Sampling Racial and Ethnic Minorities

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Sampling Racial andEthnic Minorities

• William D. Kalsbeek
• Director, Survey Research Unit
• Professor, Department of Biostatistics
• University of North Carolina
• June 15, 2000

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Acknowledgements

• Ms. Gayle Shimokura
• For significant contributions to this
  presentation through her meticulous background
  research.
• CDC/National Center for Health Statistics
  (Contract No. UR6/CCU417428-01)
• For funding support for this presentation
• UNC-CHs Center for Health Statistics Research
• http//www.sph.unc.edu/chsr

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Race/Ethnic Minorities ( of Population March
2000 CPS)

• Hispanics (11.7 )
• Settled (95)
• Mobile (5 )
• African-American (12.8 )
• Settled (99.9)
• Mobile (0.1)
• Asian-American (4.0)
• Native-American (0.9)

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Overview

• Some basics on probability sampling
• Problems in sampling rare population subgroups
• A review of some existing remedies
• Note that a reference list is available

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Context Sampling Race/Ethnic Minorities
lt-------------------- General Population
-------------------gt
Targeted
With Oversampling
Ethnic Minority

• As the population subgroup of interest in a
  specially targeted study (targeted sampling)
• As a key subgroup in a general population study
  (oversampling)

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Probability vs. Nonprobability Sampling?

• Probability sampling
• Random sampling methods used
• Each member of the target population with a
  known, nonzero selection probability
• Nonprobability sampling in exceptional
  circumstances
• Judgment used
• Requires models to analyze
• Probability sampling is generally preferred

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Sampling Frames and Linkage

• Sampling Frame List(s) used to select a
  probability sample
• EXAMPLE List of patients to sample health care
  users
• Usefulness of a frame is tied to
• The linkage that exists between entries on the
  list and the population being sampled

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Sample Weights

• A number for each member of the sample
• Reflecting the inverse of the selection
  probability for the sample member
• May be adjusted for sample imbalance due to
• Nonresponse
• Incomplete frame coverage
• Other selection problems

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What are the Statistical Goals of Probability
Sampling?

• Validity
• The ability to produce estimates without bias
  tied to sampling
• Achieved if all population members have some
  known chance to be chosen in the sample
• Efficiency
• Tied to precision of estimates
• Achieved if the right sampling tools are used
• Greater efficiency costs more (cost-efficiency)

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What Selection Tools Might be Used to Sample
Race/Ethnic Minorities?

• Stratified sampling
• Separate sampling within each of a number of
  population groupings (strata)
• Screening for the targeted minority group
• Identify subgroup members in initial sample of
  the full population

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Stratified Sampling

• Population divided into a H subgroups called
  strata
• Separate probability sample in each stratum
• Combine estimates from each stratum to produce
  the estimate for the whole population
• Vs. Stratified Analysis

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Stratified Sampling Used When

• Wish to improve the efficiency of population-wide
  estimates
• AND/OR
• Wish to control the sample size of estimates for
  important population subgroups
• Isolatable to some degree by the strata

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Stratum Allocation Options

• Ch Average cost of adding another respondent
  
• to the sample in the h-th stratum

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Stratum Allocation Options
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Screening for a Targeted Population Subgroup

• Sampling in two phases
• Goal is to locate members of the population
  subgroup
• Usually done by telephone or face-to-face in
  general population surveys
• Process
• Select an initial sample
• Administer a relatively short interview
• To determine membership in the targeted subgroup
• Retain all target subgroup and (perhaps) a random
  portion of the rest

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What May Lead to Problems in Sampling Race/Ethnic
Minorities?

• Incomplete Frame(s)
• A sizable portion of the population not linked to
  entries on the list(s) used for sampling
• Rarity
• They usually comprising a relatively small
  percentage of the target population

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What May Lead to Problems in Sampling Race/Ethnic
Minorities?

• Mobility
• Some of them move around a lot, thus creating a
  more dynamic than static linkage between the
  frame and sampled population
• Dispersion
• They are somewhat scattered geographically
• May have some pockets with relatively high
  concentrations

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Some Remedies

• Targeted Sampling
• Multiple Frame Methods
• Linkage Exploitation Methods
• Network/multiplicity sampling
• Snowball sampling
• Adaptive cluster sampling
• Time and Space Sampling
• Oversampling
• Disproportionate Stratified Sampling with
  Screening

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Multiple Frame Methods Selection Approaches

• Premise
• Frame options taken alone may be inadequate or
  too costly to use,
• BUT
• Choosing the sample jointly from multiple frames
  may
• Produce better coverage of the targeted
  population and
• Be more cost-effective
• Dual-Frame Designs --- Two frames

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Multiple Frames
Frame B
Frame A
Frame C
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Multiple Frame Methods EXAMPLE

• Sampling Native Americans
• Two frames
• List of tribal rolls
• Less complete
• Less expensive to locate NAs
• Area household frame from
• List of residential dwellings in a sample of
  block groups (neighborhoods)
• More complete
• More expensive because of the need to screen
• Most cost-effective mix ?

