National data      State level data       Metropolitan and other subState area data

Substance Abuse in States and Metropolitan Areas:
Model Based Estimates from the 1991-1993 National Household Surveys on Drug Abuse

Chapter 2

2. Methodology Used:

2.1 Potential Estimation Strategies for Small Areas

2.2 Small Area Estimation Method Used

2.3 Fitting the Small Area Estimation Model

2.3.1 Data Used

2.3.2 States and MSAs selected for estimation

2.3.3 Summary of methodology

2.3.4 Confidence Intervals

The methodology that was used for these small area estimates employs logistic regression models that combine NHSDA data with local area indicators that were found to be associated with substance abuse. Several innovative strategies were used to produce these estimates.

Several procedures have been used by other researchers to produce various health and economic statistics for small areas in other fields. Schaible ^(footnote#6)  presents information describing three common indirect estimation methods that have been used by federal statistical agencies: synthetic estimators, regression estimators, and composite estimators. ^(footnote#7)  State level synthetic estimators are constructed by taking national estimates for demographic subgroups and applying them to the demographic composition of the particular States for which estimates are desired. Synthetic estimators, however, often fail to reflect the actual variation across local areas because demographic characteristics (age, gender, race/ethnicity, etc.) do not fully determine the phenomena being estimated. Regression estimators incorporate additional factors or predictors in the estimation procedure in an attempt to improve the estimates for the small area. Synthetic and regression estimators are indirect estimation methods and do not require any direct measures of the phenomena for the small area. In many cases, however, direct estimates are available for the small area but the sample size for the small area is not large enough to yield precise estimates. Composite estimators are constructed as a weighted combination of direct survey estimators and indirect estimators. They are used to take maximum advantage of any direct information from the survey for the small area, to reduce the bias associated with indirect estimators, and are likely to be more accurate than using solely either the direct or indirect estimator. ^(footnote#8)

In developing the small area estimates for the States and MSAs included in this report, we developed procedures that built on earlier small area estimation work, which focused on a variety of social, health and economic phenomena. The previously cited works by Schaible (1996) and Ghosh and Rao (1994) discuss these types of estimators and note that a variety of research has been carried out investigating the optimal weighting and estimation schemes for composite estimators. In this study, similar methods were developed to produce estimates of substance abuse.

First, logistic regression models for the relationship between substance abuse and a variety of predictors, including demographic characteristics and a number of social and economic characteristics, were fit at the block group level using Census block group and tract level predictors of substance abuse. These block level estimates were then summed to arrive at the estimates for the States and MSAs.

 

Second, additional county-level predictors were included in the model to account for still more variation across local areas.

 

Third, the survey design weights were used in the estimation of the logistic regression coefficients and the State and MSA local area effects. This innovation causes the State small area estimates to sum to the NHSDA estimates for US regions and the nation.^{(footnote#11)}

  

The final estimates of the logistic regression coefficients and the local area effects for States and MSAs were estimated using an iteratively reweighted least squares algorithm patterned after Breslow and Clayton's (1993)^{(footnote#12)}  prescription for analyzing generalized linear mixed models (GLMM).

  

Four types of data were used in the estimation: NHSDA data, Census data, county level (social indicators) correlates of substance abuse, and block group level population projections.

The NHSDA data were used to fit models for each of the 11 outcome measures described in Chapter 1. Estimates were made for four age groups (12-17, 18-25, 26-34, and 35+). In addition, separate models were fit for two geographic subpopulations comprised of 1) the six large MSAs and 2) the remainder of the nation. Altogether, this resulted in the fitting of 88 models, (11 outcome measures x 4 age groups x 2 geographic subpopulations). The dependent variables in these models were the rates for the outcome measures. In fitting these models, two types of auxiliary data were used: census data and county level indicators of drug use. After models were fit, the population projections were applied to the estimated rates at the block group level.

NHSDA data: The data that were used for the estimation came from the respondents to the NHSDA for 1991-1993. Essentially the same survey methodology was used in each of these three years: The sample was a deeply stratified, multistage national probability sample of civilian persons age 12 and older, living in households and certain group quarters, such as, college dormitories and homeless shelters. Civilians living on military installations are included in the target population. On the other hand, military personnel on active duty as well as most transient populations, such as homeless people not residing in shelters, were not included in the target population.

