Appendix A: State Estimation Methodology

This report includes estimates of 22 substance use measures (see Section A.1) using the combined data from the 2003 and 2004 National Surveys on Drug Use and Health (NSDUHs). In addition to the 21 substance use measures for which age group–specific State estimates were produced and documented in the 2003 State report (Wright & Sathe, 2005), there is a new measure, past year nonmedical pain reliever use, introduced in this report. Also included in this report are estimates of change between 2002-2003 and 2003-2004 State estimates. This report is similar to the 2000 and 2001 State reports (Wright, 2002a, 2002b, 2003a, 2003b) that contained age group–specific State estimates obtained by pooling 1999–2000 and 2000–2001 National Household Survey on Drug Abuse (NHSDA)⁸ 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. As discussed in Chapter 1 (Section 1.1), several changes were introduced to the survey in 2002; thus, estimates for 2001 and prior years are not comparable with estimates from 2002 and later years.

The survey-weighted hierarchical Bayes (SWHB) methodology used in the production of State estimates from the 1999–2003 surveys also was used in the production of the 2003-2004 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 2003-2004 small area estimation (SAE) modeling is given in Section A.2. The methodology used to select relevant predictors remains similar to the one used in prior years and is described in brief in Section A.3. The goals of SAE modeling, general model description, and the implementation of SAE modeling remain the same and are described in Appendix E of the 2001 State report (Wright, 2003b). At the end of this appendix, tables showing the 2002, 2003, 2004, pooled 2002-2003, and pooled 2003-2004 survey response rates are included (Table s A.1 to A.12).

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, for numerous reasons (including internal consistency), it is desirable to have national small area estimates exactly match the national design-based estimates. Beginning in 2002, exact benchmarking was introduced as described in Section A.4. The definition and explanation of the formula used in estimating the marijuana incidence rate is given in Section A.5.

Included in this report for the first time are estimates of underage (ages 12 to 20) alcohol use and binge alcohol use. For all other outcomes the age groups of interest were 12 to 17, 18 to 25, and 26 or older. As alcohol consumption is expected to differ significantly across the 18 to 25 age group due to the legalization of alcohol at age 21, it was decided that it would be useful to produce small area estimates for persons aged 12 to 20. A short description of methodology used to produce underage drinking estimates is described in Section A.6.

Section A.7 discusses how serious psychological distress (SPD) estimates were produced. The methodology used to produce estimates of change between the 2002-2003 and the 2003-2004 State estimates is described in Section A.8.

A.1 Variables Modeled

The 2004 NSDUH data were pooled with the 2003 NSDUH data, and age group–specific State estimates for 22 binary (0,1) outcome variables were produced and presented in this report. The estimates of change between the 2002-2003 and 2003-2004 State estimates also were produced for the following outcomes:

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

A.2 Predictors Used in Mixed Logistic Regression Models

Local area data used as potential predictor variables in the mixed logistic regression models were obtained from several sources, including Claritas Inc., 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 list of major sources and potential data items used in the modeling are provided in the following text and lists.

• 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 2002 food stamp participation rates.



• Federal Bureau of Investigation. Uniform Crime Report (UCR) arrest totals from http://fisher.lib.Virginia.EDU/collections/stats/crime/. The most current data used are 2002 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 2003 and February 2004 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), 1999–2002. 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 the Uniform Facility Data Set (UFDS). The 2003-2004 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.

Claritas Data
Description	Level
% Population aged 0–19 in block group	Block group
% Population aged 20–24 in block group	Block group
% Population aged 25–34 in block group	Block group
% Population aged 35–44 in block group	Block group
% Population aged 45–54 in block group	Block group
% Population aged 55–64 in block group	Block group
% Population aged 65+ in block group	Block group
% Blacks in block group	Block group
% Hispanics in block group	Block group
% Other race in block group	Block group
% Whites in block group	Block group
% Males in block group	Block group
% Females in block group	Block group
% American Indian, Eskimo, Aleut in tract	Tract
% Asian, Pacific Islander in tract	Tract
% Population aged 0–19 in tract	Tract
% Population aged 20–24 in tract	Tract
% Population aged 25–34 in tract	Tract
% Population aged 35–44 in tract	Tract
% Population aged 45–54 in tract	Tract
% Population aged 55–64 in tract	Tract
% Population aged 65+ in tract	Tract
% Blacks in tract	Tract
% Hispanics in tract	Tract
% Other race in tract	Tract
% Whites in tract	Tract
% Males in tract	Tract
% Females in tract	Tract
% Population aged 0–19 in county	County
% Population aged 20–24 in county	County
% Population aged 25–34 in county	County
% Population aged 35–44 in county	County
% Population aged 45–54 in county	County
% Population aged 55–64 in county	County
% Population aged 65+ in county	County
% Blacks in county	County
% Hispanics in county	County
% Other race in county	County
% Whites in county	County
% Males in county	County
% Females in county	County

2000 Census Data
Description	Level
% Population who dropped out of high school	Tract
% Housing units built in 1940–1949	Tract
% Persons 16–64 with a work disability	Tract
% Hispanics who are Cuban	Tract
% Females 16 years or older in labor force	Tract
% Females never married	Tract
% Females separated/divorced/widowed/other	Tract
% One-person households	Tract
% Female head of household, no spouse, child 18	Tract
% Males 16 years or older in labor force	Tract
% Males never married	Tract
% Males separated/divorced/widowed/other	Tract
% Housing units built in 1939 or earlier	Tract
Average persons per room	Tract
% Families below poverty level	Tract
% Households with public assistance income	Tract
% Housing units rented	Tract
% Population 9–12 years of school, no high school diploma	Tract
% Population 0–8 years of school	Tract
% Population with associate's degree	Tract
% Population some college and no degree	Tract
% Population with bachelor's, graduate, professional degree	Tract
Median rents for rental units	Tract
Median value of owner-occupied housing units	Tract
Median household income	Tract

