Health Survey Research Methods
Health Survey Research MethodsElly KaizarElizabeth Stasny2008 Summer Program in Applied Biostatistics and Epidemiological MethodsJuly 14-18, 20081Elly KaizarHealth Survey Research Methods
Outline21Introduction to Sampling2Simple Random Sampling3Stratified Sampling4Cluster Sampling5Complex Surveys6Variance Estimation7NonresponseElly KaizarHealth Survey Research Methods
Introduction to SamplingPart IIntroduction to Sampling3Elly KaizarHealth Survey Research Methods
Introduction to SamplingIntroductionErrorsExample: Ohio Family Health Survey“The OFHS obtained detailed data regarding Ohio residents’access to health insurance coverage, general health status, andtheir perceptions about, and access to, health care.”Possible Questions:What proportion of Ohio residents have trouble accessingneeded health care?What is the average cost of health care for Ohio families?How much money in total to Ohioans pay for health care?What proportion of Ohio families with private healthinsurance have that insurance provided by an employer?Are Ohio families headed by a minority less likely to becovered by health insurance?4Elly KaizarHealth Survey Research Methods
Introduction to SamplingIntroductionErrorsWhat?What is a sample?A Sample is a subset of a PopulationPopulation All families residing in Ohio in 2003-2004.Sample Some number of these families.What might we do with a sample?5Elly KaizarHealth Survey Research Methods
Introduction to SamplingIntroductionErrorsWhy?Why would one want to consider a sample?Save timeSave moneyNo choiceBetter information6Elly KaizarHealth Survey Research Methods
Introduction to SamplingIntroductionErrorsHow?Convenience samplefamilies that come to the health department to get flu shotsSystematic sampleevery 10th family in the phone bookJudgement samplefamilies that I choose to be ‘representative’ of Ohio famiilesProbability samplerandomly chosen families7Elly KaizarHealth Survey Research Methods
Introduction to SamplingIntroductionErrors‘Representing’ the PopulationNot necessary (or necessarily desirable) for the sample to be asmall version of the population.Each sampled unit will represent the characteristics of aknown number of units in the populationIn a Probability Sample, the probability of inclusion for eachunit is known and nonzero.8Elly KaizarHealth Survey Research Methods
Introduction to SamplingIntroductionErrorsExamplePart of the Ohio Family Heath Survey selected families forinclusion in the survey by randomly sampling from all residentialOhio-based land line telephone numbers.In a Probability Sample, the probability of inclusion for each unitis known and nonzero.Is this a probability sample?9Elly KaizarHealth Survey Research Methods
Introduction to SamplingIntroductionErrorsVocabularyObservation Unit: An observation on which a measurementmay be taken (Family)Target Population: All observation units we want to study(All families living in Ohio)Sampling Unit: The unit we actually sample (Phone number)Sampling frame: List of sampling units (All phone numbers)10Elly KaizarHealth Survey Research Methods
Introduction to ULATIONTARGET POPULATIONNot reachableNotincluded insamplingframeSAMPLEDPOPULATIONRefuse torespondNot eligiblefor surveyNot able torespond11Elly KaizarHealth Survey Research Methods
Introduction to SamplingIntroductionErrorsNonsampling ErrorsNonsampling Errors are biases and variability that come fromcauses other than the sampling scheme.Coverage errorNonresponse biasMeasurement biasCorrupted data (e.g, incorrect data entry)12Elly KaizarHealth Survey Research Methods
Introduction to SamplingIntroductionErrorsSampling ErrorSampling Error is the variability that comes from taking a samplerather than a census.13Elly KaizarHealth Survey Research Methods
Introduction to SamplingIntroductionErrorsDesirable PropertiesThe appropriate sample quantity is unbiasedOn average, you estimate the right thingThe appropriate sample quantity is measured with smallvariabilityIf you repeated the survey, your estimate would not change a lot14Elly KaizarHealth Survey Research Methods
