Practical Missing Data Analysis in SPSS (v17 onwards) Peter T. Donnan Professor of Epidemiology and Biostatistics
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Practical Missing Data Analysis in
SPSS (v17 onwards)
Peter T. Donnan
Professor of Epidemiology and Biostatistics
ObjectivesObjectives
•How to impute missing values How to impute missing values in SPSS, specifically MIin SPSS, specifically MI
•How to implement analyses How to implement analyses with multiple imputed valueswith multiple imputed values
•Interpretation of the outputInterpretation of the output
•Practical tipsPractical tips
Example dataExample data
From trial of pedometers+advice From trial of pedometers+advice vs advice vs controls in vs advice vs controls in sedentary elderly womensedentary elderly women
Follow-up at 3 and 6 mnthsFollow-up at 3 and 6 mnths
Main outcome measure of Main outcome measure of activity from accelerometer activity from accelerometer countscounts
210 randomised / 170 at 3 210 randomised / 170 at 3 monthsmonths
Example data – Example data – Pedometer trialPedometer trial
Read in data ‘SPSS Study Read in data ‘SPSS Study databse.sav’ databse.sav’
Main outcome is:Main outcome is:
3 mnth activity – 3 mnth activity – AccelVM2AccelVM2
Baseline activity – Baseline activity – AccelVM1aAccelVM1a
Trial arm represented by two Trial arm represented by two dummy variables:dummy variables: Grp1Grp1 = Pedom. = Pedom. Vs. controlVs. control
Grp2Grp2 = Advice vs. = Advice vs. control control
Main analysis – Main analysis – Pedometer trialPedometer trial
Regression on 3 Regression on 3 months activity months activity adjusting for adjusting for baseline activity baseline activity and two dummy and two dummy variables variables representing representing trial arm trial arm contrasts contrasts
Main analysis – Main analysis – Pedometer trialPedometer trial
Note that n =170 Note that n =170 with 40 missing in with 40 missing in complete case complete case analysis and so analysis and so potential for biaspotential for bias
Missing at Random (MAR)Missing at Random (MAR)
• Prob (Missing) is independent of: Prob (Missing) is independent of: 1) unobserved data 1) unobserved data butbut 2) 2) dependentdependent on observed data on observed data
• Essentially observed data is a random Essentially observed data is a random sample of full data sample of full data in each stratumin each stratum
• MAR is weaker version of MCAR MAR is weaker version of MCAR assumptionassumption
• If MAR is assumed, If MAR is assumed, manymany methods methods possible to impute data using observed possible to impute data using observed data.data.
• Prob (Missing) is independent of: Prob (Missing) is independent of: 1) unobserved data 1) unobserved data butbut 2) 2) dependentdependent on observed data on observed data
• Essentially observed data is a random Essentially observed data is a random sample of full data sample of full data in each stratumin each stratum
• MAR is weaker version of MCAR MAR is weaker version of MCAR assumptionassumption
• If MAR is assumed, If MAR is assumed, manymany methods methods possible to impute data using observed possible to impute data using observed data.data.