Uniform Crime Report Data
Description	Level
Drug possession arrest rate	County
Drug sale/manufacture arrest rate	County
Drug violations' arrest rate	County
Marijuana possession arrest rate	County
Marijuana sale/manufacture arrest rate	County
Opium cocaine possession arrest rate	County
Opium cocaine sale/manufacture arrest rate	County
Other drug possession arrest rate	County
Other dangerous non-narcotics arrest rate	County
Serious crime arrest rate	County
Violent crime arrest rate	County
Driving under influence arrest rate	County

Other Categorical Data
Description	Source	Level
=1 if Hispanic, =0 otherwise	Sample	Person
=1 if non-Hispanic Black, =0 otherwise	Sample	Person
=1 if non-Hispanic Other, =0 otherwise	Sample	Person
=1 if male, =0 if female	Sample	Person
=1 if MSA with 1 million +, =0 otherwise	2000 Census	County
=1 if MSA with <1 million, =0 otherwise	2000 Census	County
=1 if Non-MSA Urban, =0 otherwise	2000 Census	Tract
=1 if Urban Area, =0 if Rural Area	2000 Census	Tract
=1 if no Cubans in tract, =0 otherwise	2000 Census	Tract
=1 if no arrests for dangerous non-narcotics, =0 otherwise	UCR	County

Miscellaneous Data
Variable Description	Source	Level
Alcohol death rate, underlying cause	NCHS-ICD-10	County
Cigarettes death rate, underlying cause	NCHS-ICD-10	County
Drug death rate, underlying cause	NCHS-ICD-10	County
Alcohol treatment rate	N-SSATS (formerly called UFDS)	County
Alcohol and drug treatment rate	N-SSATS (formerly called UFDS)	County
Drug treatment rate	N-SSATS (formerly called UFDS)	County
% Families below poverty level	ARF	County
Unemployment rate	ARF	County
Per capita income (in thousands)	ARF	County
Average suicide rate (per 10,000)	ARF	County
Food stamp participation rate	Census Bureau	County
Single state agency maintenance of effort	National Association of State Alcohol and Drug Abuse Directors (NASADAD)	State
Block grant awards	SAMHSA	State
Cost of Services Factor Index	SAMHSA	State
Total Taxable Resources Per Capita Index	U.S. Department of Treasury	State

A.3 Selection of Independent Variables for the Models

The State estimates for past year nonmedical use of pain relievers (ANLYR) were not produced in prior years. Hence, in order to be consistent with the other set of outcomes, the fixed-effect predictors for ANLYR were selected using the pooled 2002-2003 NSDUH data. These fixed-effect predictors were selected based on the steps detailed in Section A.3 of Wright and Sathe (2005), and their updated versions were used to produce 2003-2004 State estimates for ANLYR. For all the other outcome variables, no new variable selection was done. The updated versions of fixed-effect predictors that were used in modeling the 2002-2003 data were used to model the 2003-2004 data. Because the interest was to estimate change between the 2002-2003 and 2003-2004 State estimates, the same set of fixed-effect predictors was used for producing both sets of estimates.

A.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 State reports prior to 2002, 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 prediction interval limits.

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 (for 2003-2004) 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 always will 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)],

where

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

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

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

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.

A.5 Calculation of Average Annual Incidence of Marijuana Use

Incidence rates typically are calculated as the number of new initiates of a substance during a period of time (such as in the past year) divided by an estimate of the number of person years of exposure (in thousands). The incidence definition used in this report employs a simpler form of the at-risk-population based on the model-based methodology. This model-based average annual incidence rate is defined 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, the incidence 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 SWHB 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 2004 to indicate first use as early as the first part of 2002 or as late as the first part of 2004. Similarly, a subject interviewed in the last part of 2004 could indicate first use as early as the last part of 2002 or as late as the last part of 2004. Therefore, in the 2004 survey, the reported period of first use ranged from early 2002 to late 2004 and was "centered" in 2003. About half of the 12 to 17 year olds who reported first use in the past 24 months reported first use in 2003, while a quarter each reported first use in 2002 and 2004. Persons who responded in 2004 that they had never used marijuana were included in the count of "never used." Similarly, reports of first use in past 24 months from the 2003 survey ranged from early 2000 to late 2003 and were centered in 2002. Half of the 12 to 17 year olds who reported first use in the past 24 months reported first use in 2002, while a quarter each reported first use in 2000 and 2003. Note that only incidence rates for marijuana use are provided in this report.

A.6 Underage Drinking

To obtain small area estimates for persons aged 12 to 20 for past month alcohol and binge alcohol use, a separate set of models was fit for these two outcomes for the 12 to 17 age group and the 18 to 20 age group. New variable selection (using the same methodology as described in Section A.3) was done for the 18 to 20 age group. Even though separate models were fit for the 12 to 17 age group along with the 18 to 20 year olds, no new variable selection was done for the 12 to 17 age group. Model-based estimates for persons aged 12 to 20 were produced by taking the population-weighted average of the individual age group (12 to 17 and 18 to 20) estimates. Estimates for underage drinking for past month alcohol and binge alcohol use were benchmarked to match national design-based estimates for that age group using the process described in Section A.4. Estimates of change between 2002-2003 and 2003-2004 underage drinking State estimates also are presented in this report.

