2002 State Estimates of Substance Use

Appendix B: State Estimation Methodology

This report includes estimates of 20 substance use measures (see Section B.1). In addition to the 19 substance use measures for which age group–specific State estimates were produced and documented in the 2001 State report (Wright, 2003a, 2003b), there was 1 new measure (needing but not receiving treatment for alcohol problems in past year) introduced in 2002. The 2000 and 2001 State reports (Wright, 2002a, 2002b, 2003a, 2003b) contained age group–specific State estimates obtained by pooling 1999–2000 and 2000–2001 National Household Survey on Drug Abuse (NHSDA) data, respectively. The 2001 State report also contained estimates of change between the 1999–2000 and 2000–2001 data for the 12 common substance use measures. Due to improvements in the data collection procedures implemented for the 2002 National Survey on Drug Use and Health (NSDUH) and the associated effects on prevalence rates, it was deemed inadvisable to compare 2002 State estimates with the earlier published State estimates from the 1999–2001 surveys. Hence, this report is based on single-year (2002) State estimates. The broad increase in prevalence rates at the national level between 2001 and 2002 that was caused by the methodological differences in those years was reflected in increased prevalence rates across most States. Due to the uneven effects of the incentive and other methodological changes on the State response rates and prevalence rates, a State's ranking for 2002 is not comparable with its rankings in prior years.

The survey-weighted hierarchical Bayes (SWHB) methodology used in the production of State estimates from the 1999–2001 surveys also was used in the production of the 2002 State estimates. The SWHB methodology is described in Appendix E of the 2001 State report (Wright, 2003b) and by Folsom, Shah, and Vaish (1999). The list of predictors used in the 2002 small area estimation (SAE) modeling is given in Section B.2. The improved methodology used to select relevant predictors is described in Section B.3. The goals of SAE modeling, general model description, and the implementation of SAE modeling remain the same and are described in the Appendix E of the 2001 State report (Wright, 2003b). The only difference is that the model used in the 2001 State report used the pooled 2000–2001 NHSDA data, whereas the model in 2002 used a single year of data. At the end of this appendix, tables showing the 2000–2001 and 2002 survey response rates are included (Tables B.1 to B.4). It should be noted that smaller sample sizes and response rates were attained in Mississippi, Nevada, and New Mexico because the review of completed records determined a number of those interviews to be fraudulent. These interviews were consequently dropped.

Small area estimates obtained using the SWHB methodology are design consistent (i.e., for States with large sample sizes, the small area estimates are close to the robust design-based estimates). The State small area estimates when aggregated by using the appropriate population totals result in national small area estimates that are very close to the national design-based estimates. However, due to many reasons, such as internal consistency, it is desirable to have national small area estimates exactly match the national design-based estimates. In the 2002 State estimation, exact benchmarking was introduced as described in Section B.4.

The year 2002 was the first year in which most of the predictors used in the SAE modeling were based on the 2000 census rather than the 1990 census. The impact on the estimates is described in Section B.5. Section B.6 includes the definition and explanation of the formula used in estimating the marijuana incidence rate.

B.1. Variables Modeled

In the 2002 NSDUH, age group–specific State estimates were produced for the following set of 20 binary (0, 1) substance use measures:

1. past month use of any illicit drug,
2. past month use of marijuana,
3. perceptions of great risk of smoking marijuana once a month,
4. average annual rates of first use of marijuana,
5. past month use of any illicit drug other than marijuana,
6. past year use of cocaine,
7. past month use of alcohol,
8. past month binge alcohol use,
9. perceptions of great risk of having five or more drinks of an alcoholic beverage once or twice a week,
10. past month use of any tobacco product,
11. past month use of cigarettes,
12. perceptions of great risk of smoking one or more packs of cigarettes per day,
13. past year alcohol dependence or abuse,
14. past year alcohol dependence,
15. past year any illicit drug dependence or abuse,
16. past year any illicit drug dependence,
17. past year dependence on or abuse of any illicit drug or alcohol,
18. needing but not receiving treatment for illicit drug problems in the past year,
19. needing but not receiving treatment for alcohol problems in the past year, and
20. past year serious mental illness (SMI).

