1. Using Stata for Subpopulation Analysis of Complex Sample Survey Data
Brady T. West
PhD Student
Michigan Program in Survey Methodology
July 30, Stata Conference

2. 2009 Stata Conference: Subpop Analysis of Survey Data
Presentation Outline
Introduction: Subclass Analysis Issues
Kish’s Taxonomy of Subclasses
Two Alternative Approaches to Inference
Variance Estimation and Methods for ‘Singletons’
Examples using NHANES and NHAMCS Data
Suggestions for Practice
Directions for Future Research
2009 Stata Conference: Subpop Analysis of Survey Data

3. Subclass Analysis Issues
Analysts of large, complex sample survey data sets are often interested in making inferences about subpopulations of the original population that the sample was selected from (e.g., Caucasian Females)
These subpopulations are referred to interchangeably in various literatures as subgroups, subclasses, subpopulations, domains, and subdomains, leading to confusion among analysts of survey data
2009 Stata Conference: Subpop Analysis of Survey Data

4. Subclass Analysis Issues, cont’d
Software procedures for analysis of complex sample survey data are becoming more powerful, flexible, and widely available, offering analysts several options
Analysts need to be careful when analyzing subclasses, and be aware of the alternative approaches to subclass analysis that are possible and their implications for inference
2009 Stata Conference: Subpop Analysis of Survey Data

5. Kish’s Taxonomy of Subclasses
Design Domains: Restricted to specific strata according to the complex sample design (usually geographically, e.g., Texas)
Cross-Classes: Broadly distributed (in theory) across the strata and primary sampling units defining a complex sample (e.g., African-Americans over age 50)
Mixed Classes: Disproportionately distributed across the complex sample design (e.g., Hispanics in a sample including Los Angeles as a stratum)
See Kish (1987), Statistical Design for Research
2009 Stata Conference: Subpop Analysis of Survey Data

6. Design Domains X = Sample Element in Subclass
Stratum
PSU 1
PSU 2 1
XXXXXXXXXXX
XXXXXXXXX 2
XXXXXXXXXX
XXXXXXXXXXXX 3 4 5
2009 Stata Conference: Subpop Analysis of Survey Data

7. 2009 Stata Conference: Subpop Analysis of Survey Data
Cross-Classes
Stratum
PSU 1
PSU 2 1
XXXXXXXXXXXX
XXXXX 2
XXXX
XXXXXXX 3
XXXXXXXXXXX
XXXXXXXXX 4
XXXXXX 5
XXXXXXXXXX
2009 Stata Conference: Subpop Analysis of Survey Data

8. 2009 Stata Conference: Subpop Analysis of Survey Data
Mixed Classes
Stratum
PSU 1
PSU 2 1
XXXXXXXXXXXXXX
XXXXXXXXXXXXX 2 X 3
XXXXXXXXXX 4 XX 5
XXXXXXXXXXXX
2009 Stata Conference: Subpop Analysis of Survey Data

9. Applying Kish’s Taxonomy
The type of subclass is critical for determining an appropriate analysis approach
Two possible approaches to inference motivated by the taxonomy:
1. Unconditional approach (cross-classes, mixed classes)
2. Conditional approach (design domains)
2009 Stata Conference: Subpop Analysis of Survey Data

10. The Unconditional Approach
Appropriate for Cross-Classes, and in some cases Mixed Classes; the subclass of interest theoretically can appear in all design strata and primary sampling units (PSUs)
KEY POINT: Allow the software to process the entire survey data set, and recognize all possible design strata and PSUs; DO NOT delete sample cases not in the subclass!
2009 Stata Conference: Subpop Analysis of Survey Data

11. The Unconditional Approach
Rationale: estimated variances for sample estimates of subclass parameters (based on within-stratum variance between PSUs) need to reflect sample-to-sample variability based on the full complex design
In other words, if a particular subclass does not appear in a PSU in any given sample (although in theory it could have), that PSU should contribute 0 to variance estimates, rather than be ignored completely!
2009 Stata Conference: Subpop Analysis of Survey Data

12. The Unconditional Approach
Further, the subclass sample size in each stratum is going to be a random variable, and theoretical sample-to-sample variance in realizations of this random variable should be incorporated into any variance estimation procedures
2009 Stata Conference: Subpop Analysis of Survey Data

