2016-2017
National Survey on Drug Use and Health:
Guide to State Tables and Summary of Small Area Estimation Methodology

A.1 Introduction

This document provides information on the model-based small area estimates of substance use and mental disorders in states based on data from the combined 2016-2017 National Surveys on Drug Use and Health (NSDUHs). These estimates are available online along with other related information.¹ NSDUH is an annual survey conducted from January through December of the civilian, noninstitutionalized population aged 12 or older and is sponsored by the Substance Abuse and Mental Health Services Administration (SAMHSA). The survey collects information from individuals residing in households, noninstitutionalized group quarters (e.g., shelters, rooming houses, dormitories), and civilians living on military bases. In 2016-2017, NSDUH collected data from 135,974 respondents aged 12 or older and was designed to obtain representative samples from the 50 states and the District of Columbia. NSDUH is planned and managed by SAMHSA's Center for Behavioral Health Statistics and Quality (CBHSQ). Data collection and analysis are conducted under contract with RTI International.² A summary of NSDUH's methodology is given in Section A.2. Section A.3 lists all of the tables and files associated with the 2016‑2017 state small area estimates and when and where they can be found. Information is given in Section A.4 on the confidence intervals and margins of error and how to make interpretations with respect to the small area estimates. Section A.5 discusses related substance use measures and warns users about not drawing conclusions by subtracting small area estimates from two different measures. Section A.6 discusses NSDUH questionnaire changes from 2015 and how these changes affect the small area estimates.

The survey-weighted hierarchical Bayes (SWHB) estimation methodology used in the production of state estimates from the 1999 to 2016 surveys also was used in the production of the 2016-2017 state estimates. The SWHB methodology is described in Appendix E of the 2001 state report (Wright, 2003b) and in Folsom, Shah, and Vaish (1999). A general model description is given in Section B.1 of this document. A list of measures for which small area estimates are produced is given in Section B.2. Predictors used in the 2016-2017 small area estimation (SAE) modeling are listed and described in Section B.3. Variable selection is discussed in Section B.4.

Small area estimates obtained using the SWHB methodology are design consistent (i.e., the small area estimates for states with large sample sizes are close to the robust design-based estimates). The state small area estimates when aggregated using the appropriate population totals result in national small area estimates that are very close to the national design-based estimates. However, to ensure internal consistency, it is desirable to have national small area estimates³ exactly match the national design-based estimates. This process is called "benchmarking." The benchmarked state-level estimates are also potentially less biased than the unbenchmarked state-level estimates. Beginning in 2002, exact benchmarking was introduced, as described in Section B.5.⁴ Tables of the estimated numbers of individuals associated with each measure are available online,⁵ and an explanation of how these counts and their respective Bayesian confidence intervals⁶ are calculated can be found in Section B.6. Section B.7 discusses the method to compute aggregate estimates by combining two age groups. The definition and explanation of the formula used in estimating the marijuana initiation rate are given in Section B.8. Note that, unlike the other SAE outcomes discussed in this document, marijuana initiation is calculated as a ratio of two measures.

For all measures except major depressive episode (MDE, i.e., depression), serious mental illness (SMI), any mental illness (AMI), receipt of mental health services, and serious thoughts of suicide, the age groups for which estimates are provided are 12 to 17, 18 to 25, 26 or older, 18 or older, and 12 or older.⁷

Estimates of underage (aged 12 to 20) alcohol use and binge alcohol use were also produced.⁸ Alcohol consumption is expected to differ significantly across the 18 to 25 age group because of the legalization of alcohol at age 21. Therefore, it was decided that it would be useful to produce small area estimates for individuals aged 12 to 20. A short description of the methodology used to produce underage drinking estimates is provided in Section B.9.

The remainder of Section B covers two topics:

• Section B.10 discusses the criteria used to define substance use disorder (SUD) and needing but not receiving treatment.
• Section B.11 discusses the production of estimates for MDE (i.e., depression), SMI, AMI, and suicidal thoughts. Note that for MDE, no estimates are published for individuals aged 12 or older. Also, for SMI, AMI, and serious thoughts of suicide, no estimates are produced for youths aged 12 to 17 because youths are not asked these questions.

In Section C, the 2015, 2016, 2017, pooled 2015-2016, and pooled 2016-2017 survey sample sizes, population estimates, and response rates are included in Tables C.1 to C.14, respectively. Table C.15 lists all of the measures and the years for which small area estimates were produced going back to the 2002 NSDUH, and Table C.16 lists all of the measures by age groups for which small area estimates were produced. In addition, Table C.17 provides a summary of milestones implemented in the SAE production process from 2002 to 2017.

A.2 Summary of NSDUH Methodology

NSDUH is the primary source of statistical information on the use of illicit drugs, alcohol, and tobacco by the U.S. civilian, noninstitutionalized population aged 12 or older. The survey also includes several modules of questions that focus on mental health issues. Conducted by the federal government since 1971, the survey collects data by administering questionnaires to a representative sample of the population through face-to-face interviews at their place of residence.

The survey covers residents of households, noninstitutional group quarters (e.g., shelters, rooming houses, dormitories), and civilians living on military bases. Persons excluded from the survey include homeless people who do not use shelters, military personnel on active duty, and residents of institutional group quarters, such as jails or prisons and long-term hospitals. The 1999 survey marked the first year in which the national sample was interviewed using a computer-assisted interviewing (CAI) method. The survey used a combination of computer-assisted personal interviewing (CAPI) conducted by an interviewer and audio computer-assisted self-interviewing (ACASI). Use of ACASI is designed to provide the respondent with a highly private and confidential means of responding to questions and increases the level of honest reporting of illicit drug use and other sensitive behaviors. For further details on the development of the CAI procedures for the 1999 National Household Survey on Drug Abuse (NHSDA),⁹ see the Office of Applied Studies (OAS, 2001).

The 1999 through 2001 NHSDAs and the 2002 through 2013 NSDUHs employed an independent, multistage area probability sample design for each of the 50 states and the District of Columbia. For this design, eight states were designated as large sample states (California, Florida, Illinois, Michigan, New York, Ohio, Pennsylvania, and Texas) with target sample sizes of 3,600 per year. For the remaining 42 states and the District of Columbia, the target sample size was 900 per year. This approach ensured that there was sufficient sample in every state to support SAE while at the same time maintaining efficiency for national estimates. The design also oversampled youths and young adults, so that each state's sample was approximately equally distributed among three major age groups: 12 to 17 years, 18 to 25 years, and 26 years or older.

