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

2

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

3

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

4

Meet two users of survey data

The Describer The Modeller

5

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

7

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)

8

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

10

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

11

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

12

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

14

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

15

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…

16

Stratification WEIGHTS

They come as a pair

17

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?

18

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

20

Scenario A

People up-weighted People down-weighted

Weighted or unweighted is same slope !

21

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

22

Scenario C

Distance from airport (km)

Annoyance ratings (%)

Weighted slope

Unweighted slope

23

Scenario C

Distance from airport (km)

Annoyance ratings (%)

Weighted or unweighted curve

24

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

25

Pub. Hlth. Epis. are always DESCRIBERS

26

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

27

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

28

Message so far…

Can never ignore:– Cluster sampling– Weighting

So, HOW to analyze data?

29

2 most commonly used for complex survey variance estimation

“Taylor-Series”aka

“Linearized” variance estimation

“Bootstrap”

Usually achieved using bootstrap

replicate resampling weights

30

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

31

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

32

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

33

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

34

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

35

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.

36

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.

37

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

38

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

39

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

40

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

41

Q & A