Youth Substance  Use: State Estimates From the 1999 National Household Survey on Drug Abuse

Appendix G: State Estimation Methodology

G.1 Background

In response to the need for State-level information on substance abuse problems, the Substance Abuse and Mental Health Services Administration (SAMHSA) began developing and testing small area estimation (SAE) methods for the National Household Survey on Drug Abuse (NHSDA) in 1994 under a contract with the Research Triangle Institute (RTI). That developmental work used logistic regression models with data from the combined 1991 to 1993 NHSDAs and local area indicators, such as drug-related arrests, alcohol-related death rates, and block group/tract level characteristics from the 1990 Census that were found to be associated with substance abuse. In 1996, the results were published for 25 States for which there were sufficient sample data (SAMHSA, 1996). A subsequent report described the methodology in detail and noted areas in which improvements were needed (Folsom & Judkins, 1997).

The increasing need for State-level estimates of substance use led to the decision to expand the NHSDA to provide estimates for all 50 States and the District of Columbia on an annual basis beginning in 1999. It was determined that, with the use of modeling similar to that used with the 1991 to 1993 NHSDA data in conjunction with a sample designed for State-level estimation, a sample of about 67,500 persons would be sufficient to make reasonably precise estimates.

The State-based NHSDA sample design implemented in 1999 had the following characteristics:

1. States are stratified into field interviewer (FI) regions that covered the geography of each State. The FI regions are comprised of contiguous Census tracts and counties and designed to yield about 75 interviews per region. In the 42 smaller States (by population) and the District of Columbia, there are 12 FI regions; in the eight largest States, there are 48 FI regions.

2. Within each region, eight segments are randomly selected and two are allocated to each calendar quarter of data collection.

3. Within each segment, households are screened, and a sample of one to two persons per household is selected. An average of nine responding persons per segment is sought.

4. The samples are selected so that approximately 900 responding persons, 300 in each age group (12 to 17, 18 to 25, and 26 or older), are drawn in each of the 42 States and the District of Columbia. In the eight large States, the person samples are allocated equally to the three age groups with overall respondent sample sizes ranging from 2,669 to 4,681.

In preparation for the modeling of the 1999 data, RTI used the data from the combined 1994-96 NHSDAs to develop an improved methodology that utilized more local area data and produced better estimates of the accuracy of the State estimates (Folsom, Shah, & Vaish, 1999). That effort involved the development of procedures that would validate the results for geographic areas with large samples. This work was reviewed by a panel with expertise in smallarea estimation.1 They approved of the methodology, but suggested further improvements for the modeling to be used to produce the 1999 State estimates. Those improvements have been incorporated into the methodology finally used for the 1999 State estimates included in this report. The methodology, called Survey-Weighted Hierarchical Bayes Estimation (HB), is described below.

G.2 Goals of Modeling

There were several goals underlying the estimation process. The first was to model drug use at the lowest possible level and aggregate over the levels to form the State estimates. The chosen level of aggregation was the 32 age group (12 to 17, 18 to 25, 26 to 34, 35+) by race/ethnicity (white-not Hispanic, black-not Hispanic, Hispanic, Other) by gender cells at the block group level. Estimated population counts could be obtained from a private vendor for each block group for each of the 32 cells. This level of aggregation was desired because the NHSDA first stage of sample selection was at the block group level, so that there would be data at this level to fit a model. In addition, there was a great deal of information from the Census at the block group level that could be used as predictors in the models. If prevalence rates could be estimated for each of the 32 cells at the block group level, it would only be necessary to multiply by the estimated population counts and aggregate to the State level.

Another goal of the estimation process was to include the sampling weight in the model in such a way that the small area estimates would converge to the design-based (sample-weighted) estimate when they are aggregated to a sufficient sample size. There was a desire for the estimates to have this characteristic so that there would be consistency with the survey-weighted national estimates based on the entire sample.

A third goal was to include as much local source data as possible, especially data related to each substance use measure. This would help provide a better fit beyond the strictly sociodemographic information. The desire was to use national sources of these data so that there would be consistency of collection and estimation methodology across States.