A coordinated design was developed for the 2014 through 2017 NSDUHs. Similar to the 1999 through 2013 surveys, the coordinated 4-year design is state-based with an independent, multistage area probability sample within each state and the District of Columbia. This design designates 12 states as large sample states. These 12 states have the following target sample sizes per year: 4,560 interviews in California; 3,300 interviews in Florida, New York, and Texas; 2,400 interviews in Illinois, Michigan, Ohio, and Pennsylvania; and 1,500 interviews in Georgia, New Jersey, North Carolina, and Virginia. Making the sample sizes more proportional to the state population sizes improves the precision of national NSDUH estimates. This change also allows for a more cost-efficient sample allocation to the largest states while slightly increasing the sample sizes in smaller states to improve the precision of state estimates (note that the target sample size per year in the small states is 960 interviews except for Hawaii where the target sample size is 967 interviews). The fielded sample sizes for each state in 2017 are provided in Table C.5, and the combined 2016-2017 sample sizes are provided in Table C.9.

Starting in 2014, the allocation of the NSDUH sample is 25 percent for adolescents aged 12 to 17, 25 percent for adults aged 18 to 25, and 50 percent for adults aged 26 or older. The sample of adults aged 26 or older is further divided into three subgroups: aged 26 to 34 (15 percent), aged 35 to 49 (20 percent), and aged 50 or older (15 percent). For more information on the 2014 through the 2017 NSDUH sample design and for differences between the 2013 and 2014 surveys, refer to the 2014 NSDUH sample design report (CBHSQ, 2015a).

Nationally in 2016-2017, 273,249 addresses were screened, and 135,974 individuals responded within the screened addresses (see Table C.9). The screening response rate (SRR) for 2016-2017 combined averaged 76.5 percent, and the interview response rate (IRR) averaged 67.8 percent, for an overall response rate (ORR) of 51.8 percent (Table C.9). The ORRs for 2016-2017 ranged from 38.4 percent in New York to 66.0 percent in New Mexico. Estimates have been adjusted to reflect the probability of selection, unit nonresponse, poststratification to known census population estimates, item imputation, and other aspects of the estimation process. These procedures are described in detail in the 2015, 2016, and 2017 NSDUHs' methodological resource books (MRBs) (CBHSQ, 2016a, 2017, in press).

The weighted SRR is defined as the weighted number of successfully screened households (or dwelling units)¹⁰ divided by the weighted number of eligible households, or

,     D

where is the inverse of the unconditional probability of selection for the household (hh) and excludes all adjustments for nonresponse and poststratification.

At the person level, the weighted IRR is defined as the weighted number of respondents divided by the weighted number of selected persons, or

,     D

where is the inverse of the probability of selection for the ith person and includes household-level nonresponse and poststratification adjustments. To be considered a completed interview, a respondent must provide enough data to pass the usable case rule.¹¹

The weighted ORR is defined as the product of the weighted SRR and the weighted IRR or

.     D

A.3 Presentation of Data

In addition to this methodology document for the 2016-2017 state SAE results, the following files are available at https://www.samhsa.gov/data/:

• 2016-2017 NSDUH: Model-Based Prevalence Estimates (50 States and the District of Columbia) (Tables 1 to 31, by Age Group): Tables of percentages and associated 95 percent Bayesian confidence intervals are included for youths aged 12 to 17, young adults aged 18 to 25, adults aged 26 or older, adults aged 18 or older, and all individuals aged 12 or older. Also included are tables for underage (12 to 20) alcohol use and underage binge alcohol use. These tables are available in Excel and PDF formats. In order to increase the precision of small area estimates and rankings especially for small sample states and to detect year-to-year changes more efficiently, an SAE expert panel¹² recommended producing annual state estimates based on 2 consecutive years of pooled NSDUH data and to base comparisons of estimates (to measure change) on 2-year moving averages.
• 2016-2017 NSDUH National Maps of Prevalence Estimates, by State (Figures 1a to 31d): The color of each state on these U.S. maps indicates how the state ranks relative to other states for each measure. States could fall into one of five groups according to their ranking by quintiles. Because 51 states were ranked for each measure, the middle quintile was assigned to 11 states, and the remaining quintiles were assigned 10 states each. In some cases, a "quintile" could have more or fewer states than desired because two (or more) states had the same estimate (to two decimal places). When such ties occurred at the "boundary" between two quintiles, all the states with the same estimate were conservatively assigned to the lower quintile. Those states with the highest rates for a given measure are in dark red, with the exception of the perceptions of risk measures, for which the lowest perceptions of great risk are in dark red. Those states with the lowest estimates are in dark blue, with the exception of the perceptions of risk measures, for which the highest perceptions of great risk are in dark blue. These maps are available in HTML and PDF formats.
  Note that because the past year heroin use for youths aged 12 to 17 was so low and had such an abbreviated range, no U.S. map was included.
• 2016-2017 NSDUH State Estimates Categorized into Five Groups, by Age Group: This table shows the ranges of percentages for each outcome categorized into five groups (used to form the U.S. maps described above) from the lowest to highest estimate for youths aged 12 to 17, young adults aged 18 to 25, adults aged 26 or older, adults aged 18 or older, and all individuals aged 12 or older. Also included are ranges for underage (12 to 20) alcohol use and underage binge alcohol use. This table is available in HTML and PDF formats.
• 2016-2017 NSDUH: Model-Based Estimated Totals (in Thousands) (50 States and the District of Columbia) (Tables 1 to 31): Tables showing estimated numbers (counts in thousands) and confidence intervals are included for youths aged 12 to 17, young adults aged 18 to 25, adults aged 26 or older, adults aged 18 or older, and all individuals aged 12 or older. Also included are tables for underage (12 to 20) alcohol use and underage binge alcohol use. These tables are available in Excel and PDF formats.
• 2016-2017 NSDUH State-Specific Tables (Tables 1 to 112): Tables are provided for each individual state and the District of Columbia, as well as for the total United States and the four census regions (i.e., Northeast, Midwest, South, and West). The tables (two per area) show the percentages and the numbers of individuals (counts in thousands). These tables are available in HTML and PDF formats.
• NSDUH: Comparison of 2015-2016 and 2016-2017 Population Percentages (50 States and the District of Columbia) (Tables 1 to 31): Tables are presented that show the 2015-2016 (previously published data) and 2016-2017 NSDUH state estimates and an indication of the statistical significance of the difference or change (p value). Estimates are shown for youths aged 12 to 17, young adults aged 18 to 25, adults aged 26 or older, adults aged 18 or older, and all individuals aged 12 or older. Also included are tables for underage (12 to 20) alcohol use and underage binge alcohol use. Because annual state-level estimates are based on 2 years of pooled NSDUH data, two consecutive sets of estimates have a 1-year overlap (e.g., 2015-2016 and 2016-2017). If the population totals across the 3 years (e.g., 2015, 2016, and 2017) were the same, then the null hypothesis of no difference between the log odds of the 2015-2016 and 2016-2017 prevalence rates would be equivalent to testing the null hypothesis that the difference between the 2015-2016 and 2016-2017 prevalence rates is zero, which in turn would be equivalent to testing that the difference between the 2015 and 2017 prevalence rates is zero. The methodology used to compare these percentages is provided at the end of the tables. These tables are available in HTML and PDF formats.
• NSDUH: Comparison of 2008-2009 and 2016-2017 Population Percentages (50 States and the District of Columbia) (Tables 1 to 13): Tables are presented that show the 2008-2009 (previously published data) and 2016-2017 NSDUH state estimates and an indication of the statistical significance of the difference or change (p value). Estimates are shown for youths aged 12 to 17, young adults aged 18 to 25, adults aged 26 or older, adults aged 18 or older, and all individuals aged 12 or older. Also included are tables for underage (12 to 20) alcohol use. This comparison is done between the most recent estimates (in this case, 2016-2017) and the earliest comparable estimates for all outcomes, including mental health (based on 2008-2009 NSDUH data). The methodology used to compare these percentages is provided at the end of the tables. These tables are available in HTML and PDF formats.
• 2016-2017 NSDUH: Other Sources of State-Level Data: This document compares two outcomes (cigarette and alcohol use) from NSDUH with data from the Behavioral Risk Factor Surveillance System (BRFSS). This document is available in HTML and PDF formats.
• 2016-2017 NSDUH: Comparison of Population Percentages from the United States, Census Regions, States, and the District of Columbia: The p values contained in these tables for each outcome and age group can be used to test the null hypothesis of no difference between population percentages for the following types of comparisons: total United States versus census region, total United States versus state, census region versus census region, census region versus state, and state versus state. These tables are available in Excel format, and the methodology used to compute these p values is provided in a document published with these Excel tables. This methodology document is available in HTML and PDF formats.