A.7 Serious Psychological Distress

In 2004, SPD was measured using the K6 screening instrument for nonspecific psychological distress (Furukawa, Kessler, Slade, & Andrews, 2003; Kessler et al., 2003). In previous NSDUH reports, the K6 scale was referred to as a measure of serious mental illness (SMI). SMI was first measured by the National Household Survey on Drug Abuse (NHSDA) in 2001 for all persons aged 18 or older. SAMHSA's official definition of adults with SMI, based on a notice published in the Federal Register (SAMHSA, Center for Mental Health Services, 1993), is as follows:

Pursuant to section 1912(c) of the Public Health Service Act, adults with serious mental illness (SMI) are persons: (1) age 18 and over and (2) who currently have, or at any time during the past year, had a diagnosable mental, behavioral, or emotional disorder of sufficient duration to meet diagnostic criteria specified within DSM-IV or their ICD-9-CM equivalent (and subsequent revisions) with the exception of DSM-IV "V" codes, substance use disorders, and developmental disorders, which are excluded, unless they co-occur with another diagnosable serious mental illness. (3) That has resulted in functional impairment which substantially interferes with or limits one or more major life activities.

In prior NSDUH reports, the K6 scale was used to measure SMI according to the above definition. The K6 consists of six questions that ask respondents how frequently they experienced symptoms of psychological distress during the 1 month in the past year when they were at their worst emotionally. The use of this scale for SMI was based on a methodological study designed to evaluate several screening scales for measuring SMI in NSDUH. These scales consisted of a truncated version of the World Health Organization (WHO) Composite International Diagnostic Interview Short Form (CIDI-SF) scale (Kessler, Andrews, Mroczek, Üstün, & Wittchen, 1998), the K10/K6 scale of nonspecific psychological distress (Furukawa et al., 2003), and the WHO Disability Assessment Schedule (WHO-DAS) (Rehm et al., 1999).

In the 2003 NSDUH, the mental health module contained a truncated version of the CIDI-SF scale, the K10/K6 scale, and the WHO-DAS scale to mirror the questions used by Kessler et al. (2003). Thus, the module contained a broad array of questions about mental health (i.e., panic attacks, depression, mania, phobias, generalized anxiety, posttraumatic stress disorder, and use of mental health services) that preceded the K6 items, and the four extra questions in the K10 scale were interspersed among the items in the K6 scale. To create a score, the responses to six items on the K6 scales were coded from 0 to 4. Summing across all the responses resulted in a score with a range from 0 to 24. Respondents with a total score of 13 or greater were classified as having a past year SMI. This cutpoint was chosen to equalize false positives and false negatives.

In the 2004 NSDUH, however, the sample of respondents aged 18 or older was split evenly between the "long-form" module, which included all items in the mental health module used in the 2003 NSDUH (sample A), and a "short-form" module consisting only of the K6 items (sample B). The short-form version was introduced to reduce interview time, removing questions that were not needed for estimation of SMI, and to provide space for a new module on depression. Inclusion of the long-form version in half of the sample was to measure the impact on the K6 responses of changing the context of the K6.

Results from the 2004 NSDUH showed large differences at the national level between the two samples in both the K6 total score and the proportion of respondents with a K6 total score of 13 or greater. These differences were most pronounced in the 18 to 25 age group. These differences suggested that the K6 scale was not context-independent; that is, respondents appeared to respond to the K6 items differently depending on whether the scale was preceded by a broad array of other mental health questions. There were other concerns as well. For example, the face validity of the K6 scale suggests that it may be more useful as a measure of psychological distress or of affective-mood and anxiety-type disorders. A direct consequence of these concerns was that a decision was made that the K6 would no longer be used to measure SMI. However, the K6 data are still useful as an indicator of psychological distress (see Section B.4.4 of OAS, 2005c).

The 2004 national SPD estimates therefore were based only on data from sample A (respondents who got the long-form module). For the purpose of producing State-level estimates for this report, however, an adjusted measure of SPD, which was produced for the entire sample of respondents aged 18 or older in 2004, was used, and SMI data from 2003 were pooled with data using this adjusted measure of SPD from 2004. The adjustment made to the SPD score on the short-form module is described in brief here.

A logistic regression model was used to estimate differences between the short- and long-form SPD prevalence rates (i.e., propensities). Several demographic and drug use covariates were included in the model, and it was found that the propensities varied according to race/ethnicity and age group. Five propensity strata based on race/ethnicity and age group were constructed from the results of this analysis. Tests suggested that a gross adjustment approach might be more appropriate than an item-based adjustment approach. As a consequence, the cumulative distribution function (CDF) (gross) adjustment method was applied within each of the five propensity strata, and the method appeared to work quite well in adjusting the marginal estimates of a number of important demographic and drug use variables. This method also was shown to be fairly robust to the way the propensity strata were defined.

Consideration also was given to the use of this logistic regression model to provide adjustments, as well as to provide propensity estimates. However, although this approach was useful for estimating propensities, it was not useful in determining how to adjust individual short-form respondents' SPD prevalence rates to match those of long-form respondents within covariate profiles. Using this approach, the only way to match prevalence rates would be to use long-form prevalence estimates in place of short-form prevalence estimates within covariate profiles. This is equivalent to discarding all short-form data after the logistic regression model has been fitted. A similar argument applies to the use of polytomous logistic regression models to estimate differences between short- and long-form SPD scores.