13. The Unconditional Approach
If cross-classes (or in some cases mixed classes) are being analyzed, and PSUs where the subclass does not appear (by random chance) are deleted, problems arise
Some strata may appear to have only one PSU by design (preventing variance estimation unless an ad hoc approach is used)
Entire design strata may be dropped, impacting variance estimates and calculations of degrees of freedom
2009 Stata Conference: Subpop Analysis of Survey Data

14. The Unconditional Approach: General Stata Code
svy, subpop(indicator): command varlist, options
indicator = an indicator variable for the subpop or an if condition, e.g., if male == 1
svy: mean, over(groupvar)
svy: prop, over(groupvar)
Stata drops strata* with no subpopulation observations from degrees of freedom calculations
* Exercise: repeat 10 times really fast
2009 Stata Conference: Subpop Analysis of Survey Data

15. The Conditional Approach
Appropriate for Design Domains, where a subclass cannot appear outside of specific design strata
The rationale behind the unconditional approach no longer applies
Certain design strata should not contribute to variance estimation or calculation of degrees of freedom
2009 Stata Conference: Subpop Analysis of Survey Data

16. The Conditional Approach
Restrict the analysis to only those design strata where the subclass of interest exists
Variance estimates reflecting sample-to-sample variability should only be based on those design strata where the subclass can appear (unlike the unconditional approach)
Subclass sample sizes in design domains are assumed to be fixed, by design
2009 Stata Conference: Subpop Analysis of Survey Data

17. The Conditional Approach: General Stata Code
svy: command varlist if (condition), options
(condition) might be male == 1, or a more complex combination of conditions (e.g., male == 1 & age >= 50 & age <= 90)
2009 Stata Conference: Subpop Analysis of Survey Data

18. Variance Estimation Methods
All of these issues are only relevant when using Taylor Series Linearization, which is a default for variance estimation in Stata
Conditional analyses are OK to perform when using replication methods, such as Balanced Repeated Replication or Jackknife Repeated Replication (Rust and Rao, 1996)
2009 Stata Conference: Subpop Analysis of Survey Data

19. Ad-hoc Fixes for ‘Singleton’ Clusters in Stata 10.1
Stata 10.1 provides users with four ad-hoc fixes for the problem where strata are identified with only a single ultimate cluster for variance estimation in a subpopulation analysis:
Report Missing Standard Errors (not really a fix)
Treat Units as Certainty Units, which contribute nothing to the standard error
Scale Variance using Certainty Units, which uses the average variance from each stratum with multiple PSUs for each stratum with only a single PSU
Center at the Grand Mean, where the variance contribution comes from a deviation from the grand mean instead of the stratum mean
2009 Stata Conference: Subpop Analysis of Survey Data

20. Example: The NHANES Data
We first consider examples based on the NHANES II data set, collected from a nationally representative multistage probability sample of the U.S. population from (oldie but a goodie)
Briefly, a sample of the U.S. population was given medical examinations in an effort to assess the health of the U.S. population
2009 Stata Conference: Subpop Analysis of Survey Data

21. Example NHANES Analysis
Analysis Subclass: African-Americans ages 50 and above (this is a cross-class of the U.S. population, which can theoretically appear in all design strata and PSUs)
Analysis Objective: Estimate the mean systolic blood pressure of this subclass and an appropriate standard error
See West et al. (2007) for more details
2009 Stata Conference: Subpop Analysis of Survey Data

22. Conditional Approach: Stata Code for NHANES Analysis
svyset ppsu [pweight = fwgtexam], strata(stratum) singleunit(missing)
svyset ppsu [pweight = fwgtexam], strata(stratum) singleunit(centered)
Also singleunit(certainty), singleunit(scaled)
gen b50subp = (race == 2 & ager >= 50)
svy: mean bpsyst if b50subp == 1
2009 Stata Conference: Subpop Analysis of Survey Data

23. Conditional Approach: Results
Method
Est. Mean
TSL SE
Design DF
Missing SE
144.09 .
50-29 = 21
Centered
1.66
Certainty
1.62
Scaled
1.90
2009 Stata Conference: Subpop Analysis of Survey Data

24. 2009 Stata Conference: Subpop Analysis of Survey Data
Conditional Approach?
This approach would not be appropriate for this particular subclass
Computed standard errors would generally be biased downward, because additional sources of sample-to-sample variability are ignored when following this approach
Same issues apply for analytic models
Evidence that the “scaled” ad-hoc fix may be overly conservative!
2009 Stata Conference: Subpop Analysis of Survey Data