B.2. Predictors Used in Logistic Regression Models

Local area data used as potential predictor variables in the mixed logistic regression models were obtained from several sources, including Claritas, the U.S. Bureau of the Census, the Federal Bureau of Investigation (FBI) (Uniform Crime Reports), Health Resources and Services Administration (Area Resource File), the Substance Abuse and Mental Health Services Administration (SAMHSA) (National Survey of Substance Abuse Treatment Services
[N-SSATS]), and the National Center for Health Statistics (mortality data). The major list of sources and potential data items used in the modeling are provided below.

• Claritas. The demographic data package called Building Block Basic, Age by Race for 2002 with projections to 2007.
  
  
• U.S. Bureau of the Census. The 2000 census (demographic and socioeconomic variables) and 1999 food stamp participation rates.
  
  
• Federal Bureau of Investigation. Uniform Crime Report (UCR) arrest totals from http://fisher.lib.Virginia.EDU/crime/. The most current data are for 2000 for most counties, with previous years' data substituted in a few cases.
  
  
• Health Resources and Services Administration. Some variables relating to income and employment from the Area Resource File (ARF) February 2002 release from the Bureau of Health Professions, Office of Research and Planning.
  
  
• National Center for Health Statistics. Mortality data using International Classification of Diseases, 10^th revision (ICD-10), 1999–2000. The ICD-10 death rate data are from the National Center for Health Statistics at the Centers for Disease Control and Prevention.
  
  
• SAMHSA, Office of Applied Studies. National Survey of Substance Abuse Treatment Services (N-SSATS), formerly known as Uniform Facility Data Set (UFDS), 2000–2002 data on drug and alcohol treatment rates are from Synectics for Management Decisions, Inc.

The following lists provide the specific independent variables that were potential predictors in the models.

B.3. Selection of Independent Variables for the Models

The variable selection process consists of multiple steps:

1. Individual SAS^® stepwise logistic regression models were fit for all outcomes by age group domains. The input list to these models included all linear polynomials (constructed from continuous predictor variables) and other categorical or indicator variables given in Section B.2. All predictors that were significant at 3 percent (except in a few cases) then were input to the 2^nd step of variable selection.
   
   
2. Almost all significant predictors from step 1 then were input to AnswerTree^® to identify significant higher order (at most three-way) interaction terms. AnswerTree^® is an SPSS^® software that uses decision-tree algorithms to build classification systems. The exhaustive chi-squared automatic interaction detector algorithm (CHAID) was used to create the trees. The constraints for making a tree were maximum depth = 3; minimum number of records in parent node = 1,000; minimum number of records in child node = 300; and splitting criterion = 3 percent.
   
   
3. All the significant variables from step 1 along with their corresponding higher order polynomials (quadratic and cubic), interaction of gender and race, and the significant interactions detected by AnswerTree^® in step 2 then were input to SAS^® stepwise logistic regression models. All predictors that remained significant at 3 percent (except in few cases) then were input to the 4^th step of variable selection.
   
   
4. All significant variables from step 3 were input to SUDAAN^® logistic regression models, and predictors that remained significant at the 1 percent level were input to PROC GIBBS and PROC GSTAT software. In all mixed logistic models, race and gender were forced.

B.4. Benchmarking the Age Group–Specific Small Area Estimates

The self-calibration built into the SWHB solution ensures that the population-weighted average of the State small area estimates will closely match the national design-based estimates. Given the self-calibration ensured by the SWHB solution, for previous State reports the standard Bayes prescription was followed; specifically, the posterior mean was used for the SAE point estimate and the tail percentiles of the posterior distribution were used for the credible interval limits.

Exploring this issue further, Singh and Folsom (2001) extended Ghosh's (1992) results on constrained Bayes estimation to include exact benchmarking to design-based national estimates. In the simplest version of this constrained Bayes solution where only the design-based mean is imposed as a benchmarking constraint, each of the State-by-age group small area estimates is adjusted by adding the common factor _a = (D_a - P_a), where D_a is the design-based national prevalence estimate and P_a is the population-weighted mean of the State small area estimates (P_sa) for age group-a. The exactly benchmarked State-s and age group-a small area estimates then are given by _sa = P_sa+ _a. Experience with such additive adjustments suggests that the resulting exactly benchmarked State small area estimates will always be between 0 and 100 percent because the SWHB self-calibration ensures that the adjustment factor is small relative to the size of the State-level small area estimates.

