Complex Survey Samples Explaining the Miracle: Statistics and Analysis in Public Health APHEO Conference 2007, October 14-16, 2007 Susan Bondy, Department of Public Health Sciences, University of Toronto
Dec 27, 2015
Complex Survey Samples
Explaining the Miracle: Statistics and Analysis in Public Health
APHEO Conference 2007, October 14-16, 2007
Susan Bondy,Department of Public Health Sciences,University of Toronto
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Outline
• Goals of complex survey analysis
• What is simple, what is complex– Issues and implications of complexities
• Working with software
• Tips for working with expert analysts
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What we report from surveys
• Descriptive statistics– Mean, median, counts, totals
• Measures of difference, association and effect– % diff, risk diff, OR, RR, rho, etc.
• Always reported with expression of variance– Margin of Error (MOE or +/- part)– Confidence intervals
– Point estimate versus variance
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Meet two users of survey data
The Describer The Modeller
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The describer
• Population inference is #1ALWAYS need true pop’n rep.
samples
• Sometimes just descriptive statistics (rates)
• Interest in comparisons:– monitoring and surveillance
(e.g., across time, space, sub-populations)
– Consistency is important
The modeller
• Hypothesis tests are #1
• Analyses simulate controlled experimentsRarely need true pop’n rep.
samples
• Interest in comparison:– Replication of experiments– Differences between studies
more interestingExtending and testing theory
Complex samples
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Simple Random Sample
• Selection into sample is entirely at random
• Each member of pop has same chance of being in the sample
• No strata, no clusters, self-weighting
• Statistically efficient (all observations are independent – tightest margins of error)
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Complex designs
1. Selection by cluster
2. Stratification
3. Probability sample weights
4. Finite population correction
• Worst of all:– Mishmashes of all the above– & where you can’t have the information
Cluster sampling
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Cluster sampling• E.g., people by FAMILY, students by CLASS, teeth by
MOUTH , etc.,
• Now WELL recognized as a problem– Non-independence means loss of statistical power (variance
understated, if ignored)
• Need:– New statistics textbooks– More expensive software
…will return to software options
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Sample logistic results
Model-based
95%CI
Linearized 95%CI
DEFF
Sex
Grade
Region 2
Region 3
Region 4
1.6
1.5
1.4
1.3
1.2
( 1.4 - 1.8 )
( 1.4 - 1.5 )
( 0.9 - 1.7 )
( 1.1 - 1.7 )
( 0.9 - 1.5 )
( 1.3 - 2.0 )
( 1.4 - 1.5 )
( 0.9 - 2.1 )
( 0.9 - 1.9 )
( 0.8 - 1.9 )
1.4
1.7
1.5
1.9
1.8
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Repeat after me:
“Failure to account for non-independence of observations, in the analysis, will always result in an underestimation of variances”
• Confidence intervals narrower…• p-values smaller… • results ‘less conservative’ …
… than they should be
Stratification
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What is: stratification?
• Division of the target population into groups or layers from which samples are drawn
• e.g., Plan for reports on– Youth – Smaller pop’n regions
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Goals of stratification
1. For PLANNED descriptions of sub-populations• E.g., regions, age-groups
2. For design correction:• To prevent extreme unrepresentativeness• e.g., empty groups; extreme weights
3. To improve precision of the overall (or full pop) estimates
Implications…
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Stratification WEIGHTS
They come as a pair
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Impact of weights in analysis
• Impacts precision – a huge DEFF issue
• Other model problems– E.g., can create highly influential observations
• Restricts software and analysis choices
When, why of weights?
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Repeat after me:
“You knew clustering affected variance estimates and had to be taken into account…
Sometimes WEIGHTS have an even bigger bad effect on precision !”
Always use software and procedures specific to complex survey data, even when weighting is your only complexity.
But wait a minute, I’ve been told unweighted is sometimes better
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Scenario A
People up-weighted People down-weighted
Weighted or unweighted is same slope !
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Scenario BSomething correlated with relative weights is associated with a different slope
Low educ.
Over educated
Exposure to materials
Rea
dine
ss to
qui
t
Weighted
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Scenario C
Distance from airport (km)
Annoyance ratings (%)
Weighted slope
Unweighted slope
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Scenario C
Distance from airport (km)
Annoyance ratings (%)
Weighted or unweighted curve
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Modeller’s adage
• If weighted and unweighted differ then, both are wrong
• There must be a complex relationship, or better model, to find and describe
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Pub. Hlth. Epis. are always DESCRIBERS
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Scenario BSomething correlated with relative weights is associated with a different slope
Low educ.
