Established by CDC, the Behavioral Risk Factor Surveillance System (BRFSS) is an ongoing state-based surveillance system tracking health conditions and risk behaviors among noninstitutionalized adults aged 18 years or older in the United States. The design of BRFSS aims at generating reliable prevalence estimates at the state level or for large metropolitan statistical areas. Sample size for counties are usually too small for making direct inferences with satisfactory precision. CDC suggests that a sample size of at least 300 is necessary for direct estimation (14,15). To overcome the limitation of small sample sizes, we developed a 2-step estimation method. This method belongs to a family of small-area estimation techniques that includes varied approaches for making inferences about geographic or social subdomains of the survey domain. The power of the small-area estimation method resides on its ability to borrow strength from multiple sources of data — data collected at other times, or in related areas, or both to increase the effective sample size and thus achieve adequate precision. Among current small-area estimation methods, the Hierarchical Bayes approach and generalized linear mixed models have been primary choices (16-18). We used a generalized linear mixed model in this study. We incorporated a generalized linear mixed model and traditional synthetic methods to meet the small-area estimation needs in this study.

We acquired individual-level BRFSS data for Mississippi for 2007 through 2009. Variables included in the analytical dataset were self-reported height and weight and demographic and socioeconomic variables, including age, race, sex, education level, employment status, annual household income, and marital status. We used the Federal Information Processing Standard code as the location variable for county. We categorized BMI as a binary variable, obesity (obesity = 0 if BMI <30 kg/m², obesity = 1 if BMI ≥30 kg/m²). In the original Mississippi BRFSS data, age is a continuous variable. Through initial exploratory data analysis, we found a quadratic relationship between BMI and age. According to the shape of the quadratic regression line, we categorized age into 4 groups: 18 to 29, 30 to 44, 45 to 64, and 65 years or older. We categorized education as less than a bachelor's degree and bachelor's degree or higher. For employment status, we grouped employed for wages and self-employed as "employed," and grouped unemployed temporarily, those unable to work, students, retired people, and homemakers as "unemployed."

The exclusion criteria were 1) missing Federal Information Processing Standard code information (n = 39); 2) missing BMI values or biologically unlikely BMI values (BMI <12 kg/m² or BMI >70 kg/m²) (n = 1,013); 3) pregnant (n = 138); 4) races other than black and white (n = 383). Taking into consideration that in Mississippi 98.5% of the population belongs to 1 of 2 categories, black alone or combined and white alone or combined (19), we excluded the small portion (1.5%) of respondents of other races to facilitate small-area estimation. Respondents who chose black alone or black and other race(s) were categorized as black alone or combined; respondents who chose white alone or white with race(s) other than black were categorized as being in the white alone or combined category. The final analytical dataset of 2007-2009 BRFSS had 25,046 observations.

The data sources for auxiliary information were the 2000 US Census (19) and the US Department of Agriculture Economic Research Service (20). We used the auxiliary information to construct predictor variables for statistical modeling. Auxiliary covariates included county-specific sociodemographic factors such as county population composition of age, sex, race, educational achievement, county unemployment rate, rural-urban continuum characteristics, economic dependence indicators, and poverty indicator. Corresponding to the 4 age categories at the individual level, the auxiliary dataset included 4 age variables, which are the percentages of each age group 18 years or older in the county population.

Modified on the basis of the multilevel logistic regression model of Li and colleagues (13), our 2-step small-area estimation method is a combination of hierarchical modeling and synthetic estimation techniques. This mixed model produces a set of fixed-effect parameter estimates, which are general to all counties, and a set of random-effect parameter estimates, which are county-specific values. First, we identified the independent variables that were significantly associated with obesity by fitting a generalized linear mixed model with the relevant variables, both individual-level and county-level. We used backward elimination to prune the model. To further improve predictability, we set the selection criterion for retaining a variable or interaction term in the model at α = 0.1 (21). In the final model, fixed effects included the following variables: age, sex, race, education level, employment status, survey year, and county-level average per capita annual household income. Random effects included individual-level variables age, sex, race, education level, and survey year. We also calculated odds ratios for associated socioeconomic factors in this step.

In the second step of the estimation, we applied a synthetic technique to link the model-generated parameter estimates to the county-specific characteristics to produce county-level estimates. This way, the strength borrowed through the model is realized for each county. Because random effects were not significant, we used only the fixed-effect values in the calculation. However, following the recommendation of Binder (22), Jiang (23), and Jia et al (24), we kept the random-effects component in the model to improve estimation for fixed effects and to enhance the proper selection of variables (Appendix). We conducted all analyses by using SAS version 9.2 (SAS Institute Inc, Cary, North Carolina) to account for the complex sampling design. We grouped the county-level obesity prevalence estimates into quartiles to examine geographic patterns. We produced the obesity map by using ArcGIS 9.2 (ESRI, Redlands, California).

We assessed the precision of our estimates by using the width of 95% confidence intervals (CIs). Following the example of another study (25), we examined correlations and mean absolute differences between model estimates and internal standards: direct estimates of the state-level obesity rate for 2007 through 2009, and direct estimates for age, sex, and race subgroups. The sample sizes for the 4 age subgroups, 2 sex subgroups, and 2 race subgroups were large enough for reliable direct estimation (range, 663-7,305). Taking into consideration the complex sampling design of BRFSS, we used SAS PROC SURVEYLOGISTIC procedure (SAS Institute, Inc, Cary, North Carolina) for direct estimations to account for the weight of each respondent.

The width of 95% CIs for all county estimates was less than 5 percentage points (range 2.5-4.7 percentage points). This precision was comparable to that of the design-based direct estimates for the state and is considered reliable (25,26). To assess accuracy, we aggregated small-area county-level estimates to the state level for 2007 through 2009 and compared them with their respective state-level direct estimates; we also compared state-level model estimates with state-level direct estimates for 2007 through 2009. We further compared model estimates of age, sex, and race subgroups with their respective direct estimates. Pearson's correlation coefficients between the 2 sets of estimates for the comparisons were 0.95, 0.95, and 0.96, respectively, and the mean absolute differences were 0.5%, 0.5%, and 1.5%, respectively.