Relative to the Bayes posterior mean, these benchmark-constrained State small area estimates are biased by the common additive adjustment factor. Therefore, the posterior mean-squared error for each benchmarked State small area estimate has the square of this adjustment factor added to its posterior variance. To achieve the desirable feature of exact benchmarking, this constrained Bayes adjustment factor was implemented for the State-by-age group small area estimates. The associated credible intervals can be recentered at the benchmarked small area estimates on the logit scale with the symmetric interval end points based on the posterior root mean-squared errors. The adjusted 95 percent prediction intervals (PIs) (Lower_sa, Upper_sa) are defined below:

Lower_sa = exp(L_sa)/[1 + exp(L_sa)] and Upper_sa = exp(U_sa)/[1 + exp(U_sa)],     D

where

L_sa = log[_sa/(1 - _sa)] - 1.96 * (MSE_sa),     D

U_sa = log[_sa/(1 - _sa)] + 1.96 * (MSE_sa), and     D

MSE_sa = (log[P_sa/(1 - P_sa)]- log[_sa/(1 - _sa)])² + posterior variance of log[P_sa/(1 - P_sa)].     D

The associated posterior coverage probabilities for these benchmarked intervals are very close to the prescribed 0.95 value because the State small area estimates have posterior distributions that can be approximated exceptionally well by a Gaussian distribution.

B.5. Change to the 2000 Census

In 2002, all census variables used in the national prediction models were updated from the 1990 census to the 2000 census. To compare the updated prediction results with the 1990 prediction estimates, small area estimates were estimated for five substances (past month alcohol, past month cigarettes, past month marijuana, past month any illicit drug, and past year cocaine) by four age groups (12 to 17, 18 to 25, 26 to 34, 35 or older), first based upon the 1990 census and then the 2000 census, using the identical set of predictors in both cases. Comparing residual variances (random effects) for the models fit using the two census' data, the 2000 census-based models had a smaller residual (a better fit) in all but 3 of the 20 substance-by-age groups. The 18 to 25 age group and the 26 to 34 age group had a better fit for all five substances, the 35 or older age group was better for four out of five substances, and the 12 to 17 age group was better for three out of five substances.

B.6. Calculation of Average Annual Incidence of Marijuana Use

Incidence rates are typically calculated as the number of new initiates of a substance during a period of time (such as in the past year) divided by the estimate of the number of person years of exposure (in thousands). The incidence definition in this report is the result of a simpler definition based on the model-based methodology and is as follows:

Average annual incidence rate = {(Number of marijuana initiates in past 24 months) /
[(Number of marijuana initiates in past 24 months * 0.5) +
Number of persons who never used marijuana]} / 2.

In this report, this rate is expressed as a percentage or rate per 100 person years of exposure. Note that this estimate uses a 2–year time period to accumulate incidence cases from each annual survey. By assuming further that the distribution of first use for the incidence cases is uniform across the 2–year interval, the total number of person years of exposure is 1 year on average for the incidence cases plus 2 years for all the "never users" at the end of the time period. This approximation to the person years of exposure permits one to recast the incidence rate as a function of two population prevalence rates, namely, the fraction of persons who first used marijuana in the past 2 years and the fraction who had never used marijuana. Both of these prevalence estimates were estimated using the survey-weighted hierarchical Bayes estimation approach.

The count of persons who first used marijuana in the past 2 years is based on a "moving" 2–year period that ranges over 3 calendar years. Subjects were asked when they first used marijuana. If a person indicated first use of marijuana between the day of the interview and 2 years prior, the person was included in the count. Thus, it is possible for a person interviewed in the first part of 2002 to indicate first use as early as the first part of 2000 or as late as the first part of 2002. Similarly, a subject interviewed in the last part of 2002 could indicate first use as early as the last part of 2000 or as late as the last part of 2002. Therefore, in the 2002 survey, the reported period of first use ranged from early 2000 to late 2002 and was "centered" in 2001. About half of the 12 to 17 year olds who reported first use in the past 24 months reported first use in 2001, while a quarter each reported first use in 2000 and 2002. Persons who responded in 2002 that they had never used marijuana were included in the count of "never used." Note that only incidence rates for marijuana use are provided in this report.

This page was last updated on June 03, 2008.

SAMHSA, an agency in the Department of Health and Human Services, is the Federal Government's lead agency for improving the quality and availability of substance abuse prevention, addiction treatment, and mental health services in the United States.