Recognizing that estimates based solely on these "fixed" effects would not reflect differences across States due to differences in laws, enforcement activities, advertising campaigns, outreach activities, and other such unique State contributions, a fourth goal was to include "random" effects to compensate for these differences. The types of random effects that could be supported by the NHSDA data were a function of the size of sample and the model fit to the sample data. For the 1999 survey, random effects were included at the State level and for substate regions comprised of three neighboring FI regions. Although this grouping of the three FI regions was principally motivated by the need to accumulate enough sample to support good model fitting for the low prevalence NHSDA outcomes, it was also reasoned that it would be possible to produce substate HB estimates for areas comprised of these FI region groups, once 2 or 3 years of NHSDA data were available, because that would yield substate region samples of at least 400 respondents. For substate areas like counties and large municipalities that do not conform to the substate region boundaries, HB estimates could be derived from their elementalblock group level contributions, but the direct survey data employed in the estimation of the associated substate region effects would not be restricted to the county or city of interest. This mismatch of FI region and county/large municipality boundaries weakens the theoretical appeal of the associated HB estimate. For this reason, substate HB estimates probably should be restricted to areas that can be matched reasonably well to FI region groups.

One of the difficulties of typical SAE has been obtaining good estimates of the accuracy of the estimates with prediction intervals that give a good representation of the true probability of coverage of the intervals. Therefore, the final major goal was to provide accurate prediction intervals-ones that would approach the usual sample-based intervals as the sample size increases.

G.3 Variables to Be Modeled

A set of 20 measures covering a variety of aspects of substance use and abuse was designated. These variables are listed below. The first seven measures in the list were considered priority variables and were discussed in the Summary of Findings from the 1999 National Household Survey on Drug Abuse (SAMHSA, 2000b). The remaining variables have been estimated. Some have been discussed in this report, and the remaining ones will be released in a separate State report later this year.

G.4 Predictors Used in Logistic Regression Models

Local area data used as potential predictor variables in the logistic regression models were obtained from several sources, including Claritas, the Census Bureau, the FBI (Uniform Crime Reports), Health Resources and Services Administration (Area Resource File), SAMHSA (Uniform Facility Data Set), and the National Center for Health Statistics (mortality data). The list of sources and potential data items used in the modeling are provided below.

Claritas

Demographic data package called Building Block Basic, Age by Race from Claritas for 1999 with projections to 2004; the estimates for 1999-population counts were used

Census Bureau

1990 Census, demographic and socioeconomic variables

July 1997 Food Stamp participation rates

Federal Bureau of Investigation

Uniform Crime Report (UCR), UCR arrest totals from: http://fisher.lib.Virginia.EDU/crime/; the most current data are for 1997 for most counties, and previous years data were used in a few cases

Health Resources and Services Administration

Area Resource File (ARF), some variables relating to income and employment from the ARF February 1999 release from the Bureau of Health Professions, Office of Research and Planning

National Center for Health Statistics

Mortality data using International Classification of Diseases, 9^th revision (ICD-9), 1992 to 1997; ICD-9 death rate data from the Centers for Disease Control and Prevention at the National Center for Health Statistics

SAMHSA, Office of Applied Studies

Uniform Facility Data Set (UFDS), 1997 to 1998 UFDS data on drug and alcohol treatment rates from Synectics for Management Decisions, Inc.

The following tables list the specific independent variables that were potential predictors in the models.

G.5 Selection of Independent Variables for the Models

Independent variables for modeling each of the substance use measures were first identified by a CHAID (Chi-squared Automatic Interaction Detector) algorithm. CHAID is an algorithm that does not use sample weights. Prior to this process, all the continuous variables were categorized using deciles and were treated as ordinal in CHAID. Race, region, and gender were treated as nominal categorical variables in CHAID. Significant independent variables from each model that were final nodes in the tree-growing process were identified as indicator variables destined for inclusion at a later step.

Independently, a SAS stepwise logistic regression model was fit for each dependent variable by age group. The SAS stepwise was used because it was able to quickly run all of the variables for all of the models, although it was recognized that the software would not take into account the complex sample design and the weights. The independent variables included all the first-order or linear polynomial trend contrasts across the 10 levels of the categorized variables plus the gender, region, and race variables. Significant variables (at the 3 percent level) were identified from this process. Based on this list, a list of variables was created that included the second- and third-order polynomials and the interaction of the first-order polynomials with the gender, race, and region variables.