A.4 Confidence Intervals and Margins of Error

At the top of each of the 31 tables showing state-level model-based estimates¹³ is the design-based national estimate along with a 95 percent design-based confidence interval, all of which are based on the survey design, the survey weights, and the reported data. The state estimates are model-based statistics (using SAE methodology) that have been adjusted (benchmarked) such that the population-weighted mean of the estimates across the 50 states and the District of Columbia equals the design-based national estimate. For more details on this benchmarking, see Section B.5. The region-level estimates are also benchmarked and are obtained by taking the population-weighted mean of the associated state-level benchmarked estimates. Associated with each state and regional estimate is a 95 percent Bayesian confidence interval. These intervals indicate the uncertainty in the estimate due to both sampling variability and model fit. For example, the state with the highest estimate of past month use of marijuana for young adults aged 18 to 25 was Vermont, with an estimate of 38.8 percent and a 95 percent confidence interval that ranged from 34.2 to 43.7 percent (see Table 3 of the state model‑based estimates' tables). Assuming that sampling and modeling conditions held, the Bayes posterior probability was 0.95 that the true percentage of past month marijuana use in Vermont for young adults aged 18 to 25 in 2016-2017 was between 34.2 and 43.7 percent. As noted earlier in a Section A.1 footnote, the term "prediction interval" (PI) was used in the 2004-2005 NSDUH state report (Wright et al., 2007) and prior reports to represent uncertainty in the state and regional estimates. However, that term also is used in other applications to estimate future values of a parameter of interest. That interpretation does not apply to NSDUH state model-based estimates, so PI was replaced with "Bayesian confidence interval."

Margin of error is another term used to describe uncertainty in the estimates. For example, if is a 95 percent symmetric confidence interval for the population proportion (p) and is an estimate of p obtained from the survey data, then the margin of error of is given by or . Because is a symmetric confidence interval, will be the same as . In this case, the probability is 0.95 that the interval ± or ± will contain the true population value (p). This defined margin of error will vary for each estimate and will be affected not only by the sample size (e.g., the larger the sample, the smaller the margin of error), but also by the sample design (e.g., telephone surveys using random digit dialing and surveys employing a stratified multistage cluster design will, more than likely, produce a different margin of error) (Scheuren, 2004).

The confidence intervals shown in NSDUH reports are asymmetric, meaning that the distance between the estimate and the lower confidence limit will not be the same as the distance between the upper confidence limit and the estimate. For example, Utah's past month marijuana use estimate is 14.7 percent for adults aged 18 to 25 years, with a 95 percent confidence interval equal to 12.0 to 17.9 percent (see Table 3 of the state model-based estimates' tables). Therefore, Utah's estimate is 2.7 (i.e., 14.7 − 12.0) percentage points from the lower 95 percent confidence limit and 3.2 (i.e., 17.9 − 14.7) percentage points from the upper limit. These asymmetric confidence intervals work well for small percentages often found in NSDUH tables and reports while still being appropriate for larger percentages. Some surveys or polls provide only one margin of error for all reported percentages. This single number is usually calculated by setting the sample percentage estimate equal to 50 percent, which will produce an upper bound or maximum margin of error. Such an approach would not be feasible in NSDUH because the estimates vary from less than 1 percent to over 75 percent; hence, applying a single margin of error to these estimates could significantly overstate or understate the actual precision levels. Therefore, given the differences mentioned above, it is more useful and informative to report the confidence interval for each estimate instead of a margin of error.

When it is indicated that a state has the highest or lowest estimate, it does not imply that the state's estimate is significantly higher or lower than the next highest or lowest state's estimate. Additionally, two significantly different state estimates (at the 5 percent level of significance) may have overlapping 95 percent confidence intervals. For details on a more accurate test to compare state estimates, see the "2016-2017 National Survey on Drug Use and Health: Comparison of Population Percentages from the United States, Census Regions, States, and the District of Columbia" at https://www.samhsa.gov/data/.

A.5 Related Substance Use Measures

Small area estimates are produced for a number of related drug measures, such as marijuana use and illicit drug use. It might appear that one could draw conclusions by subtracting one from the other (e.g., subtracting the percentage who used illicit drugs other than marijuana in the past month from the percentage who used illicit drugs in the past month to find the percentage who used only marijuana in the past month). Because related measures have been estimated with different models (i.e., separate models by age group and outcome), subtracting one measure from another related measure at the state or census region level can give misleading results, perhaps even a "negative" estimate, and should be avoided. However, these comparisons can be made at the national level because these estimates are design-based estimates. For example, at the national level, subtracting cigarette use estimates from tobacco use estimates will give the estimate of individuals who did not use cigarettes, but used other forms of tobacco, such as cigars, pipes, or smokeless tobacco.

A.6 2015 NSDUH Changes and Their Effects on Small Area Estimates

In 2015, a number of changes were made to the NSDUH questionnaire and data collection procedures. These changes were intended to improve the quality of the data that were collected and to address the changing needs of substance use and mental health policy and research.¹⁴ For a more detailed discussion of the questionnaire redesign and its effect, see Section C of the 2015 NSDUH's methodological summary and definitions report (CBHSQ, 2016b) and a brief report summarizing the implications of the changes for data users (CBHSQ, 2016c). To specifically see the impact of the 2015 questionnaire redesign as it is related to the SAE outcomes,¹⁵ refer to Section A.6 of the "2015-2016 NSDUH: Guide to State Tables and Summary of Small Area Estimation Methodology" at https://www.samhsa.gov/data/. All SAE outcomes remained comparable between the 2015, 2016, and 2017 NSDUHs.

