Small Area Models Research Articles

Small Area Estimation of PSA Testing in US States and Counties.

In 2012, the US Preventive Services Task Force recommended against prostate cancer screening using the PSA test for all age groups. In 2018, the US Preventive Services Task Force's recommendation shifted from a "D" (not recommended) to a "C" (selectively offering PSA-based screening based on professional judgment and patient preferences) in men ages 55 to 69. Limited reliable county-level prostate cancer screening data are available for cancer surveillance purposes. Utilizing data from the National Health Interview Survey (NHIS) and Behavioral Risk Factor Surveillance System (BRFSS) collected in 2012 to 2019, state- and county-level small area models were developed for estimating PSA testing. Model diagnosis, internal validation, and external validation examining associations of PSA testing and prostate cancer incidence were conducted. Model-based estimates of PSA testing rates were produced for all US states and 3,142 counties for two data periods: 2012 to 2016 and 2018 to 2019. Geographic variations across counties were demonstrated through maps. Moderate positive correlations between PSA-based screening and prostate cancer incidence were observed, e.g., the state-level weighted Pearson's correlation coefficients were 0.5025 (P value = 0.0002) and 0.3691 (P value = 0.0077) for 2012 to 2016 and 2018 to 2019, respectively. These modeled estimates showed improved precision and adjusted for the differences between the BRFSS and NHIS. The approach of combining the NHIS and BRFSS utilized strengths of the larger sample size of the BRFSS and generally higher response rates and better household coverage from the NHIS. The resulting small area estimates offer a valuable resource for the cancer surveillance community, aiding in targeted interventions, decision making, and further research endeavors.

Issues Associated With the Formulation of a Small Area Model for Estimation of State-Level Crime Victimization Rates

Subnational estimation is an important and challenging problem in the context of the National Crime Victimization Survey (NCVS). Direct estimates for subnational domains are often unreliable due to small sample sizes. Model-based procedures have potential to improve upon direct estimators. However, model-based estimation presents several new challenges. One must identify suitable covariates, and an appropriate model form must be specified. This article discusses issues associated with the formulation of a small area model for production of state-level estimates of crime victimization rates. An analysis of direct estimates and covariates motivates the development of a Bayesian multivariate model. A model in the original scale is compared to a model in the log scale. Efficiency gains from the model relative to the direct estimators are examined. One challenge is that direct estimates can equal zero. Two ways of handling zero direct estimates are discussed.

Impact of the use of small-area models on estimation of attributable mortality at a regional level.

The objective of this study is to assess the impact of applying prevalences derived from a small-area model at a regional level on smoking-attributable mortality (SAM). A prevalence-dependent method was used to estimate SAM. Prevalences of tobacco use were derived from a small-area model. SAM and population attributable fraction (PAF) estimates were compared against those calculated by pooling data from three national health surveys conducted in Spain (2011-2014-2017). We calculated the relative changes between the two estimates and assessed the width of the 95% CI of the PAF. Applying surveys-based prevalences, tobacco use was estimated to cause 53 825 (95% CI: 53 182-54 342) deaths in Spain in 2017, a figure 3.8% lower obtained with the small-area model prevalences. The lowest relative change was observed in the Castile-La Mancha region (1.1%) and the highest in Navarre (14.1%). The median relative change between regions was higher for women (26.1%), population aged ≥65 years (6.6%), and cardiometabolic diseases (9.0%). The differences between PAF by cause of death were never greater than 2%. Overall, the differences between estimates of SAM, PAF, and confidence interval width are small when using prevalences from both sources. Having these data available by region will allow decision-makers to implement smoking control measures based on more accurate data.

An Application of a Small Area Procedure with Correlation Between Measurement Error and Sampling Error to the Conservation Effects Assessment Project

County level estimates of mean sheet and rill erosion from the Conservation Effects Assessment Project (CEAP) are useful for program development and evaluation. Since county sample sizes in the CEAP survey are insufficient to support reliable direct estimators, small area estimation procedures are needed. The quantity of water runoff is a useful covariate but is unavailable for the full population. We use an estimate of mean runoff from the CEAP survey as a covariate in a small area model with sheet and rill erosion as the response. As the runoff and sheet and rill erosion are estimators from the same survey, the measurement error in the covariate is important as is the correlation between the measurement error and the sampling error. We conduct a detailed investigation of small area estimation in the presence of a correlation between the measurement error in the covariate and the sampling error in the response. In simulations, the proposed predictor is superior to small area predictors that assume the response and covariate are uncorrelated or that ignore the measurement error entirely.

Prediction in non-sampled areas under spatial small area models

Prediction in non-sampled areas under spatial small area models

Mapping TB incidence across districts in Uganda to inform health program activities.

Identifying spatial variation in TB burden can help national TB programs effectively allocate resources to reach and treat all people with TB. However, data limitations pose challenges for subnational TB burden estimation. We developed a small-area modeling approach using geo-positioned prevalence survey data, case notifications, and geospatial covariates to simultaneously estimate spatial variation in TB incidence and case notification completeness across districts in Uganda from 2016-2019. TB incidence was estimated using 1) cluster-level data from the national 2014-2015 TB prevalence survey transformed to incidence, and 2) case notifications adjusted for geospatial covariates of health system access. The case notification completeness surface was fit jointly using observed case notifications and estimated incidence. Estimated pulmonary TB incidence among adults varied >10-fold across Ugandan districts in 2019. Case detection increased nationwide from 2016 to 2019, and the number of districts with case detection rates >70% quadrupled. District-level estimates of TB incidence were five times more precise than a model using TB prevalence survey data alone. A joint spatial modeling approach provides useful insights for TB program operation, outlining areas where TB incidence estimates are highest and health programs should concentrate their efforts. This approach can be applied in many countries with high TB burden.

