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2002-2004 Sub State Report of Substance Use & Serious Psychological Distress

Appendix:

Highest and Lowest Prevalence Substate Regions within Each State and the Statistical Significance (p value) of Their Difference on Selected Variables:

bulletCocaine Use in Past Year    (table)

bulletMarijuana Use in Past Year    (table)

bulletAlcohol Use in Past Month    (table)

Estimation Method:

To test the difference between the prevalence of two substate regions, say region 1 (with the lowest estimate) and region 2 (with the highest estimate), in a particular State, let π1 and π2 denote the respective small area estimates.

We want to test the hypothesis that π2 = π1 or equivalently test π2 - π1 = 0.

The difference between π1 and π2 is defined in terms of the log-odds ratio (lor) as opposed to the simple difference because the posterior distribution of the lor is closer to Gaussian than the posterior distribution of the simple difference (π2 – π1).

The lor is defined as lor = log{[π2 /(1-π2)] ÷ [π1 /(1-π1)]}.

So, the above hypothesis is now transformed to testing lor = 0. To compute the posterior variance of lor- v(lor), we define the log-odds ratio for each of the 1,250 Markov Chain Monte Carlo (MCMC) cycles as follows:

li = log{[p2i) /(1-p2i)] ÷ [p1i /(1-p1i)]}, where i = 1, 2,...,1,250.

In the definition of li above, p2i and p1i denote, respectively, the prevalence estimates of regions 2 and 1 for the i-th MCMC cycle.

Then v(lor) is approximated by The variance v sub l is calculated using the following formula: v sub l is equal to the mean of the squares of the difference between l sub i and l bar over 1,250 cycles, where l bar is the mean of l sub i over 1,250 cycles. where l bar is the mean of l sub i over 1,250 cycles

To calculate the p-value for testing the null hypothesis of no difference (lor = 0), it is assumed that the posterior distribution of lor is normal with mean = image representing L with a bar over it and variance = vl.

With the null value of lor = 0, the Bayes p-value or posterior probability of no difference is p-value = 2*P [Z ≥ abs(z)], where Z is a standard normal random variate,

lowercase z is calculated by dividing l bar by the square root of the variance v sub l, where l bar is the mean of l sub i over 1,250 cycles and v sub l is the variance of l sub i, and abs(z) denotes the absolute value of Z.

Note that the unbenchmarked estimate of the prevalence was used in this significance testing. Also note that for States like New Hampshire, New York, and Texas, prevalences of the substate regions were tested rather than testing the prevalences of the aggregate regions presented on the map. Aggregate estimates for these States were calculated by combining several substate regions (the aggregate estimates are hence more centered, rather than being extreme). So, for the purpose of significance testing of the extreme (min, max) regions, we preferred to test the prevalences of the individual regions.

Tables for past year cocaine use, past month marijuana use, and past month alcohol use are presented in this appendix. Our intent was to choose a few measures that have varying levels of the national prevalence estimates, from very low for cocaine to very high for alcohol use.

 

