Sampling Racial and Ethnic Minoritiessph.unc.edu/files/2013/07/kalsbeek_slides_2000.pdf · Disproportionate Stratified Sampling with Screening: Selection Approach ... –Simple random

1

Sampling Racial and

Ethnic Minorities

William D. Kalsbeek

Director, Survey Research Unit

Professor, Department of Biostatistics

University of North Carolina

June 14, 2000

Copyright 2000, William Kalsbeek


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Acknowledgements

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-CH’s Center for Health Statistics Research

– http://www.sph.unc.edu/chsr

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

As the population subgroup of interest in a specially targeted

study (targeted sampling)

As a key subgroup in a general population study (oversampling)

<-------------------- General Population ------------------->

Ethnic Minority

With Oversampling

Targeted


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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

h h hf n / N Sampling rate in h-th stratum

= Standard deviation of all members of the h-th

stratum (measures intra-stratum variation) hS


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Stratum Allocation Options Analysis Priority

Option Description to Estimates for:

Proportionate Same sampling rates Overall

(fh = f in all strata) population

Optimum Most cost-efficient

sampling rates Overall population

Balanced Equal sample sizes Population

(nh = n/H) subgroups*

Disproportionate To "oversample" Key population

important subgroups subgroups*

(fh higher in subgroup strata)

* Definable by the strata

hh

h

Sf

C


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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 Copyright 2000, William Kalsbeek


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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 A

Frame C

Frame B


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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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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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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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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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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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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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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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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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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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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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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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Estimation

Contributors: Kalsbeek (1988); Kalton (1991)

Approaches:

– Multiplicity estimators similar to those used in

network samples


– Need multiplicity count for each sample member?

– Sampling scheme compromise needed between:

• Statistical precision of estimates

• Operational effectiveness


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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


– Establishing the most cost-efficient overall and

stratum-specific sampling rates


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DSS with Screening:



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

Undersampled Stratum

|

Oversampled

Stratum

|

TARGET POPULATION


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Effects of Oversampling

Assumptions:

– Simple random sampling in each stratum

– Stratum unit variances are equal

– Other minor simplifying conditions


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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

Effects of Oversampling on Sample Sizes:

Nearly Pure Strata

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

1 3 5 7 9 11 13 15 17 19 21

Degree of Oversampling (Relative Sampling Rates)

Sample

Sizes

Relative

to

Prop.

Alloc.

Overall_Eff Minority_Nom Minority_Eff


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Effects of Oversampling:

Less Pure Strata

Effects of Oversampling on Sample Size:

Less Pure Strata

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

1 3 5 7 9 11 13 15 17 19 21

Degree of Oversampling (Relative Sampling Rates)

Sample

Sizes

Relative

to

Prop.

Alloc.

Overall_Eff Minority_Nom Minority_Eff


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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:

Population

Member

(Based on Vital and Health Statistics, Series 2, Number 113


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Population Hierarchies:

EXAMPLE: African-American residents of the

US non-institutionalized household population

Resident > Household > Block Group >

Census Tract > Minor Civil Division >

County > State > 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: > 60 years


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Stratification to Oversample

Key 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:

*j j

j

Mos Mos

j = overall sampling probability for the j-th among all

cells of the cross-classification by the race/ethnicity

and age categories that define the key minority domains

jMos = Measure of size for the same cross-classification

within the ( -th) cluster


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Key Minority Domains in NHANES III

Domain Approximate

Population %

Approximate

Sample %

Black, non-

Hispanic

12 31

Mexican

American

5 26

2 months –

5 years

7 11

60 years 21 32


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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,

2

2

sn 1Deff 1

n

2s Variance of weights among sample respondents

Mean of weights among sample respondents


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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

n = 23,561

9,397.04

22s 12,405.33

Deff 2.743

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Sampling Racial and Ethnic Minoritiessph.unc.edu/files/2013/07/kalsbeek_slides_2000.pdf · Disproportionate Stratified Sampling with Screening: Selection Approach ... –Simple random