Before the CDF adjustment method was developed, consideration also was given to ad hoc adjustments to differences between short- and long-form SPD scores within covariate profiles, estimated from, say, polytomous regression models. For example, if the average difference between short- and long-form SPD scores for a particular covariate profile (e.g., white females aged 12 to 17 in the West) was 1.7, then all short-form SPD scores would be reduced by that amount in the profile. However, there are a couple of problems with this ad hoc approach. First, this approach is equivalent to shifting the entire distribution of short-form scores to the left, creating a set of adjusted values ranging from –1.7 to 22.3 instead of 0 to 24. Second, although this approach might force SPD scores to match on average within a profile, there is no guarantee that they would match at the SPD cutpoint of 13, which defines prevalence rates. A variation to this approach would be to multiply short-form scores by a factor that forced the scores to match on average, but this is equivalent to rescaling the short-form distribution so that all scores are shrunk toward zero. Neither of these ad hoc methods was optimal. Hence, the CDF adjustment method was used to transform the distribution of scores obtained from the short-form module to match that of the long-form module such that the distributional properties of the SPD scores from the short-form module matched the distributional properties of the SPD scores from the long-form module, without the scores matching exactly.

Adjusted short-form SPD scores and prevalence rates (based on the CDF adjustment method) were not used to derive national estimates for the 2004 survey. National estimates used a much finer categorization for some of the demographic and substance use variables than were used in the creation of the adjusted SPD outcome, and at these finer categorizations some notable discrepancies were observed between adjusted short-form and corresponding long-form prevalence rates. For this reason, national estimates of SPD scores and prevalence rates were derived from only long-form data.

Adjusted short-form SPD scores and prevalence rates were used to derive State-level estimates based on pooled 2003 and 2004 survey data. Because State-level estimates used a much coarser categorization of demographic and substance use variables than national estimates, the problem of discrepancies observed at the finer categorization of national estimates did not occur. In addition, unlike national estimates, which were based on large sample sizes, State-level estimates were typically based on small sample sizes. Hence, it was necessary to use all the data available, including the adjusted short-form data. For details on how the CDF adjustment was implemented, see Aldworth, Chromy, Foster, Heller, and Novak (2005).

A.8 Measuring Change in State Estimates between 2002-2003 and 2003-2004

The estimates of change between State estimates displayed in Appendix C are based on the 2002 through 2004 NSDUHs. The State estimates for 2002-2003 are the previously published model-based small area estimates (see Wright & Sathe, 2005). The State estimates for 2003-2004 are the small area estimates given in Appendix B. The moving average State prevalence estimates for the overlapping 2002-2003 and 2003-2004 time periods were obtained from independent applications of RTI's SWHB methodology; that is, the 2003-2004 models were fit independently of the previously fitted 2002-2003 models. This independent analysis approach was followed because there was no desire to revise the previously published estimates. Moreover, the same fixed predictor variables were used in the 2002-2003 and 2003-2004 models, but annual updates were made when more current versions became available. The age group–specific fixed predictor variables were defined at five levels (namely, person-level, 2000 decennial census block group-level, tract-level, county-level, and State-level). Also, each age group model had 51 State-level random effects and 300 substate region–level random effects.

To estimate change in State estimates, let _sa(1) and _sa(2) denote 2002-2003 and 2003-2004 prevalence rates, respectively, for State-s and age group-a. The change between _sa(1) and _sa(2) is defined in terms of the log-odds ratio (lor_sa) as opposed to the simple difference because the posterior distribution of the lor_sa is closer to Gaussian than the posterior distribution of the simple difference (_sa(2) – _sa(1)). The lor_sa is defined as

.     D

The p value given in the Appendix C tables is computed to test the null hypothesis of no change (i.e., _sa(2) = _sa(1) or equivalently lor_sa = 0. An estimate of lor_sa is given by

,     D

where the p_sa(1) are previously published 2002-2003 State estimates and the p_sa(2) are the 2003-2004 State estimates presented in this report (see Appendix B). To compute the variance of , i.e., , let and , then

,     D

where denotes the covariance between and . This covariance is defined in terms of the associated correlation as follows:

.     D

Note that the and used here to calculate are the same variances used in calculating the previously published 2002-2003 prediction intervals (PIs) and the 2003-2004 PIs given in this report, respectively.

The correlation between and was obtained by simultaneously modeling the 2002, 2003, and 2004 NSDUH data. This simultaneous modeling approach was adopted based on the results of the validation study (see Appendix E, Section E.2., of Wright, 2003b) conducted for measuring change in 1999–2000 and 2000-2001 State estimates. For this simultaneous model, four age groups by 3 years (i.e., 12 subpopulation–specific models) were fitted, each with its own set of fixed and random effects. In this case, the general covariance matrices for the State and substate random effects were 12 by 12 matrices corresponding to the 12 element (age group by year) vectors of random effects. Note that the survey-weighted Bernoulli-type log likelihood employed in SWHB methodology was appropriate for this simultaneous model because the 12 age group by year subpopulations were nonoverlapping. The correlation [, ] was approximated by the correlation calculated using the posterior distributions of log[_sa(1) /(1 - _sa(1))] and log[_sa(2) /(1 - _sa(2))] from the simultaneous model.

To calculate the p value for testing the null hypothesis of no change (lor_sa = 0), it was assumed that . Then, the p value = P[Z abs(z)], where Z is a standard normal random variate, , and abs(z) denotes the absolute value of Z.