Over educated
Exposure to materials
Rea
dine
ss to
qui
t
Pop’n weighted is TRUE population estimate of ‘net’ or ‘average’ effect
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Model all possible interactions with age, sex and geography strata?
Yes, – Do look for effect modification where there are good
grounds (show net and specific data)
No, – In hundreds of age*sex*region strata, some random
variation by chance – In large samples lots of meaningless interactions can
be detected
– Pop average effect is still pop average effect
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Message so far…
Can never ignore:– Cluster sampling– Weighting
So, HOW to analyze data?
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2 most commonly used for complex survey variance estimation
“Taylor-Series”aka
“Linearized” variance estimation
“Bootstrap”
Usually achieved using bootstrap
replicate resampling weights
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Taylor SeriesComplex linear equations to estimate
corrected variance for every estimate• Requires assumptions about data !
–Normally distribution assumptions –Large sample sizes
• Very difficult for user to know:–when limits are being pushed–When procedure is accepted or controversial
• Requires full design information
• Even more ‘approximate’ with more complex designs
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Using “Taylor-series” type software
1) Use syntax (or even boxes) to declare the following:
• Weight variable• Stratification variable• Group unit for cluster sampling
– Primary sampling unit or PSU• (Ignore requests for finite population info)
2) Run your analysis as available in software• Using only ‘special’ commands for complex
samples
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Survey estimates
• Prevalence = 13.0 (95% CI = 10.0-16.0)
• Odds ratio = 2.1 (95% CI = 1.6-4.0)
Usual weighted point estimate Variance
calculated from a formula;
substituted in things like CIs
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Bootstrap variance weights• Sampling variability “observed” not calculated from a fixed formula
– Felt to reflect “true” sampling variability, – As due to chance alone if survey really repeated an infinite number of times
• Virtually free of assumptions– Tends to be more appropriate and conservative when assumptions for linearization fails
• Very broadly applicable
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Creation of BRR weights• Someone takes a lot of random COMPLEX sub-
samples of the full survey dataset (~500 times)
• The full algorithm for pop’n weighting is applied to each sub-sample– When obs not in sample, weight=zero– Rest re-weighted to reflect pop’n again
• RESULT– 500 weights, – When applied to full dataset, simulates taking 500 samples
again
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Bootstrapping (with weights)
• Point estimates taken from full sample– Mean = 13.0
• Same point estimate taken from 500 B.S. samples
• Observed variability in 500 B.S. estimates becomes variance for mean of 13.0.
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Survey estimates
• Prevalence = 13.0 (95% CI = 10.0-16.0)
• Odds ratio = 2.1 (95% CI = 1.6-4.0)
Usual weighted point estimate Variance reflects
OBSERVED variance in 500
estimates of prev. and OR.
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Software options (more?)Epi Info Linearized estimation only
Limited analysis options
SPSS Linearized estimation
Several analyses available
Stata Linearized or BS Weights
Good range of ‘canned’ complex analyses
SAS Linearized
Means, prop. linear and logistic (more in v10)
Wesvar Linearized or BS weights
Statistics Canada Bootvar
BS Weights,
Bonus output: CV and suppression rules
Somewhat limited analysis options
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Beware
• Stick to procedures custom-designed for complex survey samples– Will handle weights properly– Will give useful statistics, such as DEFF
• Bootstrapping without a set of BS weights– If you aren’t screaming in pain, you haven’t
got it right
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Tips for working in partnership
1. Get a geek to generate lots of useful sets of BS Weights for your survey
• e.g., your favourite standard pop’n• Does take expertise, but done once benefits many
many users
2. Get a nerd to do only your variance corrections for you
• Use your favourite software and keep very detailed programs (recodes, restrictions, etc)
• Have them repeat very defined results tables
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Table 4 Estimated precision of estimates resulting from an overall sample of 1000 residents from each of two strata of one Health Unit. Fictional smoking survey.
Percent daily smokers
Percent (95% CI) Number of cigs/day
Mean (95% CI) Whole sample Daily smokers only All ages 15-24 25+ All ages 15-24 25+ Health Unit 2000*
20% ±1.7
400* 20 ±3.8
1600* 20±1.9
380* 17±0.9
76* 17±2.1
304* 17±1.0
Rural sector 1000 20 ±2.4
200 20±5.3
800 20 ±2.7
190 17±1.3
38 17±3.0
152 17±1.5
Urban sector 1000 20 ±2.4
200 20±5.3
800 20 ±2.7
190 17±1.3
38 17±3.0
152 17±1.5
Embargoed
Not for release: Preliminary analyses pending adjustment of variance estimates to account for complex survey design
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Q & A