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Table  T1. Cocaine Use in Past Year, Differences between Lowest and Highest Prevalence Substate Regions within Each State: 2002, 2003, and 2004 NSDUHs
State Lowest Prevalence Substate Region within State Highest Prevalence Substate Region within State p value
Substate Region Name Estimate Substate Region Name Estimate
Alabama Region 1 1.93   Region 2 2.52 0.153
Alaska Rural 1.80 Southeast 2.80 0.047
Arizona Rural North 2.94 Pima 4.28 0.041
Arkansas Areas 2 and 3 1.55 Area 9 2.24 0.059
California Region 14 (Orange) 2.18 Region 4 3.63 0.010
Colorado Region 4 3.00   Regions 2 and 7 4.01 0.125
Connecticut      North Central 2.03   Eastern 2.31 0.513
Delaware Sussex 2.25   Wilmington City 3.15 0.164
District of Columbia Ward 8 2.76   Ward 2 3.70 0.281
Florida District 13 1.85 District 10 (Broward) 2.95 0.018
Georgia Region 1 1.86   Region 4 2.50 0.178
Hawaii Kauai and Maui 1.87   Honolulu 1.99 0.737
Idaho Region 5 1.50   Region 2 1.81 0.359
Illinois Region II 2.27   Region I (Cook) 2.85 0.101
Indiana Southeast 2.05   Central 2.75 0.128
Iowa      Northwest 1.77   Southeast 2.22 0.236
Kansas South Central 1.82   Wichita (Sedgwick) 2.39 0.162
Kentucky Adanta, Cumberland River, and Lifeskills 2.19   Bluegrass, Comprehend, and North Key 2.80 0.180
Louisiana Regions 7 and 8 2.16 Region 1 3.45 0.056
Maine Region 5 2.06 Region 1 (Cumberland) 2.94 0.062
Maryland Montgomery 1.41 Baltimore City 3.52 0.001
Massachusetts      Northeast 2.50 Boston 3.70 0.047
Michigan Western 2.08 Detroit City 3.53 0.024
Minnesota Region 7C 2.09   Region 7A (Hennepin) 2.74 0.154
Mississippi Region 1 1.61   Region 6 2.17 0.183
Missouri Southwest 2.36      Northwest (Jackson) 3.44 0.053
Montana Region 1 1.91   Region 5 2.62 0.106
Nebraska Region 4 1.63 Region 6 2.45 0.041
Nevada Rural 1.77 Washoe 2.44 0.089
New Hampshire Southern 1 (Rockingham) 2.29 Southern 2 3.35 0.039
New Jersey Central 2.03   Southern 2.21 0.679
New Mexico Region 1 2.51 Region 3 (Bernalillo) 3.75 0.020
New York Region 4 1.87 Region 3 3.68 0.001
     North Carolina South Central 1.97   Western 2.34 0.366
     North Dakota Lake Region and South Central 1.48 Southeast 2.27 0.029
Ohio Boards 3, 52, and 85 1.75 Board 25 (Franklin) 2.95 0.006
Oklahoma East Central 1.51 Oklahoma County 2.41 0.025
Oregon Region 2 1.89 Region 1 (Multnomah) 3.10 0.009
Pennsylvania Regions 21, 30, 32, and 49 1.84 Region 18 (Philadelphia) 3.46 0.001
Rhode Island Kent 3.27   Washington 3.74 0.471
South Carolina Region 3 2.40   Region 4 2.84 0.442
South Dakota Region 6 1.48 Region 3 (Minnehaha) 2.18 0.042
Tennessee Region 5 1.99 Region 4 (Davidson) 3.39 0.009
Texas Region 3bc 2.05 Region 7a 3.31 0.010
Utah Central, Four Corners, San Juan, and Southwest 1.56   Salt Lake County 2.04 0.161
Vermont Rural Southeast 2.27 Champlain Valley 3.70 0.005
Virginia Region 2 2.10   Region 5 2.53 0.387
Washington Region 6 1.97   Region 5 2.24 0.490
West Virginia Eastern Highland 2.05      Northern C and D 3.30 0.009
Wisconsin      Northern 2.31   Milwaukee 3.11 0.152
Wyoming Judicial District 8 1.68 Judicial District 2 2.93 0.003
NOTE: p value: Bayes posterior probability of no difference.
NOTE: Estimates are based on a survey-weighted hierarchical Bayes estimation approach.
a Difference is statistically significant at the 0.05 level.
b Difference is statistically significant at the 0.10 level.
Source: SAMHSA, Office of Applied Studies, National Survey on Drug Use and Health, 2002, 2003, and 2004.

60627

 

