chapter 1 basic biostatistics

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Chapter1BasicBiostatisticsJamalludinAbRahmanMDMPHDepartmentofCommunityMedicineKulliyyahofMedicine

Content

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Basicpremises– variables,levelofmeasurements,probabilitydistribution

Descriptivestatistics Inferentialstatistics,hypothesistesting

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Weobserve,webelieve.Whatweobservemightnotbethetruth

…andwecan’tobserveall.Wesample.


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Parameter Statistic

Population Sample

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Variable


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Characteristicofapopulation Cantakedifferentvalues Data=measurementscollected/observed


6Typeofdata(Levelofmeasurement)

Categorical

Nominal Ordinal

Numerical

Discrete Continuous

e.g.Gender,Race e.g.Cancerstaging,SeverityofCXRfor

PTB

e.g.Parity,Gravida e.g.Hb,RBS,cholesterol.

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Normaldistribution


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; ,1

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Otherdistributions

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Discretevs.continuousprobabilitydistribution

2,F,Weibull,Binomial&Poisson

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CharacteristicsofNormaldistribution


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Smooth,symmetrical(aroundthemean),uni‐modal,bellshapedcurve

Mean=Median=Mode Skewness =0 Kurtosis=0

TestofNormality


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Anderson–DarlingTest

CorrectedKolmogorov–SmirnovTest(Lilliefors Test)

Cramér–von‐mises Criterion

D'agostino's K‐squaredTest

Jarque–Bera Test

Pearson'sChi‐squareTest

Shapiro–Francia

Shapiro–Wilk Test

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UseNormalitytestwithcaution


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Smallsamplesalmostalwayspassanormalitytest.NormalitytestshavelittlepowertotellwhetherornotasmallsampleofdatacomesfromaGaussiandistribution.

Withlargesamples,minordeviationsfromnormalitymaybeflaggedasstatisticallysignificant,eventhoughsmalldeviationsfromanormaldistributionwon’taffecttheresultsofattestorANOVA.

Statisticalobjectives


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1. Determinepresenceofdifference(orsimilarity)2. Determinedegreeofdifference3. Determinethedirectionofchanges(outcome)4. Predictchanges(outcomes)

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A B C

IsthereanydifferencebetweenA&B?

HowbigisthedifferencebetweenA&B?

Whichoneistaller?AorB?

IsCdifferentfromA&B?

Isthereanypatternnow?

IftherewillbeD,canyoupredicthowtallisD?

Association


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avalueandwhoseassociatedvaluemaybechanged

DependentIndependent

e.g.Smoking e.g.LungCancer

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Diseasemodel


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Time

Exposure Exposure

Exposure

Outcome

Diseasemodel(example)


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Time

Smoking MineralDust

Age

LungCancer

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Causalrelationship


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Outcome

Factor1

Factor2

Factor3

Factor4

Factor5

Factor6Factor7

Data

CategoricalFrequency(count)&Percentage

Numerical

Normal Mean(SD)

NotNormal Median(Range/IQR)

Descriptivestatistics


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HypothesisTesting


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Involvemorethanonevariables‐ exposure&outcome,‐ predictor&criterion,‐ risk&disease

TrytoprovethatExposurecausestheDiseasee.g.SmokingcausingLungCancer

Example~Ho:NodifferenceofrisktogetLungCancerbetweensmokerandnon‐smoker

LungCancerNoLungCancer

Smoking 20(18.2%) 90(81.8%)

NotSmoking 5(4.5%) 105(95.5%)

2 (df=1)= 10.150, p =0.001, OR = 4.7 (CI95% 1.7 – 13.0)

Becausep<0.05,werejectH0.Thereforethereisadifferentbetweensmoker&nonsmoker


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StatisticalTest


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Univariate~Onedependent&oneindependentMultivariate~Multipledependent&multipleindependentvariable

Whattesttouse?


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Variable1 Variable2 Test

Categorical Categorical Chi‐square

Categorical(2pop) Numerical(Normal) Independent samplet‐test

Categorical(2pop) Numerical(NotNormal) Mann‐WhitneyUtest

Categorical(>2pop) Numerical(Normal) One‐wayANOVA

Categorical(>2pop) Numerical(NotNormal) Kruskal‐Wallis test

Numerical(Normal) Numerical(Normal) Pearson CorrelationCoefficientTest

Numerical(Normal/NotNormal)

Numerical(NotNormal) Spearman CorrelationCoefficientTest

Numerical(Normal) Numerical(Normal) – Paired Pairedt‐test

Numerical(NotNormal) Numerical(NotNormal)–Paired

Friedmantest

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Butlifeisnotsimple!