Each year, roughly 120 primary sampling units (PSUs) were selected at the first stage of sampling. These PSUs were generally individual counties or groups of adjacent counties constituting Metropolitan Statistical Areas (MSAs). At the second stage of selection, groups of Census blocks, called sample segments, were selected. Within each segment, dwelling units were selected; within each successfully screened dwelling unit, either zero, one or two occupants were selected for the NHSDA interview. Generally, the NHSDA yields dwelling unit screening response rates of approximately 94 percent and interview response rates of approximately 80 percent. The pooled 1991-1993 NHSDAs yielded a combined sample size of 87,915 people. In 1991-1993, the NHSDA included a special sample from six large MSAs. This sample was designed to provide independent estimates of prevalence of substance abuse in Chicago, Denver, Los Angeles, Miami, New York, and Washington, D.C.

Since nearly all of the substance abuse data that are collected in the survey are highly sensitive, rigorous methods are used in the NHSDA to protect the privacy and confidentiality of responses. The interviewer works with the respondent to find a private place for the interview. After the respondent answers some of the less sensitive questions by responding to interviewer queries, he or she is trained in the completion of a series of self-administered questionnaires. These self-administered questionnaires allow the respondent to conceal his or her answers from both the interviewer and any household members who may be nearby. These methods that are undertaken to protect the privacy and confidentiality of respondents have been shown to increase the reporting of substance abuse.^{(footnote#13)}

Census data: Exhibit 2.1 lists the Census data that were used in the modeling. Exhibit 2.1 lists nineteen groups of variables that were considered as potential predictors in each of the 88 models formulated for this study. All of the attributes come from the 1990 U.S. Census long form sample.^{(footnote#15)}

  

Exhibit 2.1  1990 Census Variables Used to Model Prevalence of Substance Abuse.From Summary Tape File 3; 1990 Census of Population and Housing. 

1.  Race x Hispanic - -   Percent:

White nonHispanic  Black nonHispanic  Hispanic  Other

2.  Education for persons 18 or older- - Percent with:

0-8 years  9-12 years and no H.S. diploma  H.S. graduate  some college and no degree  associate degree  bachelors, graduate, or professional degree

3.  Age - - Percent aged:

0-18 years  19-24 years  25-34 years  35-44 years  45-54 years  55-64 years  65 and over

4.  Poverty - - Percent:

families below poverty level

5.  Public Assistance - - Percent of:

households with public assistance income

6.  Disability - - Percent:

persons 16-64 with a work disability

7.  Household composition - - Percent:

one-person households

of households with female heads (no spouse present) with children under 18

8.  Employment - - Percent:

of men 16 years and older in the labor force  of women 16 years and older in the labor force

9.Housing value - owner occupied units:

Median value of owner occupied housing units

10.  Housing rent - rental units - -

Median rents for rental units

11.  Sex by marital status  (persons 16 years and older) - - Percent:

Females currently married and not  separated  Females separated, divorced, or widowed  Females never married  Males currently married and not separated  Males separated, divorced, or widowed  Males never married

12.  Income - -

Median Household Income

13.  Urbanicity - - Percent:

of persons residing in an urban place

14.  Urbanized Area - - Percent:

of persons in an MSA urbanized area

15.  Age of Housing  Units (HU) - - Percent:

of HUs built before 1939  of HUs built from 1940 to 1949

16.  High School Dropout Rate (Tract level only) - - Percent:

of high school age children who have  dropped out

17.  Underclass Tract Indicator (Tract level only)

18.  Hispanic Subpopulations - - Percent:

of Hispanics that are Cuban  of Hispanics that are Puerto Rican

19.  Other Race Subpopulations - - Percent:

Population that is Asian and Pacific Islander  Population that is Native American, Alaskan, or Aleut

From Summary Tape File 3; 1990 Census of Population and Housing.(footnote#14)

 