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Multiple Frame Methods Estimation Approaches

• Work by Hartley (1962), Choudry (1989), and
  Skinner and Rao (1996)
• Special Requirements
• Identify/eliminate overlap prior to sampling
• OR
• Require knowledge of membership in intersection
  groups for analysis adjustments

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Multiple Frame Methods Estimation Approaches

• Eliminate frame duplication treat as a
  stratified sample
• OR
• Select with duplication present and either
• Combine estimates for intersection groups
• OR
• Determine frame membership for sample respondents
  and weight accordingly

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Multiple Frame Methods Implications for Sampling
Race/Ethnic Minorities

• Advantages
• Improved sample coverage over using a single list
• Potential cost savings if cost of frame use
  differs among frames
• Disadvantages
• Higher design/selection/analysis complexity
  relative to single frame use
• Challenge in finding the most cost-effective mix
  of sample sizes for frames

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Linkage Exploitation Methods Selection Approaches

• Premise
• Population members with a rare attribute can
  often identify others with the same attribute
• Various adaptations
• Based in the notion of multiplicity in frames
• Differ according to how multiplicity is utilized

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Multiplicity
Frame Listing
Population Member
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Linkage Exploitation Methods Various Adaptations

• Network/multiplicity sampling
• Network --- social/spatial/organizational linkage
  among members of the targeted subgroup
• EXAMPLES relatives, friends, co-workers,
  co-habitants, organization co-members, etc.
• Linkages may be
• Asymmetric
• Complex
• EXAMPLE friends

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Linkage Exploitation Methods Various Adaptations

• Network/multiplicity sampling
• Sampling Process
• Chose an initial sample of targeted subgroup
• Sample members interviewed and asked to nominate
  other members of their network who are members of
  the targeted subgroup
• Interview those nominated and have them nominate
  others in like manner
• Selection probability directly tied to size of
  network

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Linkage Exploitation Methods Various Adaptations

• Snowball sampling
• Network sampling but with multiple phases of
  nomination
• Snowballing may be best used to construct frames
  to sample rare populations
• Continue waves of nomination until list expansion
  ceases

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Linkage Exploitation Methods Various Adaptations

• Adaptive cluster sampling
• Exploits the tendency for members of some
  targeted subgroups to cluster together
• Original motivation from ecology and geology
• Sampling Process
• Select a random sample of the population
• Where one identifies members of the targeted
  subgroup, sample others in the neighborhood

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Linkage Exploitation Methods EXAMPLE

• Snowballing sampling frame of prenatal care
  providers
• Study of recent female immigrants from Central
  and South America
• Process
• Contact OB-GYNs in private practices and public
  clinics
• Those providing prenatal care to immigrants
  nominate others doing the same
• Continue iteratively until the no new providers
  are discovered

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Linkage Exploitation Methods Estimation

• Major contributors Sirken (network), Goodman
  (snowball), and Thompson (adaptive)
• Approaches
• Weighted multiplicity estimation (Sirken)
• Rao-Blackwellization to improve estimator
  efficiency (Thompson)
• Special requirements
• Network membership information
• Multiplicity counts

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Linkage Exploitation Methods Implications for
Sampling Race/Ethnic Minorities

• Advantages
• Greater operational efficiency in locating
  members of the target population
• Find a hotspot then sample nearby
• Disadvantages
• Difficult to determine selection probabilities
  for weights
• Asymmetric linkages (A nominates B, but not vice
  versa)
• Valid probability samples?

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Time and Space Sampling Selection Approach

• Premise
• Portions of ethnic subpopulations are relatively
  mobile (e.g., migrant farm workers, homeless)
• Sampling a chunk of time
• Linkage between members of the target subgroup
  and the frame is dynamic overtime
• Those moving more frequently have greater chance
  of selection
• Sample space and time to address this potential
  for bias

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Time and Space Sampling EXAMPLE

• Sampling migrant seasonal farm workers
• Process
• Spatial dimension sample migrant housing
  locations
• On farms
• In other residential housing areas
• Time dimension sample time periods during the
  data collection period
• Three consecutive days

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Time and Space Sampling Estimation

• Contributors Kalsbeek (1988) Kalton (1991)
• Approaches
• Multiplicity estimators similar to those used in
  network samples
• Special Requirements
• Need multiplicity count for each sample member?
• Sampling scheme compromise needed between
• Statistical precision of estimates
• Operational effectiveness

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Time and Space Sampling Implications for
Sampling Race/Ethnic Minorities

• Advantages
• Deals with the fluidity of frame-population
  linkage in mobile populations
• Provides a framework for finding a cost-efficient
  solution
• Disadvantages
• Added complexity to selection, data gathering,
  and analysis of sample

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Disproportionate Stratified Sampling with
Screening Selection Approach

• Premise
• Concentrations of the targeted subgroup vary in
  the population
• Sample strata with higher concentrations more
  heavily
• Result larger sample size for the target
  subgroup relative to a proportionate sample