Introduction to SamplingIntroductionErrorsHow are surveys different from experiments?ExperimentsSample SurveysTheoretical infinite populationReal finite populationiid observationsNot necessarily iidBoth want good estimates in terms of bias and varianceBoth use ideas like blocking to reduce variance15Elly KaizarHealth Survey Research Methods
Set UpEstimatorsInferenceWeightsPart IISimple Random Sampling: Means, Proportionsand Totals16Elly KaizarHealth Survey Research Methods
Set UpEstimatorsInferenceWeightsNotationU the finite population (the Universe)(All Ohio families*)N the number of units (families) in the population(Number of families in Ohio)S the sample(Families sampled for this survey)n the number of units in the sample(Number of families in this survey 39,953 completedsurveys*)17Elly KaizarHealth Survey Research Methods
Set UpEstimatorsInferenceWeightsSimple Random Sample (Without Replacement)A Simple Random Sample (SRS) is a sample where everypossible subset of n sampling units has the same probability ofbeing the sample.Conditions:Sample size (n) is fixedNo unit can be selected more than onceProbability of selection is equal for all unitsJoint probability of selection is equal for all pairs, triplets, etc.of unitsIf we assume all Ohio families have one telephone, we can think ofa survey that randomly dials telephone numbers as approximately aSRS.18Elly KaizarHealth Survey Research Methods
Set UpEstimatorsInferenceWeightsMore NotationEach unit in the sample is associated with some characteristic(s) orattributes(s) that we want to measure:Unit #Attribute 1Attribute 2Attribute 3191x1y1z12x2y2z2.NxNyNzNElly KaizarHealth Survey Research Methods
Set UpEstimatorsInferenceWeightsExample Attributesxyz20Number of adult members of the householdNumber of child members of the householdYes/No: the household contains children 1 if yes, 0 if noElly KaizarHealth Survey Research Methods
Set pling DistributionsEstimandsEstimands Population Values the values we would like toestimateAverage/Mean(Average yearly family expenditure for health care) P(Average number of adults in a household; ȳU N1 Ni 1 yi )Proportion(Proportion of adults with dental insurance)(Proportion of households with children; p 1NPNi 1 zi )Total(Total number of children with healthPinsurance)(Total number of adults in Ohio; t Ni 1 yi )21Elly KaizarHealth Survey Research Methods
Set pling DistributionsEstimators: Simple Random SamplePopulationȳU 1XyiNi U1Xp ziNi Ut Xyiȳ 1Xyini S1Xp̂ zini St̂ N1Xyini Si U22EstimateElly KaizarHealth Survey Research Methods
Set pling DistributionsAttributesPopulation quantities (ȳU , p, t)Do not depend on the sample that we chooseFixed, not randomIndividual unit quantities (xi , yi , zi )Do not depend on the sample that we chooseFixed, not randomWhat is random?23Elly KaizarHealth Survey Research Methods
Set pling DistributionsSampling DistributionThe Sampling Distribution describes the values of the samplestatistics you would get over all possible samples from thepopulation (using the same sampling scheme).24Elly KaizarHealth Survey Research Methods
Set pling DistributionsToy ExamplePopulation: 4 coins (penny, nickel, dime, quarter)Sample size: 2Attribute of interest: valueEstimand: total (truth 41 )Samplepenny, nickelpenny, dimepenny, quarternickel, dimenickel, quarterdime, quarter25Average Estimate (ȳ )(1 5)/2 3 (1 10)/2 5.5 (1 25)/2 13 (5 10)/2 7.5 (5 25)/2 15 (10 25)/2 17.5 Elly KaizarTotal Estimate (t̂ 4ȳ )12 22 52 30 60 70 Health Survey Research Methods
Set pling Distributions260.00 0.05 0.10 0.15 0.20probablityExample, cont.Mean 41Variance 44112223041 t52Elly Kaizar6070Health Survey Research Methods
Set pling DistributionsExample, cont.N 100 (25 of each coin)1500 t2500Estimated Probability0.00000.0020Sample Size 10Mean 1025 Variance 7.538e 04275001500 t2500Elly KaizarEstimated Probability0.0000 0.0025500Sample Size 5Mean 1028 Variance 1.596e 055001500 t2500Sample Size 25Mean 1025 Variance 2.494e 04Estimated Probability0.0000 0.0020Estimated Probability0.000 0.004Sample Size 2Mean 1028 Variance 4.102e 055001500 tHealth Survey Research Methods2500