Next, the variables from the CHAID process and the SAS process were entered into a SAS stepwise logistic model at the 1 percent significance level. Because of past concerns about overfitting of the data in earlier estimation using the 1991 to 1993 NHSDA data, the significance levels were made quite stringent. These variables were then entered into a SUDAAN logistic regression model because the SUDAAN software would adjust for the effects of the weights andother aspects of the complex sample design. All variables that were still significant at the 1 percent significance level were entered into the survey weighted HB process.

Independently, a factor-analytic approach was used to determine the important variables to include in the model. This approach would allow the data to self-identify the important dimensions. The concern here was to use an alternate method that would have a certain face validity. That method was utilized to identify an independent set of variables that were then processed through the HB estimation. The results, however, in terms of model-fit and prediction intervals were generally not as good as with the CHAID/SAS/SUDAAN screening process for candidate independent variables. Also, the factor-analytic approach involves an inherently subjective step to attribute names to the various factor loadings, and the interest was more in the predictive ability of variables than in a substantive description of the dimensions. Nevertheless, it was encouraging to see that the results of the two approaches gave reasonably similar results. For these reasons, the estimates in this report were those based on the latter method that started with the CHAID process.

G.6 General Model Description

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

8=X$ + ZU

Each of the symbols represents a matrix or vector. The leading term X$ is the usual (fixed) regression contribution, and ZU represents random effects for the States and FI region groups that the data will support and for which estimates are desired. Not obvious from the notation is that the form of the model is a logistic model used to estimate dichotomous data. The 8 vector has elements ln[B_ijk /(1-B_ijk)], where the B_ijk is the propensity for the k^th person in the j^th FI composite region in the i^th State to engage in the behavior of interest (e.g., to use marijuana in the past month). Also not obvious from the notation is that the model fitting utilizes the final "sample" weights as discussed above. The "sample" weights have been adjusted for nonresponse and poststratified to known Census counts.

The estimate for each State behaves like a "weighted" average of the direct survey estimate in that State and the predicted value based on the national regression model. The "weights" in this case are functions of the relative precision of the sample based estimate for the State and the predicted estimate based on the national model. The eight large States have large samples, and thus more "weight" is given to the sample estimate relative to the model-based regression estimate. The 42 small States and the District of Columbia put relatively more "weight" on the regression estimate because of their smaller samples. The national regression estimate actually uses national parameters that are based on the full sample of approximately 67,000 persons; however, the regression estimate for a specific State is based on applying the national regression parameters to that State's "local" county, block group, and tract level predictor variables and summing to the State level. Therefore, even the national regression component of the estimate for a State includes "local" State data.

The goal then was to come up with the best estimates of $ and U. This would lead to the best estimates of 8, which would in turn lead to the best estimate of B. Once the best estimate of B for each block group and each age/race/gender cell within a block group has been estimated, the results could be weighted by the projected Census population counts at that level to make estimates for any geographic area larger than a block group.

G.7 Implementation of Modeling

The solution to the equation for 8 in the above section is not straightforward but involves a series of iterative steps to generate values of the desired fixed and random effects from the underlying joint distribution. The details of the technique will be described in more detail in a methodological report currently in progress. In the interim, the basic process can be described as follows.

Let $ denote the matrix of fixed effects, 0 be the matrix of State random effects i = 1-51, and < denote the matrix of FI composite region effects j within State i. Because the goal is to estimate separate models for four age groups, it is assumed that the random effects vectors are four variate Normal with null mean vectors and 4X4 covariance matrices D₀ and D_<, respectively. To estimate the individual effects, a Bayesian approach is used to represent the joint density function given the data by f($, 0 , <, D_< , D₀ | y). According to the Bayes process, this can be estimated once the conditional distributions are known:

f₁( $ | 0, <, D_< , D₀ , y), f₂(D_< , D₀ | $ 0 , <, y), and f₃(0 , < | $, D_< , D_{0 ,} y).

To generate random draws from these distributions, Markov Chain Monte Carlo (MCMC) processes need to be used. These are a body of methods for generating pseudo-random draws from probability distributions via Markov chains. A Markov chain is fully specified by its starting distribution P(X₀) and the transition kernel P(X_t |X_t-1).