County level (social indicator) correlates of substance abuse: In addition to the Census variables, recoded county level 'social indicators' of substance abuse were also considered. These county level variables were obtained from three sources: The first of these sources is the FBI's Uniform Crime Reports data base for 1991. This source yielded data on arrest rates per 10,000 persons for illegal drug possession, and drug sales/manufacture by several reported drug categories, and on total violent crime arrest rates. The second source combined data from the 1991 and 1992 National Drug and Alcoholism Treatment Unit Survey (NDATUS) conducted by the Substance Abuse and Mental Health Services Administration. From this source, data was obtained on the 1991 and 1992 average treatment rates per 1,000 county residents for (1) alcohol treatment alone and (2) for illicit drug treatment (includes treatment for both drug and alcohol use). Thirdly, 1990 alcohol related death rates per 10,000 county residents were obtained from the National Center for Health Statistics national death certificate registry. Two such rates were considered in this research: (a) the A any related rate@ which includes all ICD-8 cause-of-death codes that are deemed to have a significant link to alcohol abuse, and (b) a more restrictive rate which requires explicit mention of alcohol on the death certificate.

Block group level population projections: Population projections for 1992 for each Census block group, were obtained from Claritas, Inc.^{(footnote#16)}   These projections included counts by age group (12-17, 18-24, 25-29, 30-34, 35+ years old), by gender, by race (white, black, American Indian plus Asians & Pacific Islanders, and other races) and by Hispanic indicator. These block group level population projections were adjusted by gender category to conform to the four age groups and the four race ethnicity groups employed for data reporting by the NHSDA.

  

Composite small area estimators require at least some direct information for the small areas under consideration. Thus, only those States and MSAs which had some NHSDA sample points were included in the study. The States and MSAs selected for small area estimation are presented in Exhibit 2.2. This exhibit shows the number of people who responded to the combined 1991-1993 NHSDA surveys plus information on the NHSDA sample including numbers of the sample MSA/County units, sample block groups, and the estimated 1992 population.

The States and MSAs presented in Exhibit 2.2 were chosen for small area estimation because:

• The NHSDA sample size was large enough (~ 400 persons) to support model based, indirect estimation, and not necessarily large enough to support direct NHSDA estimation,
• The number of distinct sample MSA/County units was greater than or equal to 4 units, and
• The number of distinct sample segments was greater than 40 segments.

Four exceptions to the four or more MSA/County unit rule were allowed for States that met the sample person and area segment minimums.

  

Exhibit 2.2A States Selected for Inclusion in the Study: Population Size and NHSDA Sample Characteristics.

	STATE	SAMPLE MSA/ COUNTIES1	SAMPLE BLOCK GROUPS2	SAMPLE RESPONDING PERSONS3	1992 POPULATION PROJECTION4
	TOTAL UNITED STATES	213	8,942	84,974	205,945
	NORTH EAST REGION	34	1,489	13,681	42,236
	New Jersey	6	167	1,523	6,443
	New York	7	843	8,505	14,892
	Pennsylvania	11	269	2,133	9,945
	SOUTH REGION	49	1,723	15,456	71,396
	Florida	13	964	10,066	11,265
	Georgia	5	118	1,061	5,442
	Kentucky	6	112	1,081	3,053
	Louisiana	6	133	1,099	3,387
	North Carolina	12	222	1,863	5,641
	Oklahoma	4	63	494	2,563
	South Carolina	4	48	330	2,939
	Tennessee	4	92	780	4,117
	Texas	13	503	5,082	13,751
	Virginia	9	362	3,538	5,227
	West Virginia	3	44	394	1,497
	NORTH CENTRAL REGION	85	3,271	32,346	48,968
	Illinois	6	799	8,088	9,378
	Indiana	6	114	978	4,581
	Kansas	4	60	515	2,010
	Michigan	5	175	1,187	7,615
	Minnesota	3	76	684	3,576
	Missouri	6	120	1,059	4,223
	Ohio	12	264	2,021	8,946
	Wisconsin	3	55	475	4,021
	WEST REGION	45	2,459	23,491	43,346
	California	22	1,320	12,364	24,342
	New Mexico	5	74	676	1,199
	Oregon	4	59	412	2,397
	Washington	3	73	690	4,094

¹MSA/Counties refers to geographic entities formed to estimate random effect terms in the logistic model and which are generally analogous to NHSDA primary sampling units (PSUs). The exceptions are the distinct MSA constituents of PSUs that crossed State boundaries or combined more than one MSA.