Set pling DistributionsBias: Simple Random SampleRecall Expectation for a mean:XE [ȳ ] ȳk Pr (S Sk )kDefinition of Bias for a mean:Bias [ȳ ] E [ȳ ] ȳUȳ is an unbiased estimator of ȳUp̂ is an unbiased estimator of pt̂ is an unbiased estimator of t28Elly KaizarHealth Survey Research Methods
Set pling DistributionsVariance: Simple Random SampleDefinition of variance of a mean:hiV [ȳ ] E (ȳ E [ȳ ])2X(ȳk E [ȳ ])2 Pr(S Sk ) k29Elly KaizarHealth Survey Research Methods
Set pling DistributionsVariance: Simple Random SampleEstimatorTrue VarianceS2 n 1 nNMean, ȳp(1 p)nProportion, p̂1 X(yi ȳU )2 ,N 1i U30N nN 1 Elly Kaizarp̂(1 p̂) n 1 n 1N N 2 V̂ [ȳ ]N 2 (V [ȳ ])Total, t̂S2 Estimated Variances2 n 1 nNs2 1 X(yi ȳ )2n 1i SHealth Survey Research Methods
Set pling DistributionsFinite Population CorrectionNote that the difference between the variance of a mean for anexperiment (infinite population)V[ȳ ] s 2 /nAnd the variance of a mean for a survey sample (finite population) n V[ȳ ] s 2 /n 1 Nis the Finite Population Correction: n 1 N31Elly KaizarHealth Survey Research Methods
Set UpEstimatorsInferenceWeightsExampleInference: Confidence IntervalsCentral Limit Theorem for large n, N and N-nȳ ȳq U Normal (0, 1)Vd[ȳ ]100(1-α)% Confidence Interval:qqdȳ zα/2 V [ȳ ] OR ȳ tn 1,α/2 Vd[ȳ ]Margin of Error 1/2 the width of a 95% CIqqdzα/2 V [ȳ ] OR tn 1,α/2 Vd[ȳ ]32Elly KaizarHealth Survey Research Methods
Set UpEstimatorsInferenceWeightsExampleExampleConvert OFHS to a toy SRS example:Only use data from Butler CountyPretend completed interviews sampled householdsPretend we know the population size N 123,082 (fromCensus)33Elly KaizarHealth Survey Research Methods
Set UpEstimatorsInferenceWeightsExampleExample CodeMeanby handusing built-in toolsProportion (two ways)Total (whoops - this doesn’t work!)34Elly KaizarHealth Survey Research Methods
Set UpEstimatorsInferenceWeightsAn Alternative Formulationȳ 1Xyini SN Pnn i 1 yinN1Xyini 1Pn Pn Ni 1 n yiPn Ni 1 nwi 35NnElly Kaizar Nn yiNi 1 nPi 1nPnwi yiPi 1ni 1 wifor all i SHealth Survey Research Methods
Set UpEstimatorsInferenceWeightsWhat’s a Weight?For SRS, wi N/n.Inverse probability of being selected (n/N)Number of units in the population that sampled unit irepresentsThe sum of the weights population sizenXXNN n Nwi nni S36i 1Elly KaizarHealth Survey Research Methods
Set UpEstimatorsInferenceWeightsNice properties for meansFor a SRS:Multiplying by a constant does not change the point estimation.Let wi cwiPnwi yiPi 1n i 1 wi 37Elly KaizarPncwi yiPi 1ncwiPi 1nc i 1 wi yiPc ni 1 wiPnwi yiPi 1ni 1 wiHealth Survey Research Methods
Set UpEstimatorsInferenceWeightsExample CodeExact weightsProportional weights38Elly KaizarHealth Survey Research Methods
RatiosDomain EstimationRegressionSummaryPart IIISimple Random Sampling: Ratios, Domains,Regression39Elly KaizarHealth Survey Research Methods
RatiosDomain r UsesUnit-Level RatiosDefine a new variable zi yi /xiz̄U N1 XziNi 1Proportion of income spent on health care in each familyyi income spent on health carexi total family incomeHealth care costs per person in each familyyi health care costsxi number of people in familyProportion of household members that are under 18yi number of children in householdxi number of people in household40Elly KaizarHealth Survey Research Methods
RatiosDomain r UsesPopulation-level ratiosPNyityȳU Pi 1B Ntxx̄Ui 1 xiProportion of population income spent on health care in Ohioyi income spent on health carexi total family incomeTotal health care costs per Ohioanyi health care costsxi number of people in familyProportion of Ohio population that is under 18yi number of children in householdxi number of people in household41Elly KaizarHealth Survey Research Methods
RatiosDomain r UsesRatio EstimatorB̂ ȳx̄Attributes:BiasVariance42Elly KaizarHealth Survey Research Methods
RatiosDomain r UsesAttributes: .25300.301 x .00.252.50.30xElly KaizarHealth Survey Research Methods