Each MCMC step that involves the vector of binary outcome variables y in the conditioning set needs first to be modified by defining a pseudo-likelihood using survey weights. In defining pseudo-likelihood, weights are introduced after scaling them to the effective sample size based on a suitable design effect. Note that with the pseudo-likelihood, the covariance matrix of the pseudo-score functions is no longer equal to the pseudo-information matrix, and therefore a sandwich-type of covariance matrix was to compute the design effect. In this process, weights are largely assumed to be noninformative (i.e., unrelated to the outcome variable y). The assumption of noninformative weights is useful in finding tractable expressions for the appropriate information matrix of the pseudo score functions. The pseudo log-likelihood remains an unbiased estimate of the finite-population log-likelihood regardless of this assumption.

Step I [$_" | 0, v, y] (this does not depend on D₀, D_v )

With flat prior for $_", the conditional posterior is proportional to the pseudo-likelihood function. For large samples, this posterior can be approximated by the multivariate normal distribution with mean vector equal to the pseudo-maximum likelihood estimate and with asymptotic covariance matrix having the associated sandwich form. Assuming that the survey weights are noninformative makes the age group specific $_" vectors conditionally independent of each other. Therefore, the $_" can be updated separately at each MCMC cycle.

Step II [0_i | $, v_i, D₀, y] (this does not depend on D_v )

Here the conditional posterior is proportional to the product of the prior g(0_i|.), the pseudo-likelihood function f(y|.) as well as the prior p($,D₀); this last prior can be omitted as it does not involve 0_i. To calculate the denominator (or the normalization constant) of the posterior distribution for 0_i requires multidimensional integration and is numerically intractable. To get around this problem, the Metropolis-Hastings (M-H) algorithm is used that requires a dominating density convenient for Monte Carlo sampling. For this purpose, the mode andcurvature of the conditional posterior distribution are used; these can be simply obtained from its numerator. Then a Gaussian distribution is used with matching mode and curvature to define the dominating density for M-H. As with the age group specific $_" parameters, the State-specific random effect vectors 0_i are conditionally independent of each other and can be updated separately at each MCMC cycle.

Step III [v_ij | $, 0_i, D_v, y] (this does not depend on D₀)

Similar to step II.

Step IV [D₀ | 0] , [D_v | v] (here, 0 and v include all the information from y)

Here, the pseudo-likelihood involving design weights comes in implicitly through the conditioning parameters 0 and v evaluated at the current cycle. An exact conditional posterior distribution is obtained because the inverse Wishart priors for D₀ and D_v are conjugate.

Remarks

• In the NHSDA application, three FI regions were combined to form a minimum of four substate regions with corresponding random effects. This was done to ensure adequate sample sizes for estimation purposes.

• There is self-calibration built in to the modeling. This is achieved via design effect-scaling of survey weights incorporated in the conditional posterior density so that small area estimates for large States become asymptotically equivalent to the direct estimates. Similarly, survey-weighted estimates of the fixed parameters (in particular the intercept) give calibration of the aggregate of small area estimates to the national direct estimate.

• For posterior variance estimation purposes, the survey weights were largely assumed to be noninformative. The survey design effects on the posterior variance are therefore restricted to unequal weighting effects. It was assumed that all the design-related clustering effects are represented by between State and between substate (within State) variability of random effects. This does not take care of variability at lower levels of clustering. However, sample size is not sufficient at lower levels to support stable estimates of random effects for area segments.

• If the logistic mixed model fits well, the variance estimates should be reasonable. The self-calibration property provides some protection against model breakdown. Research is currently under way to develop a new MCMC algorithm that fully accounts for survey design effects on the small area estimate posterior prediction intervals.

G.8 Validation and Other Results

The following validation methodology was implemented at the time of the first release of the 1999 NHSDA data (SAMHSA, 2000b) and is based on the seven variables discussed in that report. Subsequently, an error in the imputation program was discovered, and the corrected estimates have been made available on the SAMHSA website. The imputation error should not have affected the results of the validation process in which estimates from repeated simulated samples were compared to the overall direct estimates because the imputation error would have been reflected in both the simulated data and the overall direct estimate. Therefore, those results are presented again below.