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LungCancer

Smoking Exposuretomineraldust

Radiation

Outcome

Noofcigarettesmokedperday

RadiationAbsorbeddose(mGy)perday

PM2.5,PM10(g/m3)

Factor Factor

Factor

Themultivariatemodel


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LungCA=Smoking+Radiation+Mineraldust+Others

Regression Residual

AgoodmodeliswhenRegression>Residual

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MultivariateAnalysis


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Hypothesistesting&controlforconfounders– e.g.GeneralLinearModel,LogisticRegression

Modeling– e.g.LinearRegression

Datareduction– e.g.FactorAnalysis,ClusterAnalysis

Writingplanforstatisticalanalysis#1


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DatawereanalyzedusingthecomplexsamplefunctionofSPSS(version13.0).Samplingerrorswereestimatedusingtheprimarysamplingunitsandstrataprovidedinthedataset.Samplingweightswereusedtoadjustfornonresponsebiasandtheoversamplingofblacks,MexicanAmericans,andtheelderlyinNHANES.Theprevalenceofhypertension,aswellastheawareness,treatment,andcontrolrates,wereageadjustedbydirectstandardizationtotheUS2000standardpopulation.Toanalyzedifferencesovertime,the2003–2004datawerecomparedwiththe1999–2000data.Estimateswithacoefficientofvariation>0.3wereconsideredunreliable.A2‐tailedPvalue<0.05wasconsideredstatisticallysignificant.(Ongetal.2009)

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Writingplanforstatisticalanalysis#2


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Toassesstheeffectoftheselectionprocessonthecharacteristicsofthecases,wecomparedcasesincludedinthefinalanalysistotherestofthecases.Sincecontrolsincludedinthepresentanalysisweredifferentfromtherestofthediabetesfreeparticipantsbydesign,nosimilarcomparisonswereperformedforthatgroup.Tocomparebaselinecharacteristicsofcasesandcontrolsappropriateunivariatestatisticswereused.SimilarbinarylogisticandmultiplelinearregressionmodelswerebuiltwithincidentdiabetesorHbA1casrespectiveoutcomesandadditiveblockentryofadiponectin andpotentialconfounders.ForlinearregressionCRPandtriglycerideswerelogtransformed.SinceHbA1ccouldbemodifiedbydrugtreatment,weranasensitivityanalysisexcludingallparticipantsonantidiabetic medication.Ap‐valueof<0.05wasconsideredsignificant.AnalyseswereperformedwithSPSS14.0forWindows.

Reportinganalysis(example)


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Summary1. Identify&definevariables2. Type– independentvs.dependent3. Levelofmeasurements– nominal,ordinalor

continuous4. Checkdistribution– Normalvs.NotNormal5. Decidewhattodo‐ descriptivevs.analytical

Chapter2IntroductiontoSPSSIBMSPSSStatisticsv21forWindows

JamalludinAbRahmanMDMPHDepartmentofCommunityMedicineKulliyyahofMedicine

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IBMSPSSStatistics

IBMCorporationSoftwareGroupRoute100Somers,NY10589ProducedintheUnitedStatesofAmericaMay2012


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SPSSisNOT

StatisticalPackageforSocialSciences

anymore!!!

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SPSSLAYOUT


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Layout


36Mainmenu

Toolbar

Variables

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Dataeditor


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Rows=variablesRows=eachdata

Define&describeyourvariableshere

Enteryourdatahere

Viewer


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Theoutputofanalyseswillbedisplayedhere.Outputisseparatedfrom

data

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Syntax


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Wecancompileallthestepsoftheanalyseshere.ExtendtheprogrammingfunctioninSPSS.Abilitytoperformcomplexstepse.g.

“looping”

CREATINGDATASET


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BeforeevenyoustartSPSS!


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Youmustidentify&definerelevantvariables Definemeans

1. Name– preferablyshortsinglename,beginswithalphabet,nospecialcharacter,nospace

2. Typeofdata– e.g.Numeric,Date,String3. Width&DecimalPlaces(ifnumeric)4. Label– descriptionfortheName(willbedisplayedinViewer)5. Values– labelsforvaluee.g.1=Male,2=Female6. Missing– definemissingvaluee.g.999forN/A

Defineyourvariables


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VariableTypes


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VariableType


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Decidethesuitable

variabletype

Fornumeric,determineWidth&Decimal.

Decimal<Width

ForString,nooptionfor

DecimalPlace

NewoptionforNumerics withleadingzeros

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ValueLabels


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MissingValue


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ThisquestionisNotApplicable

tomale

e.g.Assign999torepresentN/A

value&thiswon’tbeincludedinany

analysis

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Chapter3DescriptiveStatisticsIBMSPSSStatisticsv22forWindows


Datasetfortheexercise


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Filename:bp.sav Hypothetical Studytodescribefactorsrelatedtobloodpressure N=150 13variables

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Retrievefileinformation


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Exercise#1


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1. Describesocio‐demographiccharacteristicsoftherespondent

2. Describetheexplanatoryvariables1. Smoke2. BMI3. Glucose4. Cholesterol

3. Measureprevalenceofhighbloodpressure(usingSBP140,DBP90)

DESCRIBENUMERICALDATA


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Explore


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Results


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Check for Normality.Is Age data distributed Normally?