Section B: State Model-Based Estimation Methodology

B.1 General Model Description

The model can be characterized as a complex mixed¹⁶ model (including both fixed and random effects) of the following form:

,     D

where is the probability of engaging in the behavior of interest (e.g., using marijuana in the past month) for person-k belonging to age group-a in grouped state sampling region (SSR)-j of state-i.¹⁷ Let denote a vector of auxiliary (predictor) variables associated with age group-a (12 to 17, 18 to 25, 26 to 34, and 35 or older) and denote the associated vector of the regression parameters. The age group-specific vectors of the auxiliary variables are defined for every block group in the nation and also include person-level demographic variables, such as race/ethnicity and gender. The vectors of state-level random effects and grouped SSR-level random effects are assumed to be mutually independent with and where is the total number of individual age groups modeled (generally, ). For hierarchical Bayes (HB) estimation purposes, an improper uniform prior distribution is assumed for , and proper Wishart prior distributions are assumed for and . The HB solution for involves a series of complex Markov Chain Monte Carlo (MCMC) steps to generate values of the desired fixed and random effects from the underlying joint posterior distribution. The basic process is described in Folsom et al. (1999), Shah, Barnwell, Folsom, and Vaish (2000), and Wright (2003a, 2003b).

Once the required number of MCMC samples (1,250 in all) for the parameters of interest are generated and tested for convergence properties (see Raftery & Lewis, 1992), the small area estimates for each race/ethnicity × gender cell within a block group can be obtained for each age group. These block group-level small area estimates then can be aggregated using the appropriate population count projections for the desired age group(s) to form state-level small area estimates. These state-level small area estimates are benchmarked to the national design-based estimates as described in Section B.5.

B.2 Variables Modeled

The 2017 National Survey on Drug Use and Health (NSDUH) data were pooled with the 2016 NSDUH data, and age group-specific state estimates for 30 binary (0, 1) outcomes listed below were produced. Comparisons between the 2015-2016 and the 2016-2017 state estimates also were produced for all measures.

1. past month use of illicit drugs,
2. past year use of marijuana,
3. past month use of marijuana,
4. perceptions of great risk from smoking marijuana once a month,
5. average annual rate of first use of marijuana,¹⁸
6. past month use of illicit drugs other than marijuana,
7. past year use of cocaine,
8. perceptions of great risk from using cocaine once a month,
9. past year use of heroin,
10. perceptions of great risk from trying heroin once or twice,
11. past year use of methamphetamine,¹⁹
12. past year misuse of pain relievers,
13. past month use of alcohol,²⁰
14. past month binge alcohol use, ²¹
15. perceptions of great risk from having five or more drinks of an alcoholic beverage once or twice a week,
16. past month use of tobacco products,
17. past month use of cigarettes,
18. perceptions of great risk from smoking one or more packs of cigarettes per day,
19. past year illicit drug use disorder,
20. past year pain reliever use disorder,
21. past year alcohol use disorder,
22. past year substance use disorder (SUD),
23. past year needing but not receiving treatment for illicit drug use at a special facility,
24. past year needing but not receiving treatment for alcohol use at a special facility,
25. past year needing but not receiving treatment for substance use at a special facility,
26. serious mental illness (SMI) in the past year,²²
27. any mental illness (AMI) in the past year,
28. received mental health services in the past year,
29. had serious thoughts of suicide in the past year, and
30. past year major depressive episode (MDE, i.e., depression).

B.3 Predictors Used in Mixed Logistic Regression Models

Local area data used as potential predictor variables in the mixed logistic regression models were obtained from a number of sources, as noted in the following discussion. Variable selection was done using combined 2016 and 2017 data for all outcomes. Fixed-effect predictors were selected using the method described in Section B.4.

Sources and potential data items used in the 2016-2017 modeling are provided in the following text and lists.

• Claritas. The demographic data package used from Claritas²³ contains data for 2013 with projections to 2018. The population projections are used to update these predictor variables each year. The 2016 and 2017 population projections were used for producing the 2016-2017 state small area estimates.
• U.S. Census Bureau. The 2010 census (demographic and geographic variables) and 2015 food stamp participation estimates were used (https://www.census.gov/data/datasets/time-series/demo/saipe/model-tables.html). The Census Bureau's Small Area Income and Poverty Estimates (SAIPE) program obtains Food Stamp program (now known as the Supplemental Nutrition Assistance Program [SNAP]) participation estimates from the U.S. Department of Agriculture, Food and Nutrition Service. Also, the Census Bureau's 2012-2016 American Community Survey (ACS) 5-year ACS demographic and socioeconomic variables at the tract level and poverty variable at the county level were used (https://www.census.gov/programs-surveys/acs/).
• Federal Bureau of Investigation (FBI). Uniform Crime Report (UCR) arrest totals were obtained from https://www.icpsr.umich.edu/icpsrweb/NACJD/series/57 . The most current data used are from 2014 for most counties, with previous years' data substituted in a few cases.
• Bureau of Labor Statistics (BLS). The 2017 county-level unemployment estimates were used (https://www.bls.gov/lau/tables.htm). The BLS uses results from the Current Population Survey (CPS) to provide county-level unemployment estimates. The CPS is a monthly survey of households conducted by the Census Bureau for the BLS.
• Bureau of Economic Analysis (BEA). The 2016 county-level per capita income estimates were used (https://www.bea.gov/data/income-saving/personal-income-county-metro-and-other-areas). These county-level per capita income estimates are produced by the Regional Income Division of the BEA.
• National Center for Health Statistics (NCHS). Mortality data using International Classification of Diseases, 10th revision (ICD-10), 2008-2013, were used. The ICD-10 death data are from the NCHS at the Centers for Disease Control and Prevention (CDC).
• SAMHSA, Center for Behavioral Health Statistics and Quality (CBHSQ, formerly the Office of Applied Studies [OAS]). Data were used from the National Survey of Substance Abuse Treatment Services (N-SSATS), formerly known as the Uniform Facility Data Set (UFDS). The 2013 and 2015 data on drug and alcohol treatment estimates were obtained. Maintenance of effort expenditures, block grant awards, cost of services, and total taxable resources data were also used.

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

B.4 Selection of Independent Variables for the Models

State estimates for past year methamphetamine (METHAMYR) use were not produced in prior years. Hence, in order to be consistent with the other sets of outcomes, the fixed-effect predictors for this outcome were selected using the pooled 2015-2016 NSDUH data. These fixed-effect predictors were selected based on the steps detailed in Section B.4 of the "2015-2016 NSDUH: Guide to State Tables and Summary of Small Area Estimation Methodology" at https://www.samhsa.gov/data/, and their updated versions were used to produce 2016-2017 state estimates for METHAMYR. 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 2015-2016 data were used to model the 2016-2017 data. Because the interest was to estimate change between the 2015-2016 and 2016-2017 state estimates, the same set of fixed-effect predictors was used for producing both sets of estimates.