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DSS with Screening EXAMPLE

• Oversampling African-Americans
• A simple process
• Stratify the population
• By relatively high and low concentrations of
  African-Americans
• High concentration areas in the South and large
  cities
• Sample with relatively higher rates in the high
  concentration stratum

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DSS with Screening Estimation

• Approaches
• Weighted estimate to account for sample
  disproportionality
• Effect of variable weights is to lower precision
  of some population estimates
• Special Requirements
• Establishing the most cost-efficient overall and
  stratum-specific sampling rates

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DSS with Screening Implications for Sampling
Race/Ethnic Minorities

• Advantages
• Increased sample size for the targeted subgroups
• Are target subgroup non-members in the
  (oversampled) high concentration strata)
• Disadvantages
• Loss in precision on overall population estimates

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A Two-Stratum Model for Effects of Oversampling

• Setting
• Oversampling a minority group
• 10 of the population
• Two sampling strata
• One with higher minority (to oversample)
• One with lower minority (to undersample)
• Two alternative sets of strata
• Nearly Pure --- strata virtually all members or
  non-members
• Less Pure --- strata mostly all members or
  non-members

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Nearly Pure Strata
Oversampled Stratum
Undersampled Stratum
TARGET POPULATION
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Less Pure Strata
Oversampled Stratum
Undersampled Stratum
TARGET POPULATION
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A Two-Stratum Model for Effects of Oversampling

• Assumptions
• Simple random sampling in each stratum
• Stratum unit variances are equal
• Other minor simplifying conditions

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A Two-Stratum Model for Effects of Oversampling

• Sample Sizes (Relative to Proportionate)
• Minority_Nom Nominal Sample Size for Minority
• Observed increase in size of minority sample
• Due to oversampling of the predominantly minority
  stratum
• Minority_Eff Effective Sample Size for Minority
• Adjusted size of minority sample
• Considering the (downward) effect of variable
  sample weights on statistical quality of
  estimates
• Overall_Eff Effiective Size of Overall Sample
• Adjusted size of overall sample
• Considering the (downward) effect of variable
  sample weights on statistical quality of
  estimates

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Effects of Oversampling Nearly Pure Strata
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Effects of OversamplingLess Pure Strata
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Summary

• Sampling rare ethnic groups is possible
• BUT
• Accomplishing it effectively is likely to be
• Complex (dealing with multiplicity, dealing with
  multiple frames, resolving statistical-operational
  dilemmas)
• Costly (screening, stratification)
• Adverse effect on overall population estimates
  (if oversampling done)
• Loss of sampling validity? (snowball sampling)

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A Case-Study in Oversampling Blacks and
Mexican-Americans

• The Third National Health and Nutrition
  Examination Survey (NHANESIII)

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Cluster Sampling

• Random selection applied to one or more levels of
  a population hierarchy
• Sampling Stage Level of hierarchy at which
  sampling is done
• Jargon
• PSU Primary Sampling Unit is what is sampled in
  the first selection stage
• SSU Secondary Sampling Unit is what is sampled
  in the second stage

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Population Hierarchies
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Population Hierarchies

• EXAMPLE African-American residents of the US
  non-institutionalized household population

Resident gt Household gt Block Group gt Census Tract
gt Minor Civil Division gt County gt State gt US
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NHANES III Overview

• National health survey
• U.S. civilian noninstitutionalized population
• Stratified multi-stage sample design
• Detailed profile and predictors of health status
• Data gathering timeline
• 1988-94
• Data collected by
• Face-to-face interviews in the home
• Detailed examination at mobile sites

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NHANES III Target Population

• U.S. residents
• Two months and older
• Including those living in Alaska and Hawaii
• Civilians only
• Excludes housing on military bases
• Noninstitutionalized population only
• Excludes some residents of hospitals, nursing
  homes, prisons, and other comparable institutions
  
• Eligibility determined as of the time of interview

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NHANES III in General

• Key minority domains
• Black (non-Hispanic)
• Mexican American
• Children 2 months 5 years
• The Elderly gt 60 years

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Stratification to OversampleKey Minority Domains
Applied at

• The PSU level
• Race/ethnicity or income indicator
• The segment level
• Density of Mexican-Americans
• The household level
• Race/ethnicity
• The (sample) person level
• Age

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Oversampling of Key Minority Domains

• Implementation accomplished by
• Disproportionate allocation favoring key minority
  domains
• Using a weighted measure of size

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Stratification to Oversample Key Minority
Domains in NHANES III
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Stratification to Oversample Key Minority
Domains in NHANES III

• Oversampling implies more widely variable
  selection probabilities and sample weights
• Effect of variable weights is to increase
  variances of estimates
• One model Increased variance by a factor of,

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Stratification to Oversample Key Minority Domains
in NHANES III

• EXAMPLE
• Effect of variable sample weights on total
  population estimates using data from the
  MEC-examined NHANES III sample