RatiosDomain r UsesAttributes: BiasApproximated using a Taylor Series Expansion: h i 1n BSx2 RSx SyBias E B̂ B 1 2Nnx̄U1 [BV (x̄) Cov (x̄, ȳ )]x̄U2R Population Correlation CoefficientPNi 1 (xi x̄U ) (yi ȳU ) (N 1) Sx Sy44Elly KaizarHealth Survey Research Methods
RatiosDomain r UsesAttributes: BiasBias is small when:The sample size n is largeThe sampling fraction n/N is largex̄U is largeSx is small.The correlation R between x and y is close to 145Elly KaizarHealth Survey Research Methods
RatiosDomain r UsesAttributes: MSEMSE E 46 B̂ B 2 i1 h2E(ȳ Bx̄)x̄U21V [(ȳ B x̄)]x̄U2Elly KaizarHealth Survey Research Methods
RatiosDomain r UsesAttributes: MSEApproximate MSE is small when:Same criteria for the bias:The sample size n is largeThe sampling fraction n/N is largex̄U is largeThe correlation R between x and y is close to 1Deviations about the line y Bx are small47Elly KaizarHealth Survey Research Methods
RatiosDomain r UsesAttributes: VarianceUsing a TS expansion, one can show:"P# N2h in 1i 1 (yi Bxi )1 V B̂ N(N 1)nx̄U2 1n 2 1 Sy 2BSx Sy R B 2 Sx22Nnx̄UWe estimate the variance: 2 P hi y B̂xi\1n i S i 1 V B̂ 2N(n 1)nx̄U 481nx̄U2 1 Elly Kaizarin h 2sy 2B̂sx sy r B̂ 2 sx2NHealth Survey Research Methods
RatiosDomain r UsesExample: Ratio49Elly KaizarHealth Survey Research Methods
RatiosDomain r UsesOther Uses for the Ratio EstimatorEstimate the population total when the population size isunknownIncrease the precision (decrease the variance) of estimatedmeans and totalsAdjust estimates to reflect known demographic totals (later)Adjust for nonresponse (later)50Elly KaizarHealth Survey Research Methods
RatiosDomain r UsesEstimate the population total when the population size isunknownYou must know the population total of something also measured inthe survey: tx (total Ohio population)!1 PXXyȳUii Uty Btx xi yitx N1 Px̄Ui U xiNi Ui Ut̂ry B̂tx51Elly KaizarHealth Survey Research Methods
RatiosDomain r UsesExample: Ratio for unknown population sizeFrom Census: Butler County population is 332,80752Elly KaizarHealth Survey Research Methods
RatiosDomain r UsesIncrease the precision (decrease the variance) of estimatedmeans and totalsRatio estimate for a mean:ȳˆr B̂ x̄UEstimated variance of ratio estimate:se2 n 1 nNei yi B̂xiRecall the estimated variance for a non-ratio mean:sy2 n 1 nN53Elly KaizarHealth Survey Research Methods
RatiosDomain r UsesExample: Ratio for unknown population sizeFrom Census: Butler County has an average of 2.61persons/household54Elly KaizarHealth Survey Research Methods
RatiosDomain r UsesWhen do we do better? MSE ȳˆr MSE [ȳ ]if and only ifCV(x)BSx 2Sy2CV(y )pV [y ]CV(y ) yR A straight line through the originVariance of y about the line is proportional to x55Elly KaizarHealth Survey Research Methods
RatiosDomain EstimationRegressionSummaryDomain EstimationDomain subpopulationExamples:Of low income families, what percentage have dentalinsurance?Of households with children, what is the average number ofadults?56Elly KaizarHealth Survey Research Methods
RatiosDomain EstimationRegressionSummaryDomain EstimatorPopulation quantity:ȳUd 1 XyiNUdi UdNatural estimator:ȳd 1 Xyindi SdNote that nd is random!57Elly KaizarHealth Survey Research Methods
RatiosDomain EstimationRegressionSummaryDomain Estimation as Ratio EstimationLet: yi if i Ud0 if i / Ud 1 if i Ud0 if i / Udui xi Then:Pi Sȳd P di Sduixiis a ratio estimator.58Elly KaizarHealth Survey Research Methods
RatiosDomain EstimationRegressionSummaryExample59Elly KaizarHealth Survey Research Methods
RatiosDomain EstimationRegressionSummaryRegression Mean EstimatorRegression Model:yi B0 B1 xiPredict the population mean:yU B0 B1 xUEstimate the population mean:ȳˆreg60 Bˆ0 Bˆ1 x̄UElly KaizarHealth Survey Research Methods
RatiosDomain EstimationRegressionSummaryCoefficient EstimatesEstimates of coefficients are the same as in usual linear regression:B̂0 ȳ B̂1 x̄X(xi x̄) (yi ȳ )B̂1 i SX(xi x̄)2i S61Elly KaizarHealth Survey Research Methods
RatiosDomain EstimationRegressionSummaryAttributes bias Cov B̂1 , x̄s2 n variance e 1 nN ei yi B̂0 B̂1 xi62Elly Kaizar Health Survey Research Methods
