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Prev Chronic Dis ; King County, Washington, fares well overall in many health indicators. However, county-level data mask disparities among subcounty areas. For disparity-focused assessment, a demand exists for examining health data at subcounty levels such as census tracts and King County health reporting areas HRAs.

To overcome small sample size at the census tract level, we used hierarchical Bayesian models to obtain smoothed estimates in cigarette smoking rates at the census tract and HRA levels. We also used multiple imputation to adjust for missing values in census tracts. The Bayesian model provided estimation with improved precision at the census tract and HRA levels. Multiple imputation can be used to account for missing geographic data.

Small-area estimation, which has been used for King County public health programs, has increasingly become a useful tool to meet the demand of presenting data at more granular levels. King County, Washington, is the 13th largest county in the United States; it had 2. Although King County fares well in many health indicators compared with other large counties in the United States 1 , county-level data mask large disparities among subcounty areas 2.

For disparity-focused assessment, a strong demand exists for examining data at the subcounty level, such as census tracts and locally defined areas. Although zip codes are useful for subcounty-level analysis, they do not conform to the boundaries of city, county, or other census geographic units such as census tracts. The intersections are geocoded to define subcounty areas with more granularity and flexibility while protecting respondent confidentiality by not asking for home addresses.

For smaller areas, small sample size becomes an issue. In such situations, small area estimation SAE techniques can be used to derive optimal estimates and increase precision 3. In recent years, many SAE studies examined the geographic distribution of health indicators at the county and subcounty levels 3� The methods used were synthetic estimation, the head-banging algorithm, multilevel regression, and Bayesian models.

The subcounty-level studies showed significant geographic disparities and demonstrated the importance of examining data below the county level. Cigarette smoking was chosen for illustration, but the method may be applied to other indicators. The modeling method is described here briefly in a less technical way than the modeling method described in the Appendix. In Washington State, the Department of Health manages data collection, and the survey is administered in English and Spanish.

The department gives organizations an opportunity to add questions beyond the core questions. However, zip code�defined areas are still relatively large, and they do not align well with census tracts or census block-group�based areas such as cities or the King County HRAs.

This information will never be released or analyzed individually and will be used to group your responses with others from your neighborhood.

Please name the 2 cross-streets of this intersection. For this analysis of BRFSS data, we examined 5 years of combined data from through on 16, respondents, excluding respondents with non-King County zip codes or missing data on zip codes. We manually reviewed each address that did not batch match.

Of the census tracts in King County, 3 were dropped from the analysis because of their special features During the 5-year period for the remaining census tracts, the sample size ranged from 4 to , with a median sample of Excluding respondents with missing data on census tracts might mask some of the subcounty disparities at the census-tract level; therefore, we employed a multiple imputation procedure so that all respondents could be included.

Another common subcounty reporting geographic unit in King County is the HRA, which is defined by census blocks. Forty-eight HRAs encompass individual cities, groups of smaller cities or unincorporated areas, and neighborhoods in larger cities. Because the size of HRAs is generally larger than zip code areas, subjects with missing HRAs can be imputed based on zip codes with a relatively lower rate of misclassification than at the census tract level.

In addition, routine direct estimation requires fixed HRA designation of the respondents, making the multiple imputation method impractical.

For example, the adult population in zip code is 23, divided among 3 HRAs: We randomly assigned respondents in zip code with missing data on geocode to one of these 3 HRAs by this distribution. Sample size for the 5-year combined data ranged from to respondents with a median of per HRA. Although the sample sizes at the HRA level are sufficiently large for direct estimation, SAE models can be used for HRA-level analysis for single-year estimation, for indicators that are limited to subpopulations eg, mammography screening among women aged 50�74 y , and for other situations where improved precision is desired.

A current smoker was defined as a respondent who smoked at least cigarettes in his or her entire life and who now smokes every day or some days. Iterative proportional fitting or raking 16 was the method used for generating survey weights, which were based on single years of data and 8 raking margins using King County population estimates.

Missing census tracts can be imputed on the basis of zip codes. Single imputation methods are fixed or random assignment using certain weights 17, However, on average, in King County a zip code contains 7 census tracts. When sample size at the census tract level is relatively small, single imputation methods are subject to high levels of misclassification. In addition, single imputation does not take uncertainty associated with imputation into account and therefore underestimates variance.

Multiple imputation is a method that can reduce differential bias because it does not assign Expensive Lake Boats Zip Codes a respondent to a fixed, single census tract. Rather, through an iterative process, respondents with missing data on census tracts are randomly allocated to a census tract within a zip code multiple times.