²Block groups refers to the sample segments which were selected at the second stage of selection in the 1991-1993 NHSDA.

³87,915 people responded to the 1991-1993 NHSDA however 2,941 people were omitted from the small area estimation research because of missing local area indicator variables which were used as potential predictors in the models.

⁴Population projections presented in 1000's.

  

Exhibit 2.2B - - MSA Small Areas Selected for Inclusion in the Study:  Population Size and NHSDA Sample Characteristics

	MSA	SAMPLE BLOCK GROUPS2	SAMPLE RESPONDING PERSONS3	1992 POPULATION PROJECTION4
	Anaheim-Santa Ana, CA	*	*	1,996
	Atlanta, GA	*	*	2,425
	Baltimore, MD	*	*	1,996
	Boston, MA	*	*	3,145
	Chicago, IL	735	7,537	4,981
	Dallas, TX	*	*	2,120
	Denver, CO	719	7,585	1,346
	Detroit, MI	*	*	3,593
	El Paso, TX	*	*	456
	Houston, TX	*	*	2,661
	Los Angeles, CA	768	7,533	7,127
	Miami-Hialeah, FL	725	8,142	1,600
	Minneapolis-St. Paul, MN	*	*	2,035
	Nassau-Suffolk, NY	*	*	2,178
	New York, NY	730	7,676	7,086
	Newark, NJ	*	*	1,500
	Oakland, CA	*	*	1,727
	Philadelphia, PA-NJ	*	*	4,037
	Phoenix, AZ	*	*	1,770
	San Antonio, TX	*	*	1,040
	San Bernardino, CA	*	*	2,122
	San Diego, CA	*	*	2,089
	St. Louis, MO-IL	*	*	2,006
	Tampa-St. Petersburg, FL	*	*	1,822
	Washington, DC	725	7,795	3,345

*Number of sample block groups ranged from 40 to 110; number of respondents ranged from 400 to 1200 in these MSAs.

²Block groups refers to the sample segments which were selected at the second stage of selection in the 1991-1993 NHSDA.

³87,915 people responded to the 1991-1993 NHSDA however 2,941 people were omitted from the small area estimation research because of missing local area indicator variables which were used as potential predictors in the models.

⁴Population projections presented in 1000's.

See Appendix B for a list of counties included in each MSA.

  

In summary, the estimates were produced by completing the following three basic steps:

• Estimate regression parameters: Using NHSDA data, logistic regression models were developed which identified (and estimated the parameters associated with) local area indicators that were significant predictors of the eleven substance abuse measures in NHSDA sample locations. Separate models were run for each of the 11 outcome measures and for each of four age groups (12-17, 18-25, 26-34, and 35+). Because the 1991-1993 NHSDA included very large samples for six large US cities, separate models were fit collectively for these six large cities and for the remainder of the nation. Thus, a total of 88 separate models were used for this small area estimation. An important feature of these logistic regression models was the inclusion of random-effect parameters that adjust for the actual A direct@ estimates obtained from NHSDA sample data in the States and MSAs for which small area estimates were to be generated.
• Apply regression parameters to the entire U.S.: Predicted estimates of substance abuse rates were generated for every Census block group in the U.S. by applying the regression parameters to the local area indicators, which were known for every block group. Within each Census block group, estimates were made for each of the 11 measures and for 32 demographic groups defined by four age groups, four race/ethnicity (Hispanic, non-Hispanic black, non-Hispanic white, non-Hispanic other race) groups, and gender, (4x4x2 = 32 demographic subgroups).
• Sum up block group estimates to the State and MSA levels: Estimated rates were multiplied by population estimates for each block group, resulting in estimated numbers of people for each of the eleven attributes. Data from all block groups in States and MSAs were then summed to give final State and MSA total estimates.

  

Asymmetric 95 percent confidence intervals were constructed based on the logit transformation. This is the typical procedure that is used when estimating characteristics with small prevalence. The mean square errors that are used to construct the confidence intervals include a contribution that accounts for the variances and covariances of the logistic regression coefficients incorporated in the indirect component (∏ ) and the sampling variance of the direct local area estimate. The weight put on these mean square error contributions depends on the values of the weights in Equation (1).

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