Table A.1 Sample Sizes, Weighted Screening and Interview Response Rates, and Population Estimates, by State, for Persons Aged 12 or Older: 2002

State	Total Selected DUs	Total Eligible DUs	Total Completed Screeners	Weighted DU Screening Response Rate	Total Selected	Total Responded	Population Estimate	Weighted Interview Response Rate	Weighted Overall Response Rate
Overall	178,013	150,162	136,349	90.72%	80,581	68,126	235,143,245	78.56%	71.27%
Alabama	2,403	2,028	1,852	91.31%	1,103	960	3,686,602	81.85%	74.74%
Alaska	2,408	1,898	1,751	92.13%	1,067	915	496,025	82.05%	75.59%
Arizona	2,346	1,908	1,770	92.66%	1,078	924	4,361,020	79.66%	73.81%
Arkansas	2,540	2,102	2,005	95.28%	1,054	877	2,216,033	76.09%	72.50%
California	8,425	7,601	6,816	89.60%	4,363	3,599	28,231,483	74.93%	67.14%
Colorado	2,099	1,827	1,664	91.01%	1,087	914	3,655,496	81.67%	74.32%
Connecticut	2,718	2,440	2,227	91.44%	1,188	977	2,827,588	76.73%	70.16%
Delaware	2,585	2,116	1,908	89.64%	1,159	964	665,926	78.55%	70.42%
District of Columbia	3,701	3,100	2,608	84.08%	979	864	482,635	84.79%	71.29%
Florida	10,742	8,622	7,723	89.47%	4,340	3,653	13,832,088	77.23%	69.10%
Georgia	2,206	1,896	1,660	87.50%	1,066	897	6,842,168	77.76%	68.04%
Hawaii	2,276	1,942	1,759	90.38%	1,111	925	962,485	76.50%	69.14%
Idaho	2,033	1,634	1,515	92.80%	1,052	907	1,074,515	82.81%	76.86%
Illinois	9,263	8,181	6,986	85.45%	4,613	3,729	10,258,735	75.32%	64.36%
Indiana	2,261	1,961	1,856	94.61%	1,123	945	5,019,711	77.60%	73.42%
Iowa	2,252	1,939	1,835	94.68%	1,028	894	2,440,614	84.42%	79.93%
Kansas	1,933	1,683	1,579	93.86%	1,041	898	2,202,285	81.96%	76.92%
Kentucky	2,641	2,273	2,155	94.79%	1,098	909	3,395,143	79.55%	75.41%
Louisiana	2,189	1,816	1,701	93.64%	1,070	930	3,607,669	84.44%	79.07%
Maine	2,828	2,290	2,082	90.85%	1,017	906	1,104,764	87.35%	79.36%
Maryland	1,984	1,801	1,610	89.42%	1,039	919	4,449,299	81.71%	73.07%
Massachusetts	2,567	2,216	1,930	86.95%	1,142	916	5,387,071	71.93%	62.55%
Michigan	9,820	8,073	7,414	91.75%	4,432	3,792	8,255,399	81.82%	75.06%
Minnesota	2,173	1,895	1,765	93.09%	996	873	4,154,504	83.23%	77.48%
Mississippi1	2,261	1,750	1,508	86.58%	988	839	2,307,320	77.37%	66.99%
Missouri	2,725	2,236	2,098	93.87%	1,039	890	4,656,459	82.05%	77.02%
Montana	2,772	2,174	2,057	94.64%	1,075	914	759,543	81.98%	77.58%
Nebraska	1,954	1,746	1,652	94.59%	1,042	891	1,411,983	82.01%	77.57%
Nevada1	2,534	2,069	1,956	94.67%	1,147	954	1,742,004	73.54%	69.62%
New Hampshire	2,597	2,154	1,966	91.27%	1,092	910	1,065,165	78.10%	71.28%
New Jersey	2,554	2,290	2,042	89.28%	1,065	854	7,075,581	74.61%	66.61%
New Mexico1	1,950	1,586	1,236	77.38%	794	674	1,500,281	81.83%	63.32%
New York	10,480	9,032	7,516	83.31%	4,615	3,716	15,882,822	73.14%	60.94%
North Carolina	2,289	1,940	1,792	92.57%	1,046	902	6,726,205	80.99%	74.98%
North Dakota	2,307	1,873	1,770	94.52%	1,011	913	527,574	84.91%	80.26%
Ohio	9,194	7,970	7,476	93.76%	4,221	3,554	9,369,125	78.58%	73.68%
Oklahoma	2,300	1,932	1,791	92.64%	1,100	922	2,822,615	78.63%	72.84%
Oregon	2,456	2,158	2,019	93.43%	1,071	917	2,916,974	80.74%	75.44%
Pennsylvania	10,104	8,482	7,710	90.86%	4,251	3,606	10,298,942	79.56%	72.29%
Rhode Island	2,458	2,117	1,883	89.14%	1,107	925	896,699	74.12%	66.07%
South Carolina	2,332	1,824	1,729	94.77%	1,091	913	3,371,646	80.90%	76.67%
South Dakota	2,053	1,717	1,632	95.03%	1,013	914	619,768	86.83%	82.52%
Tennessee	2,732	2,357	2,212	92.82%	1,057	920	4,766,688	83.26%	77.28%
Texas	7,730	6,408	5,960	93.05%	4,212	3,649	17,207,615	82.73%	76.98%
Utah	1,487	1,336	1,264	94.52%	990	889	1,807,003	84.94%	80.29%
Vermont	2,410	1,914	1,803	94.36%	1,013	896	525,061	88.02%	83.06%
Virginia	2,426	2,104	1,873	89.03%	1,069	884	5,862,299	75.20%	66.95%
Washington	2,454	2,002	1,832	91.35%	1,079	901	4,962,300	78.20%	71.44%
West Virginia	2,763	2,299	2,169	94.33%	1,059	898	1,527,885	79.91%	75.38%
Wisconsin	2,152	1,709	1,587	92.87%	1,029	887	4,511,335	82.44%	76.56%
Wyoming	2,146	1,741	1,645	94.49%	1,059	907	413,099	79.40%	75.02%
1 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. DU = dwelling unit. Source: SAMHSA, Office of Applied Studies, National Survey on Drug Use and Health, 2002.