Each multiple allocation is based on the ratio of residential Donzi Boats Models Zip Codes addresses in a census tract to the total number of residential addresses in the entire zip code. The allocation process was integrated into the SAE model and repeated times. In addition, multiple imputation accounts for the uncertainty of missing data imputation in calculating the standard errors of the estimates 20 Appendix B.

Our approach summarized the data in each census tract via the asymptotic distribution of the Horvitz�Thompson 21 , or direct, estimator of the census tract level proportion. In this way the design is acknowledged in both the estimator and the variance.

We defined the area-level data summary as the empirical logistic transform of the direct estimator. This approach constrained the probability to lie in 0,1. This inverse logit transformation allowed us to fit our spatial model but still constrained the prevalence estimates to be between 0 and 1.

We employed 3-stage models; the first stage was given by the asymptotic distribution. The second stage of the model introduced spatial random effects at the census tract or HRA level, which allowed for borrowing information between areas and induced smoothing. The third stage required the selection of hyperparameters 22, This approach performed well in an SAE context and was applied to one year of zip code-level BRFSS data 22 and extended for SAE of complex survey data with smoothing in time and space; this approach was applied to estimating child mortality We calculated the sum of log-transformed conditional predictive ordinates to compare various models for the spatial random effects at the second stage.

The hierarchical Bayesian model with the highest sum log-conditional predictive ordinates was selected and is described further in Appendix C. No other covariates were included, because many of the covariates of interest were already accounted for in the raking procedure. The modeling procedures were programmed in the R survey package, version 3. Direct estimates were calculated by using the svyglm function of the R survey package 25 from which the design-based variance was extracted.

Appendix D provides details for how the smoothed estimates from each imputed data set were combined to generate the final census tract estimates and credible intervals. Because of the small sample sizes and wide CIs, results from direct estimation for most of the census tracts are unreliable.

In addition, 38 census tracts had no respondents self-identifying as a current smoker. Missing census tract data not only reduced sample size but also could have resulted in biased estimates. Method A generates an unreliable and biased estimate, method B is subject to missing data bias, and method C attempts to correct for both the small sample size and missing data problems.

Appendix D describes how to create such intervals. The corresponding CI-half-width for census tract with nonzero rates ranged from 1 percentage point to 37 percentage points with a median of 13 percentage points. Method C rates ranged from 5 percentage points to 28 percentage points with a median of 12 percentage points, and the CI-half-width ranged from 4 percentage points to 13 percentage points with a median of 8 percentage points Table 1.

Appendix E presents scatter plots that compare direct estimates with smoothed estimates. Results varied by geographic estimation methods Figure 1. By method A, high smoking rates are scattered throughout different regions of the county. By methods B and C, however, high smoking rates are more or less concentrated in south Seattle and South County. Figure 1. Current smoking prevalence by census tract among King County adults. Maps illustrate 3 methods for estimating smoking prevalence rates by census tract.

Map A is based on the direct estimation method. Map B shows smoothed estimates derived from our small area estimation model hierarchical Bayesian model for respondents with complete information on geocoded census tracts.

Respondents with missing data on census tracts were excluded from this analysis. Map C combines the smoothed and the multiple imputation methods to present estimates generated by using both the small area estimation model and multiple imputation to include all Taylor Jet Boats Models Zip Codes respondents.

The correlation coefficients are 0. The SAE smoothed rates ranged from 7. Figure 2. Model-based current smoking prevalence percentage among King County adults by King County health reporting areas. The map shows smoothed smoking prevalence rates. Estimates were generated by using a spatial hierarchical Bayesian model. Using the BRFSS data for King County, Washington, we generated hierarchical Bayesian models to estimate the prevalence Cigarette Boats Models 020 of current smoking among adults at the level of subcounty geographic areas, including census tracts and HRAs.

We defined these more granular geographic areas on the basis of answers to the nearest intersection question we added to the King County BRFSS sample, which provided a convenient method for generating geocoded data while protecting the privacy of survey respondents. To overcome the problem of small sample size for small areas, we used a spatial Bayesian model to generate smoothed estimation to improve precision. The model also took into account survey weights to adjust for selection bias.

Multiple imputation was used to account for missing data in census tracts. The smoothing models did not rely on auxiliary demographic or socioeconomic-status data, making it easier to apply the models to various BRFSS indicators. A limitation of our study was use of data on nearest intersection as a proxy for actual home address, making misclassification into census tract and HRA a possibility. Possible solutions for this limitation could be combining more years of data or aggregating the census tract to even larger areas.

Finally, we were unable to identify reliable direct-estimate data to serve as gold standards to validate our SAE census tract results.

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