To validate the fit of the SAE models, the eight large sample States were used as internal benchmarks. For this purpose, 12 pseudo FI regions within each large sample State were created by pooling the 48 initial regions into groups of 4. Each of these pseudo FI regions were then expected to have 8 area segments per calendar quarter. For each of these pseudo FI region by quarter sets of 8 area segments, any segments that were devoid of interviews were first randomly replaced by a selection from the non-empty segments in the set. The completed set of 8 segments from each pseudo FI region by quarter combination was then randomly partitioned into 4 replicates of 2 segments each. Combined across the 12 pseudo FI regions and the 4 calendar quarters, each of the 4 substate replicates mimicked the size and design structure of a small State sample.

Having created four pseudo small State samples and associated universe level files for each large State, SAEs were then produced for 75 States (43 + 32), including the 43 small States and 32 substate territories defined across the eight large sample States. Tables G.3 and G.4 show these 32 substate SAEs and their direct survey weighted analogs for two of the seven substances included in the validation analysis-one with a medium prevalence, and one with a low prevalence. Full State sample estimates have been included for comparison purposes. Relative absolute biases of the substate estimates are shown where the full State sample direct estimate is used as the benchmark value.

The State specific relative absolute bias (RB) quantities in Tables G.3 and G.4 equal the absolute differences of the averaged four substate small area estimates (SS1, .., SS4) and the State full sample design based benchmark (e.g., California, etc.) divided by the benchmark. The average relative absolute bias (ARB) is the simple average across the eight large States of the RBs. For the two highest prevalence items, binge alcohol and cigarette use, these ARB quantities are quite small; namely 1.30 and 1.71 percent, respectively, for the total age 12 or older age group. For the three items with prevalence rates in the middle range, dependence on illicit drugs or alcohol, marijuana use and any illicit drug use, the ARB measures range from 4.75 to 5.82 percent for the total age group. The two lowest prevalence items, dependence on illicit drugs and use of any illicit drug other than marijuana, have ARBs of 8.38 and 11.49 percent for the total age group. The age groups with the lowest prevalence rates are seen to have the largest ARBs.

Table G.2 provides estimates of the relative absolute bias for the eight large States for three substance measures. The RB for a specific State is the absolute value of the difference between the survey weighted HB estimate and the direct survey estimate based on the full sample, divided by the direct survey estimate. Because models for these States put less reliance on the model, their biases are smaller than for the 42 States and the District of Columbia. For past month use of cigarettes (not shown) among the age 12 or older population, the ARB across the eight States was 1.4 percent. For past month use of any illicit drug, the ARB was 4.2 percent, and for the substance with the lowest prevalence, past year dependence on any illicit drug, the percentage was 7.5.

To compare the overall precision of the small area estimates with the direct survey estimates, ratios of the corresponding 95 percent Bayes (credible) intervals, which fully account for the posterior variance of the fixed and random effect parameters, were compared to the corresponding direct survey confidence intervals. These results are displayed in Tables G.5 and G.6 for past month use of any illicit drug and past year dependence on any illicit drug.

The SAE and direct intervals are summarized by showing average ratios of the relative interval widths (the interval width for a State divided by the corresponding estimate for that State) by State and overall averaged of the ratios across States by outcome. For the eight largeStates for those aged 12 or older, the average ratios are cigarettes .89, any illicit drug .84, and dependence on any illicit drug.78. For the other States and the District of Columbia, the comparable estimates are cigarettes .71, any illicit drug .62, and dependence on any illicit drug .60. This indicates that on average the HB estimates are more precise than the corresponding direct survey estimates.

G.9 Caveats

Table G.1 shows the screening, interview, and overall response rate for each State and the District of Columbia. As mentioned in the text, these variable response rates can be associated with variable levels of nonresponse bias. In addition, there may also be varying levels of response bias as a result of underreporting (and sometimes overreporting) use of illicit substances. For 1999, the assumptions being made are that the biases from these two sources are constant across States so that comparisons among States still hold.