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Describeage


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Normal Thesubjectsdistributedbetween18‐56yearsoldwiththeaverageof38(SD=8)years.

IfnotNormal Thesubjectsdistributedbetween18‐56yearsoldwiththemedianof38(IQR=10)years

DESCRIBECATEGORICALDATA


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Frequency


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Result


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TRANSFORM


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Compute


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weight / ((height / 100) ** 2)

Visualbinning


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Normal < 23Overweight 23 to < 27.5Obese >= 27.5


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Chapter4Bivariable analysesIBMSPSSStatisticsv21forWindows


Todetermineassociationoftwovariables?


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BPAge

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Thesteps


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1. Determinewhichisdependant&whichisindependent

2. Determinelevelofmeasurements3. CheckNormalityofthenumericalmeasurement4. Determinethesuitablestatisticaltest

Whatarethetests?


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Variable1 Variable2 Test

Categorical Categorical Chi‐square

Categorical(2pop) Numerical(Normal) Independent samplet‐test

Categorical(2pop) Numerical(NotNormal) Mann‐WhitneyUtest

Categorical(>2pop) Numerical(Normal) One‐wayANOVA

Categorical(>2pop) Numerical(NotNormal) Kruskal‐Wallis test

Numerical(Normal) Numerical(Normal) Pearson CorrelationCoefficientTest

Numerical(Normal/NotNormal)

Numerical(NotNormal) Spearman CorrelationCoefficientTest

Numerical(Normal) Numerical(Normal) – Paired Pairedt‐test

Numerical(NotNormal) Numerical(NotNormal)–Paired

Friedmantest

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Exercise#2


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1. Determineassociationbetweensocio‐demographiccharacteristics&alltheriskfactorswithBP

2. Determineassociationbetweensocio‐demographiccharacteristics&alltheriskfactorswithHCY

Note:Itwouldbegoodifyoucouldconstructdummytable fortheanswersevenbeforetheanalysesstarted

HCYnormalrange


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INDEPENDENTSAMPLEt‐TEST

COMPARING TWOMEANS


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Agevs.BP


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Results


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Levene’s testcheckequalitybetweenvariances.Ho:Thereisnodifferenceofvariances.SoifPissignificant,werejectHo,andthereforeequalvariancesassumed.

The original t-test (Student’s t-test) assumes equal variances for equal sample sizes. However if the variances are equal, it is robust for different sizes.

Welch's correction

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Table– Distributionofagebybloodpressurestatus


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N Mean SD Statistics df P

NormalBP 156 33.9 7.9 t=0.431 299 0.667

HighBP 145 34.4 8.9

CHI‐SQUAREDTEST

DIFFERENCE OF TWOPROPORTIONS


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Gendervs.BP


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Results


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Describe this table first. What is your impression? 49% women vs. 47% men with high BP

Some books may suggest the use of Continuity Correction at ALL time, but recent simulations showed that CC (or Yate’s correction) is OVERCONSERVATIVE. Hence, use Pearson 2 when < 20% of cells have expected count < 5

When 20% of cells have EC < 5, use Fisher’s Exact Test

This is given because we code the variables using numbers. Can be used to measure P-trend

ONE‐WAYANOVA

COMPARING MORE THANTWOMEANS


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Racevs.HbA1c


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Results


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Describe these results first. What is your impression? HbA1c between races? 6.4 (SD 2.1) vs. 6.7 (SD 2.2) vs. 6.5 (SD 2.2)

The F test shows that there is no single significant difference between any two groups

Results– BMIstatusvs.HbA1c


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The F test shows that at least there is ONE pair with significant different. Either N vs. OW, N vs. OB or OW vs. OB

We need to run Post-hoc test to determine which of the PAIR is significant.

To decide which Post-hoc test to choose, we have to test for equality of variances i.e. Homogeneity of variances (Levene’s test)

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Results– Posthoc


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The significant difference is only for Normal vs. Obese (P=0.002)

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Report


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ThereisasignificantassociationbetweenBMIStatusandHbA1c(F(2,298)=13.129,P<0.001).Post‐hoctestshowedthatObesesubjectshavesignificantlyhigherHbA1ccomparedtoNormalandOverweightsubjects(P=0.001andP<0.001respectively).

MANN‐WHITNEY U

NONPARAMETRIC TESTS


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Gendervs.HCY


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Results


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This ranks table is not to be cited in the research paper. Instead, describe their MEDIAN

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KRUSKALLWALLIS

NON‐PARAMETRIC TESTS


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Racevs.HCY


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Results


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CORRELATIONTEST

RELATIONSHIP OF TWONUMERICAL DATA


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Agevs.HbA1c


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Results


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Agevs.HCY


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chapter 1 basic biostatistics

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