B.5 Benchmarking the Age Group-Specific Small Area Estimates

The self-calibration built into the survey-weighted hierarchical Bayes (SWHB) solution ensures that the population-weighted average of the state small area estimates will closely match the national design-based estimates. The national design-based estimates in NSDUH are based entirely on survey-weighted data using a direct estimation approach, whereas the state and census region estimates are model-based. Given the self-calibration ensured by the SWHB method, for state reports prior to 2002, the standard Bayes prescription was followed; specifically, the posterior mean was used for the point estimate, and the tail percentiles of the posterior distribution were used for the Bayesian confidence 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 2016-2017 state-by-age group small area estimates is adjusted by adding the common factor where is the design-based national estimate and is the population-weighted mean of the state small area estimates for age group-a. The exactly benchmarked state-s and age group-a small area estimates then are given by Experience with such additive adjustments suggests that the resulting exactly benchmarked state small area estimates will always be between 0 percent 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 (MSE) 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 Bayesian confidence (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 (RMSEs). The adjusted 95 percent Bayesian confidence intervals are defined as follows:

     D

where

     D

     D     and

     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 after the logit transformation.

B.6 Calculation of Estimated Number of Individuals Associated with Each Outcome

Tables 1 to 31 of "2016-2017 NSDUHs: Model-Based Estimated Totals (in Thousands) (50 States and the District of Columbia)" show the estimated numbers of individuals associated with each of the 30 outcomes of interest.²⁴ To calculate these numbers, the benchmarked small area estimates and the associated 95 percent Bayesian confidence intervals are multiplied by the average population across the 2 years (in this case, 2016 and 2017) of the state by the age group of interest.

For example, past month use of alcohol among 18 to 25 year olds in Alabama was 50.18 percent.²⁵ The corresponding Bayesian confidence intervals ranged from 46.18 to 54.17 percent. The population count for 18 to 25 year olds averaged across 2015 and 2016 in Alabama was 515,697 (see Table C.10 in Section C of this methodology document). Hence, the estimated number of 18 to 25 year olds using alcohol in the past month in Alabama was 0.5018 × 515,697, which is 258,777.²⁶ The associated Bayesian confidence intervals ranged from 0.4618 × 515,697 (i.e., 238,149) to 0.5417 × 515,697 (i.e., 279,353). Note that when estimates of the number of individuals are calculated for Tables 1 to 31 in "2016-2017 NSDUHs: Model-Based Estimated Totals (in Thousands) (50 States and the District of Columbia)" (follow the link in footnote 24), the unrounded percentages and population counts are used, then the numbers are reported to the nearest thousand. Hence, the number obtained by multiplying the published estimate with the published population estimate may not exactly match the counts that are published in these tables because of rounding differences.

The only exception to this calculation is the production of the estimated numbers of marijuana initiates. Those estimates cannot be directly calculated as the product of the percentage estimate of first use of marijuana and the population counts available in Section C. That is because the denominator of that percentage estimate is defined as the number of person years at risk for marijuana initiation, which is a combination of individuals who never used marijuana and one half of the individuals who initiated in the past 24 months (see Section B.8 for more details).

B.7 Calculation of Aggregate Age Group Estimates and Limitations

Tables 1 to 31 of "2016-2017 NSDUHs: Model-Based Prevalence Estimates (50 States and the District of Columbia)" show estimates for the following age groups: 12 to 17, 18 to 25, 26 or older, 18 or older, and 12 or older.²⁷ If a user was interested in producing aggregated estimates, such as for those aged 12 to 25, the aggregated estimates could be calculated using prevalence estimates along with the population totals shown in Section C of this document. However, with the information that is provided in the tables, the confidence intervals cannot be calculated. Below is an example of this calculation for a given state.

For example, past month use of alcohol in Alabama among youths 12 to 17 was 8.88 percent, and among young adults 18 to 25 it was 50.18 percent.²⁸ The population counts for 12 to 17 year olds and 18 to 25 year olds averaged across 2016 and 2017 in Alabama were 375,632 and 515,697, respectively (see Table C.10 in Section C of this methodology document). Hence, one would calculate the estimate for individuals aged 12 to 25 by first finding the number of users aged 12 to 25, which is 292,133 ([0.0888 × 375,632] + [0.5018 × 515,697]), then dividing that number by the population aged 12 to 25, which results in a rate of 32.77 percent (292,133 / [375,632 + 515,697]).

B.8 Calculation of Average Annual Initiation of Marijuana Use

Initiation²⁹ 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 initiation definition used here employs a simpler form of the at-risk population based on the model-based methodology. This model-based average annual initiation rate is defined as follows:

     D

where is the number of marijuana initiates in the past 24 months and is the number of persons who never used marijuana.

The initiation 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 initiation cases from each annual survey. By assuming further that the distribution of first use for the initiation cases is uniform across the 2-year interval, the total number of person-years of exposure is 1 year on average for the initiation 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 initiation 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 2017 to indicate first use as early as the first part of 2015 or as late as the first part of 2017. Similarly, a subject interviewed in the last part of 2017 could indicate first use as early as the last part of 2015 or as late as the last part of 2017. Therefore, in the 2017 survey, the reported period of first use ranged from early 2015 to late 2017 and was "centered" in 2016. For example, about half of the 12 to 17 year olds who reported first use in the past 24 months reported first use in 2016, while a quarter each reported first use in 2015 and 2017. Persons who responded in 2017 that they had never used marijuana were included in the count of "never used." Similarly, reports of first use in the past 24 months from the 2016 survey ranged from early 2014 to late 2016 and were centered in 2015. Half of the 12 to 17 year olds who reported first use in the past 24 months reported first use in 2015, while a quarter each reported first use in 2014 and 2016. Note that only initiation rates for marijuana use are provided here.

B.9 Underage Drinking

To obtain small area estimates for individuals 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. Model-based estimates for individuals 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 B.5.

B.10 Substance Use Disorder / Needing But Not Receiving Treatment

The NSDUH computer-assisted interviewing (CAI) instrumentation includes questions that are designed to measure dependence or abuse of alcohol and illicit drugs (i.e., SUDs). For these substances,³⁰ dependence and abuse questions were based on the criteria in the DSM-IV (APA, 1994).

Specifically, for marijuana, hallucinogens, inhalants, and tranquilizers, a respondent was defined as having dependence if he or she met three or more of the following six dependence criteria:

1. Spent a great deal of time over a period of a month getting, using, or getting over the effects of the substance.
2. Used the substance more often than intended or was unable to keep set limits on the substance use.
3. Needed to use the substance more than before to get desired effects or noticed that the same amount of substance use had less effect than before.
4. Inability to cut down or stop using the substance every time tried or wanted to.
5. Continued to use the substance even though it was causing problems with emotions, nerves, mental health, or physical problems.
6. The substance use reduced or eliminated involvement or participation in important activities.