25. Unconditional Approach: Stata Code for NHANES Analysis
svyset ppsu [pweight = fwgtexam], strata(stratum) singleunit(missing)
Note: choice of single unit option does not matter when following this approach!
gen b50subp = (race == 2 & ager >= 50)
svy, subpop(b50subp): mean bpsyst
2009 Stata Conference: Subpop Analysis of Survey Data

26. Unconditional Approach: Results
Method
Est. Mean
TSL SE
Des. DF*
Missing SE
144.09
1.66
58-29 = 29
Centered
Certainty
Scaled
* Note: Stata dropped three strata with no sample units in the subpopulation.
2009 Stata Conference: Subpop Analysis of Survey Data

27. Unconditional Approach?
This approach would be the appropriate choice for a cross-class such as African-Americans over the age of 50
Inferences are theoretically appropriate
Same idea for analytic models
Results suggest that the “centered” and “certainty” ad-hoc fixes for conditional analyses are reasonable
2009 Stata Conference: Subpop Analysis of Survey Data

28. Example: The NHAMCS Data
Analysis Subclass: Visits to Emergency Departments (ED) by African-American men ages 60 and above (this is another cross-class of the U.S. population, which can theoretically appear in all NHAMCS design strata and PSUs)
Analysis Objective: Estimate the percentage of all ED visits by members of this subclass for dizziness and/or vertigo in 2004
See West et al. (2008) for more details
2009 Stata Conference: Subpop Analysis of Survey Data

29. Stata Code for NHAMCS Analyses
svyset cpsum [pweight = patwt], strata(cstratm) singleunit(…)
generate subc = (settype == 3 & sex == 2 & agecat == 5 & race == 2)
svy: tabulate dizzyrfv if subc == 1, se ci percent * conditional
svy, subpop(subc): tabulate dizzyrfv, se ci percent * unconditional
2009 Stata Conference: Subpop Analysis of Survey Data

30. NHAMCS Analysis Results
Method
Est. %
TSL SE
Design DF
Missing SE
4.82
1.576
106
Centered
Certainty
Scaled
Unconditional
1.590
286
2009 Stata Conference: Subpop Analysis of Survey Data

31. NHAMCS Analysis Implications
No problems with strata having only a single ultimate cluster: ad-hoc fixes all give the same results
Weighted point estimates are identical
Substantially fewer design-based degrees of freedom when following the conditional approach; the full complex design will not be reflected in estimation of sample-to-sample variance (many ultimate clusters are lost)
Conditional analysis assumes that each sample will be of fixed size n = 397 for variance estimation purposes; no random variance!
Conditional analysis results in overly liberal inferences
2009 Stata Conference: Subpop Analysis of Survey Data

32. Suggestions for Practice
Consider Kish’s Taxonomy when determining an appropriate subclass analysis approach
Utilize the appropriate software options for unconditional analyses when analyzing cross-classes
Be careful with missing values when creating the subpopulation indicator
The unconditional analysis approach generally works fine for both cases (when in doubt, use this approach)
2009 Stata Conference: Subpop Analysis of Survey Data

33. Directions for Future Research
More appropriate calculation / estimation of design-based and effective degrees of freedom for sparse subclasses or mixed classes
Development of analytic theory for interval estimation when working with small subclasses, which does not rely on asymptotic results
2009 Stata Conference: Subpop Analysis of Survey Data

34. 2009 Stata Conference: Subpop Analysis of Survey Data
References
Kish, L Statistical Design for Research. New York: Wiley.
Rust, K. F., and J. N. K. Rao Variance estimation for complex surveys using replication. Statistical Methods in Medical Research 5: 283–310.
West, B.T., Berglund, P., and Heeringa, S.G A Closer Examination of Subpopulation Analysis of Complex Sample Survey Data. The Stata Journal, 8(3), 1-12.
West, B.T., Berglund, P., and Heeringa, S.G Alternative Approaches to Subclass Analysis of Complex Sample Survey Data. Proceedings of the 2007 Joint Statistical Meetings.
2009 Stata Conference: Subpop Analysis of Survey Data

35. 2009 Stata Conference: Subpop Analysis of Survey Data
Questions / Thank You!
For additional questions, comments, or electronic copies of these slides or the papers, please send an to
2009 Stata Conference: Subpop Analysis of Survey Data