Table  T2. Marijuana Use in Past Month, Differences between Lowest and Highest Prevalence Substate Regions within Each State: 2002, 2003, and 2004 NSDUHs
State Lowest Prevalence Substate Region within State Highest Prevalence Substate Region within State p value
Substate Region Name Estimate Substate Region Name Estimate
Alabama Region 1 3.98   Region 2 5.15 0.132
Alaska Rural 8.19   Urban 10.72 0.100
Arizona Rural South 4.69   Pima 6.41 0.108
Arkansas Areas 2 and 3 4.64 Area 9 6.75 0.056
California Region 6 (Santa Clara) 5.24 Region 1 11.43 0.000
Colorado Region 4 5.60 Regions 2 and 7 8.58 0.013
Connecticut Southwest 4.96      Northwestern 8.88 0.003
Delaware Sussex 4.87 Wilmington City 7.46 0.022
District of Columbia Ward 4 6.13 Ward 2 9.60 0.019
Florida District 13 3.92 District 2 9.21 0.000
Georgia Region 1 3.87 Region 3 6.62 0.003
Hawaii Honolulu 5.89 Kauai and Maui 10.86 0.001
Idaho Region 7 3.82 Region 2 6.24 0.022
Illinois Region IV 4.48 Region I (Cook) 6.38 0.007
Indiana      Northeast 4.70 Central 6.67 0.073
Iowa      Northwest 3.72   Southeast 4.85 0.198
Kansas West 3.48 Kansas City Metro 5.65 0.015
Kentucky Adanta, Cumberland River, and Lifeskills 4.40 Seven Counties 8.40 0.001
Louisiana Regions 5 and 6 4.32 Region 1 7.32 0.009
Maine Region 7 6.74 Region 1 (Cumberland) 9.22 0.075
Maryland Western 4.30 Baltimore City 6.96 0.008
Massachusetts Metrowest 6.70 Boston 9.66 0.025
Michigan Western 5.83 Genesee 9.23 0.027
Minnesota Region 7C 5.10 Region 7A (Hennepin) 7.58 0.022
Mississippi Region 1 3.77 Region 7 5.51 0.063
Missouri Southeast 4.73      Northwest (Jackson) 7.71 0.014
Montana Region 3 6.89 Region 5 9.66 0.037
Nebraska Regions 1 and 2 4.06 Region 6 6.16 0.027
Nevada Rural 6.29 Washoe 9.02 0.037
New Hampshire Central 1 8.18 Southern 2 10.71 0.058
New Jersey      Northern 4.41   Central 5.15 0.365
New Mexico Region 4 6.66 Region 3 (Bernalillo) 9.22 0.061
New York Region 4 5.13 Region 3 10.73 0.000
     North Carolina Eastern 4.52 Western 6.69 0.021
     North Dakota Badlands and West Central 4.55 Southeast 6.87 0.012
Ohio Boards 20, 32, 54, and 69 4.19 Board 57 (Montgomery) 9.55 0.000
Oklahoma East Central 3.86 Oklahoma County 6.76 0.009
Oregon Region 5 7.16 Region 1 (Multnomah) 11.08 0.014
Pennsylvania Regions 17, 24, 27, 43, and 47 4.12 Region 1 (Allegheny) 7.56 0.000
Rhode Island Kent 8.26 Washington 12.01 0.023
South Carolina Region 3 4.91   Region 4 5.66 0.454
South Dakota Region 6 3.72 Region 2 6.87 0.004
Tennessee Region 5 3.75 Region 4 (Davidson) 6.78 0.003
Texas Region 11c (Hidalgo) 3.41 Region 7a 7.51 0.000
Utah Central, Four Corners, San Juan, and Southwest 2.79 Salt Lake County 5.08 0.003
Vermont Rural Southeast 8.37 Champlain Valley 10.96 0.065
Virginia Region 4 5.09   Region 3 5.84 0.449
Washington Region 2 5.66   Region 4 (King) 7.30 0.171
West Virginia South Central I 4.62      Northern C and D 6.49 0.072
Wisconsin Western 4.87 Milwaukee 7.25 0.035
Wyoming Judicial District 8 3.89 Judicial District 2 7.21 0.002
NOTE: p value: Bayes posterior probability of no difference.
NOTE: Estimates are based on a survey-weighted hierarchical Bayes estimation approach.
a Difference is statistically significant at the 0.05 level.
b Difference is statistically significant at the 0.10 level.
Source: SAMHSA, Office of Applied Studies, National Survey on Drug Use and Health, 2002, 2003, and 2004.