For alcohol, cocaine, heroin, methamphetamine, pain relievers, sedatives, and prescription stimulants, a seventh withdrawal criterion was added. The seventh withdrawal criterion is defined by a respondent reporting having experienced a certain number of withdrawal symptoms that vary by substance (e.g., having trouble sleeping, cramps, hands tremble). A respondent was defined as having dependence if he or she met three or more of seven dependence criteria for these substances.

For each illicit drug and alcohol, a respondent was defined as having abused that substance if he or she met one or more of the following four abuse criteria and was determined not to be dependent on the respective substance in the past year (i.e., because dependence takes precedence over abuse):

1. Serious problems at home, work, or school caused by the substance, such as neglecting your children, missing work or school, doing a poor job at work or school, or losing a job or dropping out of school.
2. Used the substance regularly and then did something that might have put you in physical danger.
3. Use of the substance caused you to do things that repeatedly got you in trouble with the law.
4. Had problems with family or friends that were probably caused by using the substance and continued to use the substance even though you thought the substance use caused these problems.

For additional details on how respondents were classified as having substance use disorder, see Section B.4.3 in Section B of the 2017 NSDUH methodological summary and definitions report (CBHSQ, 2018).

Additionally, the NSDUH CAI instrument included a series of questions that are designed to measure treatment need for an alcohol or illicit drug use problem and to determine persons needing but not receiving treatment. Respondents were classified as needing substance use treatment in the past year if they met either of the following criteria:

1. presence of an SUD in the past year for alcohol or illicit drugs (i.e., dependence or abuse) (see Section B.4.3 in Section B of CBHSQ, 2018); or
2. receipt of treatment at a specialty facility (i.e., drug and alcohol rehabilitation facility [inpatient or outpatient], hospital [inpatient only], or mental health center) in the past year for the use of alcohol or illicit drugs (or both).

A respondent was classified as needing but not receiving treatment for an alcohol problem if he or she met the criteria for alcohol dependence or abuse in the past year, but did not receive treatment at a specialty facility for an alcohol problem in the past year.

For additional details on how respondents were classified as needing substance use treatment, see Section B.4.4 in Section B of the 2017 NSDUH methodological summary and definitions report (CBHSQ, 2018).

B.11 Mental Health Measures

This section provides a summary of the measurement issues associated with three of the mental health outcome variables—SMI, AMI, and MDE. Additional details can be found in Sections B.4.6 through B.4.8 in Section B of the 2017 NSDUH methodological summary and definitions report (CBHSQ, 2018).

B.11.1 Mental Illness

In the 2000-2001 and 2002-2003 NSDUH state SAE reports (Wright, 2003a, 2003b; Wright & Sathe, 2005), the Kessler-6 (K6) distress scale was used to measure SMI (Kessler et al., 2003). However, SAMHSA discontinued producing state-level SMI estimates beginning with the release of the 2003-2004 state report (Wright & Sathe, 2006) because of concerns about the validity of using only the K6 distress scale without an impairment scale; see Section B.4.4 in Appendix B of the 2004 NSDUH national findings report (OAS, 2005). The use of the K6 distress scale continued in the 2003-2004 and the 2004-2005 state reports (Wright & Sathe, 2006; Wright et al., 2007), not as a measure of SMI, but as a measure of serious psychological distress (SPD) because it was determined that the K6 scale measured only SPD and merely contributed to measuring SMI and AMI (see the details that follow).

In December 2006, a new technical advisory group was convened by SAMHSA's OAS (which later became CBHSQ) and the Center for Mental Health Services (CMHS) to solicit recommendations for data collection strategies to address SAMHSA's legislative requirements. Although it was recognized that the ideal way to estimate SMI in NSDUH would be to administer a clinical diagnostic interview annually to all 45,000 adult respondents, this approach was not feasible because of constraints on the interview time and the need for trained mental health clinicians to conduct the interviews. Therefore, the approach recommended by the technical advisory group and adopted by SAMHSA for NSDUH was to utilize short scales in the NSDUH interview that separately measure psychological distress and functional impairment for use in a statistical model that predicts whether a respondent had mental illness.

In response, SAMHSA's CBHSQ initiated a Mental Health Surveillance Study (MHSS) under its NSDUH contract with RTI International to develop and implement methods to estimate SMI. Based on recommendations from this panel, estimates of SMI were presented based on a revised methodology and, thus, were not comparable with estimates for SMI or SPD shown in NSDUH state reports prior to 2009. However, in 2013, another revision to the methodology for creating SMI estimates was made, and the estimates presented for 2011 and 2012 are based on this revised methodology (and therefore are not comparable with previously published estimates of SMI). Thus, the 2008-2009, 2009-2010, and 2010-2011 SMI estimates were reproduced using the new 2013 methodology.

To develop methods for preparing the estimates of SMI and AMI presented in this and other NSDUH reports and documents, the MHSS was initiated as part of the 2008 NSDUH design and analysis. Because of constraints on the interview time in NSDUH and the need for trained mental health clinicians, it was not possible to administer a full structured diagnostic clinical interview to assess mental illness on approximately 45,000 adult respondents; therefore, the approach adopted by SAMHSA was to utilize short scales separately measuring psychological distress (K6) and functional impairment that could be used in a statistical model to accurately predict whether a respondent had a mental illness. Two impairment scales—the World Health Organization Disability Assessment Schedule (WHODAS) and the Sheehan Disability Scale (SDS)—were included in the 2008 survey for evaluation. The collection of clinical psychiatric interview data was achieved using a subsample of approximately 1,500 adult NSDUH participants in 2008. These participants were recruited for a follow-up clinical interview consisting of a gold-standard diagnostic assessment for mental disorders and functional impairment. In order to determine the optimal scale to measure functional impairment, a split-sample design was incorporated into the full 2008 NSDUH data collection in which half of the adult respondents received the WHODAS and half received the SDS (only the WHODAS scale was used starting in 2009). The 2008 statistical models (subsequently referred to as the "2008 model") using the data from the subsample of respondents collected as part of the MHSS then were developed for each half sample in which the short scales (the K6 in combination with the WHODAS or the K6 in combination with the SDS) were used as predictors in models of mental illness assessed via the clinical interviews. The model parameter estimates then were used to predict SMI in the full 2008 NSDUH sample. SMI probabilities and SMI predicted values (as well as for AMI) were computed for respondents in NSDUH samples from 2008 to 2011 using model parameter estimates from the 2008 model.