Completers (n =172)Dropped out at 3 months (n = 32)
Chi-squared or t-test p-value
Age Mean (SD) 77.1 (5.0) 78.5 (5.6) 0.137
Accelerometer VM Mean (SD)
130695 (47991) 113381 (50444)0.065
Limb Function Mean (SD) 8.69 (2.25) 7.41 (2.86) 0.028
NHS Costs previous 3 months Mean (SD)
£199.59 (306.74) £404.29 (1289.54)0.402
Pedometer Group N (%) 58 (85.3%) 10 (14.7%) 0.052
BCI Group N (%) 52 (77.6%) 15 (22.4%)
Control Group N (%) 62 (92.5%) 5 (7.5%)
Stairs difficult Yes 48 (76.2%) 15 (23.8%) 0.033
No 124 (87.9% 17 (12.1%)
Comparison of completers at 3 months
and drop-outs
Execution of MI in SPSSExecution of MI in SPSS
So assuming MAR we can use the So assuming MAR we can use the available data to predict missing available data to predict missing values in SPSS:values in SPSS:
AnalyzeAnalyze
Multiple ImputationMultiple Imputation
Impute Missing Data Impute Missing Data ValuesValues
Execution of MI in SPSSExecution of MI in SPSS
Enter ALL Enter ALL variables you variables you think associated think associated with missingnesswith missingness
Note default Note default imputation imputation number = 5number = 5
Create new Create new dataset to store dataset to store resultsresults
Note icon Note icon indicating indicating procedures that procedures that allow MI analysisallow MI analysis
Execution of MI in SPSSExecution of MI in SPSS
Automatic Automatic method lets SPSS method lets SPSS chosechose
Custom gives Custom gives more flexibilitymore flexibility
Can include all 2-Can include all 2-way interactionsway interactions
Linear Regression Linear Regression model predictionmodel prediction
Execution of MI in SPSSExecution of MI in SPSS
List of variables List of variables chosenchosen
Define Each Define Each variable for variable for imputation or imputation or predictor or BOTHpredictor or BOTH
N.b. Recommend N.b. Recommend including the including the OUTCOME as both OUTCOME as both predictor and predictor and outcomeoutcome
Output of MI in SPSSOutput of MI in SPSS
Note main Note main interest in interest in outcome VM2 but outcome VM2 but other factors with other factors with missing values missing values also imputedalso imputed
Step 2 - Using Imputed Step 2 - Using Imputed datasets in analysisdatasets in analysis
Note new dataset has IMPUTATION Note new dataset has IMPUTATION number as first column and contains in number as first column and contains in order the original dataset (n = 210), order the original dataset (n = 210), IMPUTATION = 0IMPUTATION = 0
and concatenated below it a further 5 and concatenated below it a further 5 new datasets (each n = 210) but now new datasets (each n = 210) but now with imputed values, IMPUTATION = 1 with imputed values, IMPUTATION = 1 to 5to 5
Most analyses can now be implemented Most analyses can now be implemented if the fossil shell spiral symbol is if the fossil shell spiral symbol is presentpresent
Repeat Main analysis – Repeat Main analysis – Need Pooled ResultsNeed Pooled Results
Procedure Procedure exactly same as exactly same as before before
SPSS will do the SPSS will do the pooled analysis if pooled analysis if the icon (above)the icon (above)
is present in the is present in the drop-down menudrop-down menu
Pooled Analysis in SPSSPooled Analysis in SPSS
Results Results presented for presented for the original the original data and for data and for each imputed each imputed dataset dataset separatelyseparately
Results of pooled analysis Results of pooled analysis from 5 imputed datasetsfrom 5 imputed datasets
Model B SE t Sig. Fraction missing
Pooled
Constant 15607 7808 1.999 0.047 0.173
AccelVM1a
0.852 0.051 16.630 0.000 0.124
Pedometer Group
11310 6131 1.845 0.066 0.138
Advice only
17536 6526 2.687 0.009 0.266
Larger Larger effect effect sizes in sizes in both both groupsgroups
Greater power gives Greater power gives more significancemore significance
InterpretationInterpretation
Compare pooled results with the original Compare pooled results with the original as a form of sensitivity analysisas a form of sensitivity analysis
If results similar suggests the original If results similar suggests the original results fairly robustresults fairly robust
Consider whether MAR is reasonable Consider whether MAR is reasonable assumptionassumption
Consider whether you have included Consider whether you have included allall factors (including the outcome) related factors (including the outcome) related to the missingness in the imputation to the missingness in the imputation model as a crucial assumptionmodel as a crucial assumption
SummarySummary
• SPSS now includes Multiple imputation SPSS now includes Multiple imputation in its armouryin its armoury
• Consider assumptions of MIConsider assumptions of MI
• Compare results under different Compare results under different assumption to assess robustness of assumption to assess robustness of resultsresults
• If MAR assumption o.k. then MI If MAR assumption o.k. then MI provides results that are provides results that are lessless biased biased than complete case analysisthan complete case analysis
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