-obesehypertensivepatientsduringa5yearfollow-upperiod
• Itisacohortstudywithtwogroups• Exposedisobesehypertensive• Non-exposedisnon-obesehypertensive• OutcomeisincidenceofDM
• Estimatingadifferencebetweentwoincidenceratesinacohortstudy
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Scenario2– Step1
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• Thisproblemcanbevisualisedinanumberofways:
1. Comparingtwoincidenceratesinacohortstudy(RelativeRisk– hypothesistest)
2. Comparingtwoincidence ratesinacohortstudy(RelativeRisk– statedprecision)
3. Comparingtwoincidence ratesinacohortstudywithsmallproportionandfixedstudyduration(Riskdifference– hypothesistest)
4. Comparingtwoproportions(Riskdifference–hypothesistest)
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Scenario2– Step2
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• Method1:SSformulaforestimatingRRwithstatedprecision• Inputsrequiredareexpected proportionofdiseaseamongexposed&unexposed,RR,Precision,
confidence level
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Scenario2– Step2
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• Method2:SSformulaforhypothesistestingofRR• Inputsrequiredareexpected proportionofdiseaseamongexposed&unexposed,RR,power,
confidence level
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Scenario2 – Step2
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• SSformulafordifferenceintwoproportions(akariskdifference)canalsobeusedforthisscenario
Riskdifferencebetween2proportions Riskdifferencebetween2incidence rateswith fixedstudyduration
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Scenario2 – Step2
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Scenario2– Step3
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• AcasualliteraturereviewshowedthattheriskofDMwas5timesamongobeseHTNascomparedtonon-obeseHTN,theincidenceamongnon-obesewas5.4andamongobesewas24.2per1000personyears
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Scenario2– Step4
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• Method1&2:Substitutingthevaluesforanumberofscenariosinthesoftware
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Scenario2– Step5
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• Consideringalosstofollow-upof10%
• Finalsamplesize=716/0.90=795pergroup
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Scenario3:Comparisonofproportionsinatwogroupcohortstudy
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Scenario3– Step1
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• Hypothesis:theproportionofLBWneonateswillbehigherinthesicklecellmothersascomparedtothenon-sicklecellmother
• Itisacohortwithtwogroups• Exposedismotherswithsicklecelldisease• Non-exposedisnormalmothers• OutcomeisproportionofLBW
• Estimatingadifferencebetweentwoproportionsinacohortstudy
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Scenario3– Step1
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• Thisproblemcanbevisualisedinanumberofways:
1. Comparingtwoincidence ratesinacohortstudy(RelativeRisk– hypothesistest)
2. Comparingtwoincidence ratesinacohortstudy(RelativeRisk– statedprecision)
3. Comparingtwoincidence ratesinacohortstudywithsmallproportionandfixedstudyduration(Riskdifference– hypothesistest)
4. Comparingtwoproportions(Riskdifference–hypothesistest)
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Scenario3– Step2
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• Method1:SSformulaforestimatingriskdifference(hypothesistest)• Inputsrequiredareexpectedproportionofdiseaseamongexposed&unexposed,power,confidence level
Differencebetween2proportions
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Scenario3– Step3
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• AliteraturereviewshowedthatproportionofLBWamongSCDmotherswas16.5%andinthenormalmothersitwas8.3%,withanRRof~2
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Scenario3– Step4
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Substitutingthevaluesforanumberofscenariosinthesoftware
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Scenario3– Step5
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Consideringalosstofollow-upof10%
• Finalsamplesize=331/0.90=368pergroup
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Scenario4:ComparisonofproportionsintwogroupclusterRCT
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Scenario4– Step1
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Hypothesis:theproportionofstudentsbeingabsentduetoILIwillbehigherinthecontrolschools ascomparedtotheschoolsimplementingthehandwashing programduringafollowupperiodof6weeks
• ItisaclusterRCTwithtwogroups• Exposedishandwashingprogram• Non-exposedisnohandwashingprogram• OutcomeisproportionofILIabsenteeism• Schoolistheunitofrandomisation
• EstimatingadifferencebetweentwoproportionsinaclusterRCT
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Scenario4– Step1
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Thisproblemcanbevisualisedinanumberofways:
1. Comparingtwoproportions(Riskdifference–hypothesistestusingICC)
2. Comparingtwoproportions(Riskdifference–hypothesistestusingDesignEffect)
3. Comparingtwoproportions(Riskdifference–hypothesistestusingCoefficientofvariation)
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Scenario4– Step2
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Method1:SSformulaforcomparisonofproportionsusingdesigneffect• Inputsrequiredareproportionofoutcomeintheexp.group&controlgroup,sizeofcluster,DE,power,
confidence level
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Scenario4– Step2
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Method2:SSformulaforcomparisonofproportionsusingintraclustercorrelationcoefficient• Inputsrequiredareproportionofoutcomeintheexp.group&controlgroup,sizeofcluster,ICC,
power,confidencelevel
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Scenario4– Step3
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• AliteraturereviewshowedthatincidenceofILIabsenteeismwas0.043intheexp.groupand0.070inthecontrolgroup
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Scenario4– Step4
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Substitutingthevaluesforanumberofscenariosinthesoftware
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Scenario4
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Method3:SSformulaforcomparisonofincidencerates(persontime)• Inputsrequiredareincidence rates(PT)intheexp.group&controlgroup,coeff.ofvariation,power,
confidence level
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Scenario4 – Step5
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Consideringalosstofollow-upof10%
• Finalsamplesize=1625/0.90=1805pergroup
• No.ofclustersrequired=1805/40=45pergroup
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Review
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Whyissamplesizecalculationimportant?
• WhatarethefivestepstocalculatetheSS?
• Whatarethesomeofthecommoninputs requiredforsamplesizeformulae?
• HowwillyouselectanappropriatesourcefortheinputsofSSformula?
• HowwillyourelatetheSSofyourstudyaftertheresults?
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Takehomemessages
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Apriorisamplesizecalculationisverycrucialformakingvalidconclusions
• Followthestepwiseapproach
• Samplesizeestimationdoesnotneedtobeveryaccurate,onlyadequate
• Incaseofnon-significantfindingsinastudy,calculatepowerfordeeperunderstanding
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