In 2010, SAMHSA began preliminary investigations to assess whether improvements to the model were warranted using all of the clinical data that had been collected since 2008. In 2011 and 2012, the clinical sample was augmented to include 1,500 respondents per year, leading to a combined sample of approximately 5,000 clinical interviews for 2008 to 2012. SAMHSA determined that the 2008 model had some important shortcomings that had not been detected in the original model fitting because of the small number of respondents in the 2008 clinical subsample. Specifically, the 2008 model substantially overestimated SMI and AMI among young adults aged 18 to 25 relative to the clinical interview data. In addition, improvements were needed in the weighting procedures for the MHSS sample data to account better for nonresponse and undercoverage. Therefore, SAMHSA decided to modify the model for the 2012 estimates using the combined 2008-2012 clinical data (subsequently referred to as the "2012 model"). To reduce bias and improve prediction, additional mental health-related variables and an age variable were added in the 2012 model. To provide consistent data for trend assessment, state mental illness estimates for 2008-2009, 2009-2010, and 2010-2011 were also recomputed using the new 2012 model. Note that tables or maps showing estimates of AMI and SMI based on these 2012 models include "Revised October 2013" in the source line for estimates using 2008 through 2011 data.

The next few paragraphs describe the instruments and items used to measure the variables employed in the 2012 model. Specifically, the instrument used to measure mental illness in the clinical interviews is described, followed by descriptions of the scales and items in the main NSDUH interviews that were used as predictor variables in the model (e.g., the K6 and WHODAS total scores, age, MDE, and suicidal thoughts).

Clinical Measurement of Mental Illness. Mental illness was measured in the MHSS clinical interviews using an adapted version of the Structured Clinical Interview for the DSM-IV-TR Axis I Disorders, Research Version, Non-patient Edition (SCID-I/NP) (First, Spitzer, Gibbon, & Williams, 2002) and was differentiated by the level of functional impairment based on the Global Assessment of Functioning (GAF) scale (Endicott, Spitzer, Fleiss, & Cohen, 1976). Past year disorders that were assessed through the SCID included mood disorders (e.g., MDE, manic episode), anxiety disorders (e.g., panic disorder, generalized anxiety disorder, posttraumatic stress disorder), eating disorders (e.g., anorexia nervosa), intermittent explosive disorder, and adjustment disorder. In addition, the presence of psychotic symptoms was assessed. SUDs also were assessed, although these disorders were not used to produce estimates of mental illness.

• Respondents were defined as having any mental illness (AMI) if they were determined to have any of the mental disorders assessed in the SCID (not including SUDs), regardless of the level of functional impairment.
• Respondents were defined as having serious mental illness (SMI) if they had any of the mental disorders assessed in the SCID (not including SUDs), and these disorders resulted in substantial impairment in carrying out major life activities, based on GAF scores of 50 or below. The SMI diagnosis was used as the response variable in both the 2008 and 2012 prediction models.

The SCID and the GAF in combination were considered to be the gold standard for measuring mental illness.

Kessler-6 (K6) Distress Scale. The K6 in the main NSDUH consists of two sets of six questions that asked adult respondents how frequently they experienced symptoms of psychological distress during two different time periods: (1) during the past 30 days, and (2) if applicable, the one month in the past year when they were at their worst emotionally. Respondents were asked about the second time period only if they indicated that there was a month in the past 12 months when they felt more depressed, anxious, or emotionally stressed than they felt during the past 30 days.

The six questions comprising the K6 scale for the past month are as follows:

NERVE30
During the past 30 days, how often did you feel nervous?

1 All of the time
2 Most of the time
3 Some of the time
4 A little of the time
5 None of the time
Don't know/Refused

Response categories are the same for the remaining questions shown below.

HOPE30
During the past 30 days, how often did you feel hopeless?

FIDG30
During the past 30 days, how often did you feel restless or fidgety?

NOCHR30
During the past 30 days, how often did you feel so sad or depressed that nothing could cheer you up?

EFFORT30
During the past 30 days, how often did you feel that everything was an effort?

DOWN30
During the past 30 days, how often did you feel down on yourself, no good or worthless?

To create a score, the six items (NERVE30, HOPE30, FIDG30, NOCHR30, EFFORT30, and DOWN30) on the K6 scale were recoded from 0 to 4 so that "all of the time" was coded 4, "most of the time" 3, "some of the time" 2, "a little of the time" 1, and "none of the time" 0, with "don't know" and "refused" also coded as 0. Summing across the transformed responses in these six items resulted in a score with a range from 0 to 24.

If respondents were asked about a month in the past 12 months when they felt more depressed, anxious, or emotionally stressed than they felt during the past 30 days, they were asked comparable K6 items for that particular month in the past 12 months. The scoring procedures for these K6 items for the past 12 months were the same as those described above. The higher of the two K6 total scores for the past 30 days or past 12 months was used both for MHSS analysis purposes and in the adult respondents' final data.

An alternative K6 total score also was created in which K6 scores of less than 8 were recoded as 0 and scores from 8 to 24 were recoded as 1 to 17. The rationale for creating the alternative past year K6 score was that SMI prevalence was typically extremely low for respondents with past year K6 scores of less than 8, and the prevalence rates started increasing only when scores were 8 or greater. The alternative K6 score was used in both the 2008 and 2012 SMI prediction models.

WHODAS. An initial step of the MHSS was to modify the WHODAS for use in a general population survey, including making minor changes to question wording and reducing its length (Novak, 2007). That is, a subset of 8 items was found to capture the information represented in the full 16-item scale with no significant loss of information.

These eight WHODAS items that were included in the main NSDUH interview were assessed on a 0 to 3 scale, with responses of "no difficulty," "don't know," and "refused" coded as 0; "mild difficulty" coded as 1; "moderate difficulty" coded as 2; and "severe difficulty" coded as 3. Some items had an additional category for respondents who did not engage in a particular activity (e.g., they did not leave the house on their own). Respondents who reported that they did not engage in an activity were asked a follow-up question to determine if they did not do so because of emotions, nerves, or mental health. Those who answered "yes" to this follow-up question were subsequently assigned to the "severe difficulty" category; otherwise (i.e., for responses of "no," "don't know," or "refused"), they were assigned to the "no difficulty" category. Summing across these codes for the eight responses resulted in a total score with a range from 0 to 24. More information about scoring of the WHODAS can be found in the 2015 NSDUH public use file codebook (CBHSQ, 2016d).

An alternative WHODAS total score was created in which individual WHODAS item scores of less than 2 were recoded as 0, and item scores of 2 to 3 were recoded as 1. The individual alternative item scores then were summed to yield a total alternative score ranging from 0 to 8. Creation of an alternative version of the WHODAS score was based on the assumption that a dichotomous measure dividing respondents into two groups (i.e., severely impaired vs. less severely impaired) might fit better than a linear continuous measure in models predicting SMI. This alternative WHODAS score was the variable used in both the 2008 and 2012 SMI prediction models.

Suicidal Thoughts, MDE, and Age. In addition to the K6 and WHODAS scales, the 2012 model included the following measures as predictors of SMI: (a) serious thoughts of suicide in the past year; (b) having a past year MDE; and (c) age. The first two variables were added to the model to decrease the error rate in the predictions (i.e., the sum of the false-negative and false-positive rates relative to the clinical interview results). A recoded age variable reduced the biases in estimates for particular age groups, especially 18 to 25 year olds.