RatiosDomain EstimationRegressionSummaryMSEMSE ȳˆreg n 1 21 Sy 1 R 2N nSd2 n 1 nNdi yi [ȳU B1 (xi x̄U )] Approximate MSE is small when:The sample size n is largeThe sampling fraction n/N is largeThe correlation R between x and y is close to 1 or -1Sy is small63Elly KaizarHealth Survey Research Methods
RatiosDomain EstimationRegressionSummaryExample64Elly KaizarHealth Survey Research Methods
RatiosDomain EstimationRegressionSummarySummary of Mean Estimation Variancen sy2N n n se2V̂ ȳˆr 1 ;N n n se2V̂ ȳˆreg 1 ;N nV̂ [ȳ ] 65 1 Elly Kaizarei yi B̂xi ei yi B̂0 B̂1 xiHealth Survey Research Methods
RatiosDomain EstimationRegressionSummarySummary of EstimationMean/Proportion/Total Estimation:Population CharacteristicsLinearRInterceptBest EstimatorYes10Ratio or RegressionRegressionYes16 0Yes-1anythingRegressionYes0anythingSRSNoanything anythingSRSAlso use ratio estimation to estimate:RatiosTotals when you don’t know the population size66Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsPart IVStratified Sampling67Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsReview SRSProsEasy to calculate estimatesEasy theory about estimatesConsMust know either N or probability of samplingMay be inefficientMay not represent the population the way you think68Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeights“Bad” SRS ningHancockAshlandCrawfordWyandotVan linClarkHarrisonGuernseyMiamiPrebleImpossibleNot useful precisionCarrollHolmesMorrowLoganShelbySRS samples can be “bad”Subpopulation e69Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsEstimatorsStrata: DefinitionStrata GroupsNon-overlappingConstitute the whole populationWe must know the stratification variable for all units in thepopulation before we sample!SamplingIndependent probability sample within each strataIf SRS, called stratified random sampling70Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsEstimatorsOhio Family Health ingHancockAshlandCrawfordWyandotVan lerWarrenProblem: Too rowGoal: Estimate insurance rateswithin each county at a certainprecisionSolution: Estimate insurancerates within groups of miltonHighlandNote that this is different fromdomain oGalliaLawrence71Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsEstimatorsAttributesThis is different from domain estimation because in this case,the subgroup membership is known in advance.Stratified sampling is like doing a whole bunch of SRS andthen putting them together to analyze.This works because the sampling within each of the strata isdone independently from each other.Does not produce an SRS overall!72Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsEstimatorsEstimands and Estimators: Within StrataWithin each stratum, estimators are the same as before:Strata numbered h 1 . . . Hyhj value of jth unit in stratum hWithin-Stratum h PopulationNh1 X1 XȳUh yj yhjNhNhWithin-Stratum h Estimatenh1 X1 Xȳh yj yhjnhnhNh1 X1 Xph zj zhjNhNhnh1 X1 Xp̂h zj zhjnhnhj Uhj 1j Uhth Xj Uh73j 1yj NhXyhjj 1j Shj Shj 1nh1 X1 Xt̂h Nhyj Nhyhjnhnhj ShElly Kaizarj 1Health Survey Research Methodsj 1
Review SRSStratified SamplingAttributesWeightsEstimatorsEstimands: Across StrataStratum hsizetotalmeanprop74th ȳhU ph 1Nh1NhWholePop.NtNPhNh1Nhj 1 yhjPNhj 1 yhjȳU(# with attribute)PNhj 1 zhjElly KaizarpRelationshipPN Hh 1 NhPHt h 1 th NtPȳUNh Hh 1 N ȳhUPNhp Hh 1 N phHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsEstimatorsEstimators: Across StrataStratum hsizetotalmeanprop75nhPt̂h Nh ȳh Nnhh j Sh yhjPȳh n1h j Sh yhjp̂h 1nh1nh(# with attribute)Pj Sh xhjElly KaizarWholeSamp.nt̂strȳstrp̂strRelationshipPn HnhPh 1Ht̂str h 1 t̂h t̂NstrPNh Hh 1 N ȳhPNhp̂str Hh 1 N p̂hȳstrHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsBiasVarianceExpected Value/Variance ReviewE [X Y ] E [X ] E [Y ]E [aX b] aE [X ] bV [X Y ] V [X ] V [Y ] 2Cov [X , Y ]2V [aX b] a V [X ]X and Y are random variablesa and b are constants76Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsBiasVarianceBiasExample: MeanȳstrE [ȳstr ] HXt̂strNh ȳhNNh 1 E N1 t̂str definition1N is constantN E t̂str1t̂str is unbiasedNtȳUdefinitionSample mean, proportion, and total are unbiased for populationmean, proportion and total.77Elly KaizarHealth Survey Research Methods