Table A.2 Sample Sizes, Weighted Interview Response Rates, and Population Estimates, by State and Three Age Groups: 2002

State	12–17				18–25				26+
	Total Selected	Total Responded	Population Estimate	Weighted Interview Response Rate	Total Selected	Total Responded	Population Estimate	Weighted Interview Response Rate	Total Selected	Total Responded	Population Estimate	Weighted Interview Response Rate
Overall	26,230	23,659	24,753,586	89.99%	27,216	23,271	31,024,280	85.16%	27,135	21,196	179,365,379	75.81%
Alabama	361	331	378,922	92.11%	370	324	497,362	86.86%	372	305	2,810,318	79.54%
Alaska	393	353	70,050	90.00%	353	305	58,061	85.24%	321	257	367,914	79.65%
Arizona	360	330	477,791	91.87%	346	303	593,368	86.21%	372	291	3,289,861	76.81%
Arkansas	385	340	232,228	88.68%	287	256	299,329	89.70%	382	281	1,684,476	71.97%
California	1,439	1,304	3,119,651	90.54%	1,459	1,224	3,910,445	83.32%	1,465	1,071	21,201,387	70.93%
Colorado	349	309	386,275	88.67%	380	317	488,328	82.92%	358	288	2,780,893	80.55%
Connecticut	369	335	297,332	90.70%	423	341	314,467	82.08%	396	301	2,215,789	74.39%
Delaware	392	350	64,655	88.74%	344	285	87,670	83.05%	423	329	513,601	76.54%
District of Columbia	354	326	33,553	91.52%	284	256	73,858	89.63%	341	282	375,224	83.16%
Florida	1,335	1,213	1,332,058	91.10%	1,523	1,317	1,526,407	86.35%	1,482	1,123	10,973,623	74.40%
Georgia	339	309	740,287	91.81%	332	281	931,197	85.79%	395	307	5,170,684	74.28%
Hawaii	337	306	106,624	92.14%	351	300	123,983	85.94%	423	319	731,877	72.94%
Idaho	346	314	128,019	89.27%	348	302	162,155	87.73%	358	291	784,341	80.82%
Illinois	1,475	1,304	1,081,426	88.16%	1,620	1,301	1,366,021	79.82%	1,518	1,124	7,811,288	72.73%
Indiana	351	323	537,937	90.92%	415	346	699,137	84.53%	357	276	3,782,636	74.38%
Iowa	343	312	247,154	91.07%	315	278	348,675	89.36%	370	304	1,844,784	82.50%
Kansas	324	301	242,248	93.27%	374	321	316,706	86.26%	343	276	1,643,332	79.59%
Kentucky	376	325	317,845	84.53%	342	288	457,462	84.10%	380	296	2,619,836	78.11%
Louisiana	344	311	408,864	91.56%	359	310	533,943	86.92%	367	309	2,664,863	82.83%
Maine	337	310	107,138	92.04%	336	295	128,854	88.23%	344	301	868,772	86.65%
Maryland	376	346	472,125	91.83%	331	302	525,127	90.68%	332	271	3,452,047	78.58%
Massachusetts	402	353	502,081	87.86%	350	285	670,475	84.04%	390	278	4,214,516	68.13%
Michigan	1,458	1,301	892,683	89.81%	1,570	1,371	1,078,221	87.65%	1,404	1,120	6,284,494	79.57%
Minnesota	318	289	447,909	90.45%	352	317	564,444	90.66%	326	267	3,142,151	80.71%
Mississippi1	342	312	257,043	91.28%	314	274	346,485	87.36%	332	253	1,703,792	72.96%
Missouri	364	328	489,034	90.34%	335	289	621,802	85.99%	340	273	3,545,624	80.20%
Montana	383	348	82,057	91.77%	309	262	101,662	85.48%	383	304	575,825	80.05%
Nebraska	353	317	152,803	90.07%	327	280	202,014	86.69%	362	294	1,057,166	79.90%
Nevada1	396	359	182,000	91.12%	356	308	208,607	86.18%	395	287	1,351,398	69.19%
New Hampshire	344	300	112,627	88.19%	405	343	126,521	84.89%	343	267	826,017	75.60%
New Jersey	324	290	712,611	89.35%	383	308	775,060	79.98%	358	256	5,587,910	71.75%
New Mexico1	235	213	176,221	89.25%	296	250	207,372	85.15%	263	211	1,116,688	80.02%
New York	1,426	1,241	1,564,858	86.12%	1,649	1,344	2,026,299	80.59%	1,540	1,131	12,291,665	70.20%
North Carolina	354	325	677,525	89.91%	341	292	866,820	84.88%	351	285	5,181,860	79.25%
North Dakota	357	337	54,725	94.54%	332	307	81,994	92.38%	322	269	390,856	81.86%
Ohio	1,358	1,221	991,716	89.83%	1,429	1,224	1,217,589	85.83%	1,434	1,109	7,159,820	75.66%
Oklahoma	362	308	305,129	84.00%	385	333	408,904	85.11%	353	281	2,108,583	76.37%
Oregon	354	322	297,634	90.31%	361	308	379,401	85.13%	356	287	2,239,939	78.69%
Pennsylvania	1,395	1,243	1,025,357	89.15%	1,489	1,293	1,270,338	86.58%	1,367	1,070	8,003,247	77.15%
Rhode Island	365	334	83,814	91.12%	357	306	124,681	84.64%	385	285	688,204	70.20%
South Carolina	339	304	336,271	90.47%	412	343	458,511	82.93%	340	266	2,576,865	79.24%
South Dakota	359	343	70,145	95.94%	320	286	89,870	89.15%	334	285	459,753	85.02%
Tennessee	381	352	472,625	91.52%	260	228	610,807	87.69%	416	340	3,683,257	81.42%
Texas	1,347	1,224	2,004,787	90.81%	1,427	1,251	2,477,451	87.79%	1,438	1,174	12,725,377	80.50%
Utah	316	309	227,575	97.46%	324	289	363,300	88.95%	350	291	1,216,128	81.15%
Vermont	339	312	53,892	92.84%	367	314	68,583	86.88%	307	270	402,586	87.51%
Virginia	297	278	600,443	93.43%	412	341	728,869	83.24%	360	265	4,532,987	71.75%
Washington	298	264	530,187	86.66%	361	304	640,479	84.62%	420	333	3,791,634	76.00%
West Virginia	339	305	139,243	89.85%	336	292	193,439	87.55%	384	301	1,195,204	77.58%
Wisconsin	317	280	482,456	87.97%	380	338	613,508	87.26%	332	269	3,415,371	80.85%
Wyoming	323	295	45,958	91.71%	385	339	58,222	88.37%	351	273	308,919	75.91%
1 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. Source: SAMHSA, Office of Applied Studies, National Survey on Drug Use and Health, 2002.