Since 2008, all adult respondents in NSDUH have been asked the following question: "At any time in the past 12 months, that is from [DATEFILL] up to and including today, did you seriously think about killing yourself?"³¹ Definitions for MDE in the lifetime and past year periods are discussed in Section B.11.2 of this document. For respondents aged 18 to 30, an adjusted age was created by subtracting 18 from the respondent's current age, resulting in values ranging from 0 to 12. For a respondent aged 18, for example, the adjusted age was 0 (i.e., 18 minus 18), and for a respondent aged 30, the adjusted age was 12 (i.e., 30 minus 18). For respondents aged 31 or older, the adjusted age was assigned a value of 12.

The 2012 SMI Model. The 2012 SMI prediction model was fit with data from 4,912 WHODAS MHSS respondents from 2008 through 2012. The response variable Y equaled 1 when an SMI diagnosis was positive based on the clinical interview; otherwise, Y was 0. Letting X be a vector of characteristics attached to a NSDUH respondent and letting the probability that this respondent had SMI be , the 2012 SMI prediction model was

     D

where refers to an estimate of the SMI response probability .

These covariates in equation (1) came from the main NSDUH interview data:

• = Alternative Past Year K6 Score: Past year K6 score of less than 8 recoded as 0; past year K6 score of 8 to 24 recoded as 1 to 17.
• = Alternative WHODAS Score: WHODAS item score of less than 2 recoded as 0; WHODAS item score of 2 to 3 recoded as 1, then summed for a score ranging from 0 to 8.
• = Serious Thoughts of Suicide in the Past Year: Coded as 1 if "yes"; coded as 0 otherwise.
• = Past Year MDE: Coded as 1 if criteria for past year MDE were met (see Section B.11.2); coded as 0 otherwise.
• = Adjusted Age: Coded as age minus 18 if aged 18 to 30; coded as 12 otherwise.

As with the 2008 model, a cut point probability was determined, so that if for a particular respondent, then he or she was predicted to be SMI positive; otherwise, he or she was predicted to be SMI negative. The cut point (0.260573529) was chosen so that the weighted number of false positives and false negatives in the MHSS dataset were as close to equal as possible. The predicted SMI status for all adult NSDUH respondents was used to compute SMI small area estimates.

A second cut point probability (0.0192519810) was determined so that respondents with an SMI probability greater than or equal to the cut point were predicted to be positive for AMI, and the remainder were predicted to be negative for AMI. The second cut point was chosen so that the weighted numbers of AMI false positives and false negatives were as close to equal as possible.

B.11.2 Major Depressive Episode (Depression)

According to the DSM-5, a person is defined as having had MDE in his or her lifetime if he or she has had at least five or more of the following nine symptoms nearly every day (except where noted) in the same 2-week period, where at least one of the symptoms is a depressed mood or loss of interest or pleasure in daily activities (APA, 2013). These symptoms are as follows: (1) depressed mood most of the day; (2) markedly diminished interest or pleasure in all or almost all activities most of the day; (3) significant weight loss when not sick or dieting, or weight gain when not pregnant or growing, or decrease or increase in appetite; (4) insomnia or hypersomnia; (5) psychomotor agitation or retardation at a level that is observable by others; (6) fatigue or loss of energy; (7) feelings of worthlessness or excessive or inappropriate guilt; (8) diminished ability to think or concentrate or indecisiveness; and (9) recurrent thoughts of death or suicidal ideation (i.e., recurrent suicidal ideation without a specific plan, making a specific plan, or making an attempt). Unlike the other symptoms listed previously, recurrent thoughts of death or suicidality did not need to have occurred nearly every day. Respondents who have had an MDE in their lifetime are asked if, during the past 12 months, they had a period of depression lasting 2 weeks or longer while also having some of the other symptoms mentioned. Respondents reporting experiences consistent with them having had an MDE in the past year are asked questions from the SDS to measure the level of functional impairment in major life activities reported to be caused by the MDE in the past 12 months (Leon et al., 1997).

Beginning in 2004, sections related to MDE were included in the questionnaire. These sections, which were originally derived from DSM-IV (APA, 1994) criteria for MDE, contain questions that did not change for the 2017 NSDUH questionnaire. Consistent with the more recent DSM-5 criteria (APA, 2013), NSDUH does not exclude MDEs that occurred exclusively in the context of bereavement. These questions permit prevalence estimates of MDE to be calculated. Separate modules were administered to adults aged 18 or older and youths aged 12 to 17. The adult questions were adapted from the depression section of the National Comorbidity Survey Replication (NCS-R), and the questions for youths were adapted from the depression section of the National Comorbidity Survey Replication Adolescent Supplement (NCS-A) (see https://www.hcp.med.harvard.edu/ncs/ ). To make the sections developmentally appropriate for youths, there are minor wording differences in a few questions between the adult and youth modules. Revisions to the questions in both modules were made primarily to reduce the length and to modify the NCS questions, which are interviewer-administered, to the audio computer-assisted self-interviewing (ACASI) format used in NSDUH. In addition, some revisions, based on cognitive testing, were made to improve comprehension.

Since 2004, the NSDUH questions that determine MDE have remained unchanged for both adults and youths. In the 2008 questionnaire, however, changes were made in other mental health items that precede the MDE questions for adults (K6, suicide, and impairment). Questions also were retained in 2009 for the WHODAS impairment scale, and the questions for the SDS impairment scale were deleted; see Sections B.4.6 and B.4.7 in Section B of the 2017 NSDUH methodological summary and definitions (CBHSQ, 2018) for further details about these questionnaire changes. The questionnaire changes in 2008 appear to have affected the reporting on MDE questions among adults.

Because the WHODAS was selected to be used in the 2009 and subsequent surveys, model-based adjustments were applied to MDE estimates from the SDS half sample in 2008 to remove the context effect differential between the two half samples. Additionally, model-based adjustments were made to the 2005, 2006, and 2007 adult MDE estimates to make them comparable with the 2008 through 2012 MDE estimates (for more information on these adjustments, see CBHSQ, 2012). Thus, the 2008-2009 estimates of MDE were produced using the adjusted 2008 MDE variable along with the unadjusted 2009 MDE variable. Revised estimates for 2005-2006, 2006-2007, and 2007-2008 were produced using the adjusted MDE variable.

In addition, changes to the youth mental health service utilization section questions in 2009 that preceded the questions about adolescent depression could have affected adolescents' responses to the adolescent depression questions and estimates of adolescent MDE. However, these changes in 2009 did not appear to affect the estimates of adolescent MDE. Therefore, data on trends in past year MDE from 2004 to 2017 are available for adolescents aged 12 to 17.

Section C: Sample Sizes, Response Rates, and Population Estimates