Review SRSStratified le: MeanHȳstr X Nht̂str ȳhNNh 1 V [ȳstr ] V N1 t̂str N12 V t̂str 2 PShnh2 N12 Hi 1 Nh 1 Nh nh PH Nh2Sh2nh h 1 N 2 1 Nh nhPHV\[ȳstr ] h 178Nh2N2 1 nhNhElly Kaizar definitionN is constantvariance of t̂str , independencealgebrash2nhHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsBiasVarianceCompare Variance to SRSRecall the variance of a mean for SRS: 1 n S2N nVariance for of a mean using stratified sampling: HXNh2nh Sh21 N2N h nhh 1Sh tends to be smaller than S. This usually leads to a reducedvariance for the population-wide estimate.79Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsBiasVarianceToy tify by row or column?80Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsBiasVarianceToy Example, cont.Recall:NSh2h1 X(yhi ȳh )2 Nh 1i ly Kaizar313233316741424341671.71.71.71.7Health Survey Research Methods
Review SRSStratified SamplingAttributesWeightsBiasVarianceToy Example, cont.Recall: HXNh2nh Sh2V [ȳ ] 1 N2N h nhh 1Suppose I take a sample of size 2 from each stratum: 4X42Row: V (ȳstr ) 1 162i 1 4X42Column: V (ȳstr ) 1 162i 18224 1.7 0.106224 167 10.42Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsBiasVarianceIdeal StrataIdeal strata have small within-strata population varianceImplies small within-strata sample varianceMeans units within strata are similar to each other withrespect to the survey questionshomogeneous withinImplies large between-strata population varianceMean units within different strata are different from each otherwith respect to the survey questionsheterogeneous between83Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsBiasVarianceExample: Ohio Family Health Survey84Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsWeights RevisitedRecall weights from SRS:For SRS, wi N/n.Inverse probability of being selected (n/N)Number of units in the population that sampled unit irepresentsThe sum of the weights population sizenXXNNwi n Nnni Si 1Using weights to estimate a mean:Pnwi yiȳ Pi 1ni 1 wi85Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsWeights for Stratified SampleWithin each stratum, we have a SRS, and so the weight is thesame as for the SRS:Nh.whj nhInverse probability of being selected (nh /Nh )Number of units in the population that sampled unitrepresentsThe sum of the weights population sizenjnjH XH XHHXXXXNhNhwhj nh Nh Nnhnhh i j 186h i j 1Elly Kaizarh ih iHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsUsing weights to estimate a meanȳstr HXNhh 1NPHȳh h 1 Nh ȳhNPH 87Elly Kaizar1h 1 Nh nhPHNPnhPHNPnhh 1Pnhj 1 yhjNhj 1 nh yhjNhh 1j 1 nh yhjPH Pnh Nhh 1j 1 nhPH Pnhh 1j 1 whj yhjPH Pnhh 1j 1 whjHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsUsing weights without strata notationPnhh 1j 1 whj yhjPH Pnhh 1j 1 whjPHȳstr Pwi yiPi Si S wiwherewi Nhinhiand hi is the stratum to which the unit i belongs.88Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsCounty Stratification in the OFHS“ODJFS and ODH set a new statistical constraint for the samplingmethodology: that counties, or clusters of similar counties, havesufficient sample size to produce reliable estimates of the healthinsurance status of children under the age of eighteen, with asampling error of no more than 5% at the 95% level ofconfidence. ORC Macro calculated that with approximately 35% ofhouseholds across the State of Ohio containing at least one child,and taking into account estimates of child health insurance statusfrom the 1998 FHS, a sample size of 800 completed interviewswould be necessary in counties, or county clusters.”County-Level Estimation Constraints:A minimum of 800 completed interviews in each stratum(county or county cluster)A minimum of 50 completed interviews in each county89Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsExample90Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsSummaryStratification pros:Protect yourself from a really bad sampleConvenient to administerObtain data of specified precision for subgroupsSmaller variance of estimates91Elly KaizarHealth Survey Research Methods
