We used geocoded NHANES data 2005–2010 at the Research Data Center (RDC) of the National Center for Health Statistics (NCHS), which allows area-level data to be linked to individual-level NHANES data by census tract, county and state. Details about NHANES are described in Appendix A.

We included 2304 children aged 6–9 years with data for untreated caries lesions. The mean age was 7.5 years. The study population was almost equally distributed by sex and single year of age.

Untreated dental caries was defined as a dichotomous variable, presence of at least one primary or permanent tooth with cavitated caries lesions (yes/no). NHANES 2005–2010 used the Basic Screening Examination (BSE), a simplified caries examination conducted by health technologists in 2005–2008 and dental hygienists in 2009–2010 (Centers for Disease Control and Prevention, 2005).

We considered select socio-demographic variables (sex, age, race/ethnicity, poverty status, health insurance status, and survey cycles) from NHANES based on self-report by parents or guardians. Details of these covariates are described in Appendix B.

We selected characteristics at various area levels based on the factors reported to have potential influence on children’s oral health and data availability (Fisher-Owens et al., 2007; Lin et al., 2012). Tract-level percentage of population in poverty was obtained from the 2006–2010 5-year American Community Survey (ACS) (US Census Bureau).

We obtained the following data at both the county and state levels from the Area Health Resources Files (Health Resources and Services Administration): percentage of population in poverty, 2006, 2007–2008, 2009–2010; percentage of population aged 25 + years with high school graduate or higher education, 2005–2010; percentage of children without health insurance, 2008, 2009–2010; percentages of children in individual race/ethnicity groups (Non-Hispanic white, Non-Hispanic black, Hispanic), 2005–2006, 2007–2008, 2009–2010; and dentist population ratio per 10,000 population, 2007, 2009–2010.

We also considered two state-level factors: percentage of children enrolled in Medicaid/Children’s Health Insurance Program (CHIP) receiving dental services in the past year (2005–2006, 2007–2008, 2009) from the Centers for Medicare & Medicaid Services’ CMS-416 reports (Centers for Medicare & Medicaid Services); percentage of population served by Community Water System receiving fluoridated water (2006, 2008, 2010) from biennial reports of the Centers for Disease Control and Prevention (CDC)’s Water Fluoridation Reporting System (Centers for Disease Control and Prevention, 2015). We categorized these area-level variables by quartiles. We used the 2006 NCHS 6-level urban-rural classification scheme for counties: large central metro, large fringe metro, medium metro, small metro, micropolitan, and non-core (Ingram and Franco, 2012).

First, we used NHANES 2005–2010 data linked with tract-, county- and state-level data to construct and fit multilevel logistic regression models to quantify associations between untreated caries and individual and area-level covariates. Details about the model building are described in Appendix C. The final model included sex, age, race/ethnicity, and insurance status at the individual level; poverty rate at the tract level; poverty rate, percentage of 25 + year olds with education level ≥ high school graduate, percentage of Hispanic children, dentist population ratio, and urban-rural classification at the county level; and percentage of Medicaid/CHIP enrolled children receiving dental services at the state level. We included county-level random effects to allow county-variation in the outcome and control unobserved heterogeneity. The multilevel regression models were fitted using SAS 9.3 (SAS Institute, NC) GLIMMIX procedure.

Second, we applied the estimated model parameters to census population data to predict individual-level probability of untreated dental caries given their sex, age, race/ethnicity, health insurance status, and area-level covariates. Child population counts at census tract-level by sex, single-year age and race/ethnicity were available from US Census 2010, but their corresponding health insurance status was unknown. Thus, we further applied a parametric bootstrapping approach to generate individual health insurance status using census tract-level percentages of children by health insurance status, 2008–2012 American Community Survey (ACS) (Zhang et al., 2016). Finally, population-weighted average of the estimated probability of untreated dental caries was generated at census tract level, which was further aggregated to county, state and national levels. We used the Monte Carlo simulation approach (Robert and Casela, 2004) to generate 1000 sets of model parameters and produce 1000 SAEs, which were used to generate final means, 2.5 and 97.5 percentiles (equivalent to 95% confidence intervals [CIs]) for the estimated county-level prevalence of untreated dental caries.

Finally, we compared model-based estimated prevalence of untreated caries at the national level with the direct estimate from NHANES. Although NHANES could not provide direct estimates below the national level that allow internal evaluation of the model-based estimates at state and county levels, we conducted exploratory external comparisons between model-based estimates at state and county levels limited to 8-year-olds and direct estimates from the third-grade SOHS. The Basic Screening Survey was the most common oral health examination protocol referred to by the third-grade SOHS (Centers for Disease Control and Prevention, 2015) and was similar to the BSE protocol used by NHANES 2005–2010. We used publicly available direct estimates and 95% CIs from the third-grade SOHS obtained from the websites of CDC and state health departments. We obtained state-level direct estimates for 34 states with SOHS conducted between 2005 and 2010 from the CDC website (Centers for Disease Control and Prevention, 2015). We obtained county-level direct estimates for 53 counties from the 2009–2011 New York SOHS, available on the New York state health department website (New York State Department of Health, 2016).