Another possible contributor to bias in the State estimates, and the estimates in general, was the effect of editing and imputation on two substances-past month use of marijuana and past month binge use of alcohol. In developing the editing and imputation process for 1999 and subsequent years, the desire was to minimize the amount of editing that is typically somewhat subjective, and instead let the random imputation process supply any partially missing information. Overall, the percentage of imputed information is quite small for any given substance. The method as described earlier is based on a multivariate imputation in which some demographic and other substance use information from the respondent is used to determine a donor who is similar in those characteristics but has supplied data for the drug in question. Often, information was also available from the partial respondent on the recency of drug use. For example, respondents may have indicated that they used the drug in their lifetime or in the past year, but left blank the question about use in the past month. For many of the records, this auxiliary information was available. In a small portion of the time, no auxiliary information was available, in which case a random donor with similar drug use patterns and demographic characteristics was used. For the different substances, the largest differences between the edited and the imputed estimates typically occurred when there was a lot of auxiliary information. For marijuana, the State with the largest percentage change from edited to imputed data was Alabama, whose edited rate of use of marijuana was 2.1 percent and imputed rate of use was 3.1 percent-a relative increase of almost 50 percent.

Lastly, the differences in State levels of substance use often reflect differences that are due in part to underlying socioeconomic differences. Table G.7 presents State information on a few variables that are may have some association with substance use. These variables include the percentage of persons aged 18 to 25, the percentage of persons by race/ethnicity, the percentage of persons below poverty, the percentage who are urban, the percentage of female heads of household, the unemployment rate, the mean personal income, and the median household income.

00807 (8.1) 

Table G.1 1999 NHSDA Weighted CAI Screening and Interview Response Rates, by State

Source: SAMHSA, Office of Applied Studies, National Household Survey on Drug Abuse, 1999 CAI.

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Table G.2 Percentage Relative Absolute Bias of Selected Past Month Drug Use and Past Year Dependence for the Eight Large States

	Past Month Use								Past Year Dependence Any Illicit Drug
	Cigarette				Any Illicit Drug
State	Total	12-17	18-25	26 or Older	Total	12-17	18-25	26 or Older	Total	12-17	18-25	26 or Older
National	0.57	1.14	0.38	0.79	2.45	1.37	1.16	5.32	6.85	3.30	0.78	14.54
Eight Large States
California	1.77	1.73	1.57	1.83	2.81	0.19	1.03	5.75	1.68	1.20	1.17	3.48
Florida	0.92	10.59	1.43	0.36	1.52	10.42	1.74	3.34	10.02	7.57	0.60	21.32
Illinois	0.75	0.49	0.18	1.12	1.25	3.65	0.30	1.39	7.46	1.39	17.77	3.16
Michigan	4.18	1.63	0.65	5.77	3.82	6.21	3.39	3.39	3.81	0.26	8.61	19.22
New York	1.54	2.21	0.89	2.32	14.32	8.13	2.81	30.79	22.79	16.97	3.73	69.97
Ohio	0.51	2.70	1.83	0.97	4.20	2.46	4.10	10.80	10.66	19.88	2.01	20.40
Pennsylvania	1.08	3.26	0.93	1.37	4.01	3.77	7.39	2.60	2.74	6.49	16.35	2.32
Texas	0.50	1.80	0.81	0.28	1.43	1.76	0.47	2.20	0.88	2.53	10.94	6.70
Eight Large State Average	1.41	3.05	1.04	1.75	4.17	4.58	2.66	7.53	7.51	7.04	7.65	18.32

Relative Absolute Bias=|(Small Area Estimate-Design Based Estimate)|/Design Based Estimate

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Table G.3 Simulated Small State Prevalence Rates and Relative Absolute Bias for Past Month Any Illicit Drug Use

(continued)

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Table G.3 (continued) Simulated Small State Prevalence Rates and Relative Absolute Bias for Past Month Any Illicit Drug Use

Source: SAMHSA, Office of Applied Studies, National Household Survey on Drug Abuse, 1999 CAI.

00811

Table G.4 Simulated Small State Prevalence Rates and Relative Absolute Bias for Past Year Illicit Drug Dependence

(continued)

00811

Table G.4 (continued) Simulated Small State Prevalence Rates and Relative Absolute Bias for Past Year Illicit Drug Dependence

Source: SAMHSA, Office of Applied Studies, National Household Survey on Drug Abuse, 1999 CAI.