Review SRSStratified SamplingAttributesWeightsPseudo-Stratification in the OFHSThe OFHS also sampled extra Hispanic and Asian households:Created two additional lists of telephone numbers associatedwith traditionally Hispanic and Asian surnames.Independently sampled telephone numbers from these lists.Are these true strata capturing the Hispanic and Asian population?Do I need to use domain estimation to estimate the percentage ofHispanic households that have dental insurance?92Elly KaizarHealth Survey Research Methods
DefinitionPros and ConsTwo-Stage Cluster SamplingWeightsPart VCluster Sampling93Elly KaizarHealth Survey Research Methods
DefinitionPros and ConsTwo-Stage Cluster SamplingWeightsThe Elephant in the OFHS RoomSo far we have been making inferences only about households.Remember why:Assume each household in Ohio has exactly one telephoneThen, the sampling unit (telephone number) is identical tothe householdHousehold is the effective sampling unitWe have only learned how to make inference about thesampling unit94Elly KaizarHealth Survey Research Methods
DefinitionPros and ConsTwo-Stage Cluster SamplingWeights
Health Survey Research Methods Elly Kaizar Elizabeth Stasny 2008 Summer Program in Applied Biostatistics and Epidemiological Methods . Outline 1 Introduction to Sampling 2 Simple Random Sampling 3 Strati ed Sampling 4 Cluster Sampling 5 Complex Surveys 6 Variance Estimation 7 Nonresponse 2 Elly Kaizar Health Survey Research Methods .
Survey as a health service research method Study designs & surveys Survey sampling strategies Survey errors Survey modes/techniques . Part II (preliminary) Design and implementation of survey tools Survey planning and monitoring Analyzing survey da
Digital health research methods and tools. 2017. 3 Contents Part 1: Introduction 1.1 Understanding what digital health means 1.2 Defining your research as digital health research 1.3 Drawing from health informatics for digital health research 1.4 Respecting participation in digital health research by patients, clients and citizens
new survey. Select one of those options to apply to your new survey form. 1)Create a new survey from scratch - will create a blank survey form that you can use to add your own questions 2)Copy an existing survey - can be used to create a copy of a survey form you have already created 3)Use a Survey Template - will allow you to select
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National Demographic and Health Survey, please contact The 2017 Philippines National Demographic and Health Survey (NDHS 2017) is the sixth Demographic and Health Survey (DHS) conducted in the Philippines as part of The DHS Program and the 11 national demographic survey conducted since 1968. The survey is designed to provide
The Louisiana Health Insurance Survey (LHIS) is a biennial survey designed to assess health insurance coverage in Louisiana. The survey was first conducted in 2003. This report focuses on the results of the 2019 survey. The LHIS has helped state policy makers track changes in health insurance as Louisiana's economy, health care environment,
University of Bradford, School of Management Introduction to Research Effective Learning Service 1 This workbook is a short introduction to research and research methods and will outline some, but not all, key areas of research and research methods: ¾ Definitions ¾ Research approaches ¾ Stages of the research process
ASME marks is documented and traceable to the entity authorized by ASME to use its marks. All data reports and certificates of conformance shall be retained for a period established by the appropriate code or standard. 21. CAP-21 CRITERIA FOR REAPPLICATION OF AN ASME CERTIFICATION MARK 1 After an item has been certified under an ASME standard, if the ASME certification mark (e.g. Code Symbol .