Table A.3 Sample Sizes, Weighted Screening and Interview Response Rates, and Population Estimates, by State, for Persons Aged 12 or Older: 2003

State	Total Selected DUs	Total Eligible DUs	Total Completed Screeners	Weighted DU Screening Response Rate	Total Selected	Total Responded	Population Estimate	Weighted Interview Response Rate	Weighted Overall Response Rate
Overall	170,762	143,485	130,605	90.72%	81,631	67,784	237,682,009	77.39%	70.21%
Alabama	2,071	1,712	1,558	91.14%	1,029	879	3,699,723	79.60%	72.55%
Alaska	2,314	1,814	1,666	91.97%	1,098	883	505,278	75.00%	68.98%
Arizona	2,159	1,757	1,662	94.64%	1,057	897	4,473,518	81.20%	76.85%
Arkansas	2,258	1,850	1,767	95.53%	1,092	922	2,228,670	79.84%	76.27%
California	7,687	6,858	6,015	86.86%	4,471	3,600	28,673,990	73.76%	64.07%
Colorado	2,225	1,855	1,709	92.06%	1,103	911	3,701,560	78.79%	72.53%
Connecticut	2,623	2,288	2,073	90.56%	1,128	933	2,880,493	76.25%	69.06%
Delaware	2,419	1,936	1,774	91.59%	1,105	911	671,922	75.12%	68.80%
District of Columbia	3,692	3,078	2,576	83.69%	1,116	949	476,873	80.38%	67.27%
Florida	10,451	8,453	7,575	89.77%	4,414	3,541	14,145,707	73.68%	66.14%
Georgia	2,112	1,734	1,612	92.81%	1,088	902	6,951,437	79.46%	73.74%
Hawaii	2,259	1,953	1,767	90.25%	1,142	928	1,013,259	73.21%	66.07%
Idaho	1,998	1,596	1,509	94.45%	1,112	912	1,099,895	77.63%	73.32%
Illinois	9,163	8,128	6,803	83.45%	4,652	3,711	10,319,948	74.36%	62.05%
Indiana	2,046	1,741	1,637	94.11%	1,082	903	5,049,910	79.37%	74.69%
Iowa	2,035	1,829	1,721	94.16%	993	884	2,448,928	85.81%	80.79%
Kansas	2,042	1,744	1,638	93.94%	1,041	875	2,209,221	81.11%	76.20%
Kentucky	2,266	1,991	1,878	94.25%	1,102	908	3,381,254	75.69%	71.34%
Louisiana	2,084	1,757	1,637	93.12%	1,095	943	3,618,197	81.80%	76.17%
Maine	2,827	2,240	2,045	91.21%	1,094	928	1,113,100	82.07%	74.86%
Maryland	1,899	1,673	1,475	88.04%	1,000	863	4,510,290	82.58%	72.70%
Massachusetts	2,413	2,129	1,878	88.16%	1,220	964	5,377,359	75.04%	66.16%
Michigan	9,000	7,447	6,709	90.14%	4,353	3,667	8,316,442	79.06%	71.26%
Minnesota	2,029	1,801	1,673	92.73%	1,052	909	4,193,331	82.14%	76.17%
Mississippi	2,196	1,732	1,650	95.33%	1,078	899	2,311,859	78.81%	75.13%
Missouri	2,495	2,042	1,912	93.64%	1,105	932	4,683,914	81.99%	76.77%
Montana	2,384	1,871	1,766	94.40%	1,068	911	767,946	79.57%	75.12%
Nebraska	1,996	1,716	1,622	94.51%	1,071	918	1,418,952	79.62%	75.25%
Nevada	2,071	1,751	1,663	94.91%	1,072	902	1,818,116	79.78%	75.71%
New Hampshire	2,015	1,688	1,568	92.94%	1,112	910	1,082,138	76.29%	70.90%
New Jersey	2,564	2,287	1,981	86.56%	1,126	883	7,118,305	72.97%	63.17%
New Mexico	2,260	1,822	1,740	95.42%	1,132	944	1,520,180	77.03%	73.50%
New York	9,973	8,575	7,205	83.97%	4,609	3,634	15,948,708	71.96%	60.42%
North Carolina	2,239	1,852	1,753	94.65%	1,086	904	6,805,722	79.21%	74.98%
North Dakota	2,072	1,714	1,619	94.57%	977	867	525,140	87.43%	82.69%
Ohio	8,874	7,690	7,246	94.17%	4,313	3,559	9,433,820	75.91%	71.49%
Oklahoma	2,455	1,972	1,812	91.80%	1,042	871	2,846,785	78.62%	72.17%
Oregon	2,102	1,853	1,760	94.94%	1,095	912	2,970,969	79.79%	75.75%
Pennsylvania	9,866	8,252	7,482	90.76%	4,214	3,572	10,356,055	80.56%	73.12%
Rhode Island	2,255	1,991	1,772	88.58%	1,141	914	903,348	75.20%	66.61%
South Carolina	2,205	1,807	1,723	95.45%	1,109	920	3,384,520	79.64%	76.02%
South Dakota	2,154	1,749	1,660	94.78%	980	881	621,498	86.26%	81.76%
Tennessee	2,290	1,978	1,864	94.27%	1,004	856	4,823,157	79.89%	75.32%
Texas	7,901	6,466	6,079	94.03%	4,231	3,566	17,432,369	79.14%	74.42%
Utah	1,623	1,392	1,325	95.14%	995	898	1,816,737	87.98%	83.71%
Vermont	2,638	2,047	1,909	93.19%	1,092	917	530,133	79.87%	74.43%
Virginia	2,168	1,908	1,667	87.33%	1,076	907	5,951,031	78.61%	68.65%
Washington	2,475	2,033	1,920	94.43%	1,128	941	5,053,331	78.65%	74.28%
West Virginia	2,923	2,384	2,236	93.83%	1,058	871	1,534,650	78.86%	74.00%
Wisconsin	2,282	1,793	1,655	92.28%	1,046	887	4,546,217	77.76%	71.76%
Wyoming	2,214	1,756	1,659	94.48%	1,032	885	416,105	84.33%	79.67%
DU = dwelling unit. Source: SAMHSA, Office of Applied Studies, National Survey on Drug Use and Health, 2003.