60627

 

Table  T3. Alcohol Use in Past Month, Differences between Lowest and Highest Prevalence Substate Regions within Each State: 2002, 2003, and 2004 NSDUHs
State Lowest Prevalence Substate Region within State Highest Prevalence Substate Region within State p value
Substate Region Name Estimate Substate Region Name Estimate
Alabama Region 1 35.60   Region 2 40.26 0.116
Alaska Rural 34.24 Southeast 52.56 0.000
Arizona Rural South 43.56 Pima 53.22 0.015
Arkansas Areas 4 and 7 32.50 Area 9 45.55 0.000
California Region 8 42.74 Region 4 59.91 0.000
Colorado Region 4 49.19 Region 3 61.80 0.002
Connecticut South Central 58.18        Northwestern 63.27 0.127
Delaware Sussex 44.66 New Castle (excluding Wilmington city) 57.72 0.000
District of Columbia Ward 8 42.60 Ward 3 74.68 0.000
Florida District 14 45.50 District 8 58.73 0.000
Georgia Region 1 36.50 Region 3 52.43 0.000
Hawaii Honolulu 47.30   Kauai and Maui 49.53 0.483
Idaho Region 7 36.31 Region 4 55.78 0.000
Illinois Region III 47.17 Region II 55.81 0.000
Indiana Southeast 41.01 West 51.72 0.005
Iowa Southwest 52.70        Northeast 56.49 0.271
Kansas West 42.51 Kansas City Metro 53.86 0.001
Kentucky Kentucky River, Mountain, and Pathways 30.06 Seven Counties 48.55 0.000
Louisiana Regions 7 and 8 40.66 Region 10 (Jefferson) 53.28 0.000
Maine Region 7 42.91 Region 1 (Cumberland) 59.30 0.000
Maryland Prince George's 44.28 Montgomery 60.84 0.000
Massachusetts Central 55.29 Metrowest 65.24 0.004
Michigan Detroit City 39.44 Washtenaw 62.52 0.000
Minnesota Regions 1 and 2 52.93 Region 7C 64.67 0.001
Mississippi Region 2 30.75 Region 7 43.40 0.000
Missouri Southeast 41.89 Eastern (St. Louis City and County) 57.53 0.000
Montana Region 1 50.44 Region 4 60.57 0.005
Nebraska Region 4 48.90 Region 6 56.23 0.026
Nevada Clark 47.31 Washoe 53.80 0.034
New Hampshire Central 1 57.30 Southern 1 (Rockingham) 63.43 0.078
New Jersey Southern 53.51 Central 62.30 0.009
New Mexico Region 4 40.52 Region 3 (Bernalillo) 55.12 0.000
New York Region 1 41.05 Region 5 62.56 0.000
     North Carolina Eastern 36.48 Western 43.18 0.021
     North Dakota Lake Region and South Central 49.91 Southeast 64.79 0.000
Ohio Boards 27, 71, and 73 37.28 Board 25 (Franklin) 55.49 0.000
Oklahoma East Central 35.36 Tulsa County 48.46 0.001
Oregon Region 5 51.38 Region 1 (Multnomah) 57.87 0.094
Pennsylvania Regions 5, 20, 26, 28, and 40 44.00 Region 1 (Allegheny) 58.90 0.000
Rhode Island Providence 56.72 Washington 66.23 0.004
South Carolina Region 3 40.23   Region 4 45.44 0.136
South Dakota Region 6 53.58 Region 3 (Minnehaha) 61.99 0.014
Tennessee Region 6 29.93 Region 4 (Davidson) 43.77 0.000
Texas Region 11c (Hidalgo) 33.90 Region 7a 57.73 0.000
Utah Utah County 19.75 Salt Lake County 35.14 0.000
Vermont Rural Northeast 53.95 Champlain Valley 62.39 0.004
Virginia Region 3 42.15 Region 2 58.68 0.000
Washington Region 2 46.26 Region 4 (King) 59.78 0.000
West Virginia Southern II 27.56      Northern A and B 41.51 0.000
Wisconsin Milwaukee 58.03   Southeastern 62.77 0.175
Wyoming Judicial District 3 46.95 Judicial District 2 55.75 0.014
NOTE: p value: Bayes posterior probability of no difference.
NOTE: Estimates are based on a survey-weighted hierarchical Bayes estimation approach.
a Difference is statistically significant at the 0.05 level.
b Difference is statistically significant at the 0.10 level.
Source: SAMHSA, Office of Applied Studies, National Survey on Drug Use and Health, 2002, 2003, and 2004.

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