The overall county-level variation in the estimated prevalence was significant (P = 0.004) (Table 1). The individual-level variables including age, sex, race/ethnicity and insurance status explained 7.2% of the overall county-level variation. Adding tract and county-level covariates explained the majority of the county-level variance (96.3%) and accordingly the county-level variance in untreated caries was no longer significant (P = 0.43). Fig. 1 depicts model-based county-level estimates of prevalence of untreated caries among children aged 6–9 years nationwide, using the final model. The map illustrates variation in the estimated prevalence across counties, ranging from 4.9% to 65.2% with a median of 22.1% and interquartile range of 14.7%.

The model-based national estimate of prevalence of untreated dental caries (19.9%) among children aged 6–9 years matched the direct estimate from NHANES (19.8%) (Table 2). When stratified by age, sex and race/ethnicity, the model-based estimates were generally similar to the direct estimates and all were contained in the 95% CI of the corresponding direct estimate. The model-based and direct estimates showed similar patterns of variation by the demographic characteristics where the prevalence estimate was higher among eight-year-olds, males, NHB, and Hispanic children than their counterparts.

For 34 states with third-grade SOHS available in 2005–2010, moderate positive correlations (Pearson correlation = 0.54, P = 0.001; Spearman rank correlation = 0.58, P < 0.001) (Table 3 and Fig. 2) were found between model-based state estimates of prevalence of untreated caries for 8-year-olds and the SOHS direct estimates. A paired t-test showed no significant difference between the direct and model-based estimates (P = 0.23). The quartile distribution of the direct estimates roughly mirrored the distribution of the model-based estimates although the interquartile range for model-based estimates (7.4%) was smaller than that for direct estimates (11.5%).

Similar results were found when the direct county-level estimates of prevalence of untreated dental caries for 53 counties from the New York third-grade SOHS 2009–2011 were compared with model-based estimates for these counties. Moderate positive correlation between direct and model-based estimates was observed (Pearson correlation = 0.38, P = 0.006; Spearman rank correlation = 0.29, P = 0.03) (Table 3 and Fig. 2). For example, the model-based estimates and direct estimates both identified Sullivan County with the highest prevalence although its model-based estimate (66.0%) was higher than its direct estimate (52.8%).

Figs. 3 and 4 show generally similar patterns of geographic clustering of the higher and lower prevalence of untreated caries when the model-based estimates for 8-year-olds were compared with direct estimates from the third-grade SOHS at state level for 34 states and at county level for 53 New York counties. About two-thirds of these states (70.6%, 12 out of 17 states) or counties (63%, 17 out of 27 counties) with direct estimates higher than the median were also in the higher than median group when ranked using model-based estimates.

Several limitations of this study should be noted. First, although our internal validation indicated high consistency between model-based and direct estimates at the national level, we were not able to perform internal validation at the state or county level because NHANES is not designed to provide direct estimates at those levels.

Second, although we conducted exploratory external comparisons with direct estimates at state and county levels from select SOHS, they were not external validations per se because several limitations may impact the comparability. For example, the survey design, sampling frames, and oral health examination protocols may not be comparable between SOHS and NHANES. Considering intensive resources required, states conducted independent SOHS. Different states may field SOHS in different years, depending on availability of resources. Survey years of the 34 states ranged from 2005 to 2010. Although we used SAE limited to age 8 years, assuming it to be the most prevalent age for third graders, 8-year-olds and third graders may not be completely comparable.

Third, considering the complex and multifactorial nature of untreated dental caries (Fisher-Owens et al., 2007) our multilevel model may not capture the impact of all factors associated with the outcome. In addition, although we considered various factors at different area levels, the impact of intervention programs or policies or cultural differences specifically at local levels may not be captured by our study. These limitations may explain the moderate correlations from the external comparisons versus the high internal validation performance.

Our study had notable strengths: 1) Our SAE was based on NHANES, which has a long history to provide ongoing and valid population surveillance data on dental caries for the nation based on standardized clinical examination and quality assurance. 2) Our study appears to be the first to demonstrate SAE of county-level untreated caries among children nationwide in the United States. 3) We considered a broad range of characteristics associated with untreated dental caries, ranging from socio-demographics to factors reflecting dental care access, rather than socio-demographics only. 4) We took advantage of MRP and considered factors at both individual and different area levels to capture multilevel influence on untreated dental caries. We reported the extent of county-level variation in untreated caries explained by factors at different levels. 5) Our external comparison performance was relatively comparable with recent SAE studies with MRP for chronic disease indicators using BRFSS, which had a much larger sample size than NHANES.

In addition, caries is the most reported unmet health care need (Vujicic et al., 2016). Strategies to reduce unmet need are typically implemented at local level. Model findings could help identify areas with high unmet dental care needs to inform targeted intervention programs (e.g., dental workforce expansion, school-based dental sealant programs).