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Table A.4 Sample Sizes, Weighted Interview Response Rates, and Population Estimates, by State and Three Age Groups: 2003

State	12–17				18–25				26+
	Total Selected	Total Responded	Population Estimate	Weighted Interview Response Rate	Total Selected	Total Responded	Population Estimate	Weighted Interview Response Rate	Total Selected	Total Responded	Population Estimate	Weighted Interview Response Rate
Overall	25,387	22,696	24,995,357	89.57%	27,259	22,941	31,728,286	83.47%	28,985	22,147	180,958,366	74.63%
Alabama	324	297	382,688	92.61%	394	340	501,543	86.10%	311	242	2,815,492	76.33%
Alaska	348	298	68,750	86.80%	378	314	67,522	82.66%	372	271	369,006	71.30%
Arizona	346	314	493,252	91.48%	377	317	611,163	84.15%	334	266	3,369,104	78.82%
Arkansas	352	320	233,744	91.18%	356	301	304,728	85.42%	384	301	1,690,198	77.24%
California	1,381	1,236	3,161,827	89.71%	1,463	1,195	3,928,708	81.65%	1,627	1,169	21,583,456	69.91%
Colorado	327	292	385,020	88.53%	379	305	499,513	79.29%	397	314	2,817,027	77.43%
Connecticut	313	279	292,982	88.47%	423	353	331,774	83.64%	392	301	2,255,738	73.62%
Delaware	344	305	68,298	88.69%	373	315	89,106	84.55%	388	291	514,518	71.54%
District of Columbia	370	326	32,832	88.64%	373	326	73,453	87.28%	373	297	370,589	78.33%
Florida	1,377	1,203	1,360,537	87.23%	1,418	1,171	1,626,149	81.73%	1,619	1,167	11,159,021	71.02%
Georgia	342	308	756,648	88.43%	323	267	959,782	84.93%	423	327	5,235,007	77.32%
Hawaii	388	353	100,981	90.91%	329	275	121,594	83.63%	425	300	790,684	69.33%
Idaho	331	299	128,037	90.50%	348	287	166,977	81.40%	433	326	804,881	74.87%
Illinois	1,423	1,238	1,083,365	86.69%	1,537	1,242	1,395,959	81.48%	1,692	1,231	7,840,623	71.43%
Indiana	338	308	545,217	90.65%	365	292	710,330	79.87%	379	303	3,794,364	77.73%
Iowa	329	304	245,539	89.91%	333	292	353,759	87.71%	331	288	1,849,631	84.81%
Kansas	317	280	240,109	87.93%	363	309	322,145	84.48%	361	286	1,646,967	79.40%
Kentucky	349	306	337,609	86.98%	349	293	451,685	83.75%	404	309	2,591,960	72.97%
Louisiana	353	321	405,066	92.36%	382	335	541,507	86.50%	360	287	2,671,623	79.32%
Maine	345	304	110,584	87.73%	388	330	132,168	86.27%	361	294	870,349	80.84%
Maryland	318	292	481,268	90.86%	280	237	547,577	83.87%	402	334	3,481,445	81.21%
Massachusetts