00811

Table G.5 Ratio of Relative Widths of Small Area Estimate Prediction Intervals to the Design-Based Confidence Intervals for Past Month Any Illicit Drug Use

Relative Width Ratio=100*(Length of Small Area Estimate Prediction Interval/Small Area Estimate)/(Length of Design-Based Confidence Interval/Design-Based Estimate)

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Table G.6 Ratio of Relative Widths of Small Area Estimate Prediction Intervals to the Design-Based Confidence Intervals for Past Year Illicit Drug Dependence

Relative Width Ratio=100*(Length of Small Area Estimate Prediction Interval/Small Area Estimate)/(Length of Design-Based Confidence Interval/Design-Based Estimate)

00816

Table G.7 Estimated Characteristics of Population Distribution, by State

	Aged 18-251	Hispanic1	Non-Hispanic White1	Non-Hispanic Black1	Persons Below Poverty Level2	Urban3	Female Head of Household4	Unemployment Rate5	Mean Personal Income6	Median Household Income7
Total	12.87	10.41	73.76	11.42	13.20	74.94	6.38	4.20	24,442.53	35,492.00
Alabama	13.10	0.77	74.00	24.12	14.70	60.08	7.06	4.80	20,062.43	29,518.00
Alaska	14.43	4.05	73.50	3.19	8.80	67.40	7.02	6.40	24,597.00	44,280.00
Arizona	13.19	20.17	70.83	2.82	18.10	87.75	6.22	4.40	21,338.84	32,842.00
Arkansas	13.02	1.22	83.07	14.45	17.20	53.00	6.26	4.50	18,966.82	27,392.00
California	13.47	29.77	51.18	6.31	16.30	92.38	6.36	5.20	25,375.41	38,664.00
Colorado	13.06	13.30	80.02	3.79	9.30	81.65	6.18	2.90	25,743.41	38,772.00
Connecticut	11.26	7.76	81.65	8.23	9.90	78.92	5.83	3.20	34,182.94	45,187.00
Delaware	12.26	2.95	77.34	17.51	9.50	72.17	5.94	3.50	27,784.11	39,723.00
District of Columbia	13.00	7.26	30.44	59.36	22.70	100.0	9.64	6.30	34,172.00	34,697.00
Florida	10.68	15.27	70.31	12.63	13.90	84.38	5.69	3.90	24,203.27	31,064.00
Georgia	13.51	2.14	68.89	27.06	14.30	62.57	7.79	4.00	23,034.64	33,919.00
Hawaii	12.03	7.07	29.03	1.40	12.30	88.41	4.74	5.60	25,432.27	43,815.00
Idaho	15.21	6.24	91.08	0.44	13.20	57.66	5.15	5.20	19,861.63	33,114.00
Illinois	13.23	9.58	73.01	14.01	11.10	84.46	6.46	4.30	26,860.13	39,483.00
Indiana	13.38	2.21	89.01	7.63	8.60	64.41	6.06	3.00	22,632.68	35,542.00
Iowa	13.20	1.68	94.96	1.81	9.40	61.04	4.90	2.50	22,329.15	33,783.00
Kansas	13.37	4.71	87.23	5.53	10.10	69.71	5.34	3.00	23,128.73	33,728.00
Kentucky	13.31	0.64	92.06	6.51	15.50	51.24	6.26	4.50	19,786.03	30,418.00
Louisiana	14.48	2.74	65.07	30.54	18.60	67.60	9.12	5.10	19,711.26	28,742.00
Maine	11.61	0.66	97.95	0.26	10.60	44.49	5.68	4.10	21,086.97	32,809.00
Maryland	11.75	3.75	65.59	26.45	8.60	80.43	6.86	3.50	27,679.92	44,206.00
Massachusetts	11.68	6.02	85.50	4.82	10.30	84.08	6.12	3.20	29,810.70	40,831.00
Michigan	12.98	2.46	81.79	13.62	10.80	69.68	7.68	3.80	24,604.04	38,127.00
Minnesota	13.33	1.72	92.09	2.73	9.90	69.75	5.25	2.80	25,703.22	39,690.00
Mississippi	14.34	0.78	64.16	34.10	18.30	47.17	9.12	5.10	17,558.16	26,925.00
Missouri	12.98	1.54	86.77	10.25	10.40	67.68	6.11	3.40	22,991.68	32,791.00
Montana	12.86	1.91	91.74	0.35	16.40	52.23	5.73	5.20	19,280.19	28,707.00