Mortality attributable to secondhand smoke exposure in the autonomous communities of Spain

Introduction and objectivesExposure to secondhand smoke (SHS) causes cardiovascular disease, respiratory disease, and cancer. The aim of this study was to estimate the mortality attributed to SHS in people aged ≥ 35 years in Spain and its autonomous communities (AC) by sex from 2016 to 2021. MethodsEstimates of SHS-attributable mortality were calculated by applying the prevalence-dependent method where SHS exposure was derived from the adjustment of small-area models and based on the calculation of population-attributed fractions. Sex, age group, AC, and cause of death (ischemic heart disease and lung cancer) were included. The estimates of attributed mortality are presented with their 95% confidence interval (95%CI). Crude and age-standardized rates were estimated for each sex and AC. ResultsFrom 2016 to 2021, SHS exposure caused 4,970 (95%CI, 4,787-5,387) deaths, representing 1.6% of total mortality for ischemic heart disease and lung cancer. The burden of attributed mortality differed widely among the AC, with Andalusia having the highest burden of attributed mortality (crude rate: 46.6 deaths per 100 000 population in men and 17.0/100 000 in women). In all the AC, the main cause of death in both sexes was ischemic heart disease. The highest burden of mortality was observed in nonsmokers. ConclusionsThe burden of SHS-attributable mortality was high and varied geographically. The results of this study should be considered to advance tobacco control legislation in Spain.

Small area estimates for Voting Rights Act Section 203(b) coverage determinations

The Director of the US Census Bureau every five years, under the Voting Rights Act (VRA) Section 203(b), determines which states and political subdivisions must provide ballot assistance in languages other than English. These rule-based determinations use small-area estimates of the proportions of voting-age citizen members of racial/ethnic Language Minority Groups (LMGs) who are limited Englishproficient (LEP) and of LEP LMG persons who are also illiterate. This large-scale Small Area Estimation (SAE) effort by the US Census Bureau is based on American Community Survey five-year data. This paper focuses on the unique attributes of this SAE problem, including the predominance in each LMG of tiny domains along with relatively few large domains that account for the bulk of LMG citizens. The data and small area models are treated separately for distinct LMGs, and the spirit of the law requires that the domain estimates should be produced in a similar way across LMGs for each type of geography (Jurisdictions, which are mostly counties, plus two types of American Indian and Alaskan Native areas). The paper describes and assesses the SAE models developed under unique constraints, including novel methodological aspects and the use of hybrid frequentist and Bayesian computational techniques; situates these modelling choices in the broader literature on SAE; and discusses the strengths and weaknesses of the resulting models.

Mortalidad atribuida a la exposición al humo ambiental de tabaco en las comunidades autónomas de España

Introduction and objectivesExposure to secondhand smoke (SHS) causes cardiovascular disease, respiratory disease, and cancer. The aim of this study was to estimate the mortality attributed to SHS in people aged ≥ 35 years in Spain and its autonomous communities (AC) by sex from 2016 to 2021. MethodsEstimates of SHS-attributable mortality were calculated by applying the prevalence-dependent method where SHS exposure was derived from the adjustment of small-area models and based on the calculation of population-attributed fractions. Sex, age group, AC, and cause of death (ischemic heart disease and lung cancer) were included. The estimates of attributed mortality are presented with their 95% confidence interval (95%CI). Crude and age-standardized rates were estimated for each sex and AC. ResultsFrom 2016 to 2021, SHS exposure caused 4,970 (95%CI, 4,787-5,387) deaths, representing 1.6% of total mortality for ischemic heart disease and lung cancer. The burden of attributed mortality differed widely among the AC, with Andalusia having the highest burden of attributed mortality (crude rate: 46.6 deaths per 100 000 population in men and 17.0/100 000 in women). In all the AC, the main cause of death in both sexes was ischemic heart disease. The highest burden of mortality was observed in nonsmokers. ConclusionsThe burden of SHS-attributable mortality was high and varied geographically. The results of this study should be considered to advance tobacco control legislation in Spain.

Improved Indicators for Subnational Unmet Antiretroviral Therapy Need in the Health System: Updates to the Naomi Model in 2023.

Quantifying subnational need for antiretroviral therapy (ART) for HIV is challenging because people living with HIV (PLHIV) access health facilities in areas that may differ from their residence. We defined and demonstrated new indicators for PLHIV treatment needed to guide health system target setting and resource allocation. Botswana. We extended Naomi, a Bayesian small-area model for estimating district-level HIV indicators from national household survey and HIV service delivery data. We used model outputs for ART seeking probabilities in neighboring districts to define the "PLHIV (attending)" indicator representing the estimated number of PLHIV who would seek treatment at health facilities in a district, and "Untreated PLHIV attending" representing gaps in ART service provision. Botswana 2021 district HIV estimates were used to demonstrate new outputs and assess the sensitivity to uncertainty in district population sizes. Across districts of Botswana, estimated adult ART coverage in December 2021 ranged 90%-96%. In the capital city Gaborone, there were 50,400 resident PLHIV and 64,200 receiving ART, of whom 24% (95% CI: 20 to 32) were estimated to reside in neighboring districts. Applying ART attendance probabilities gave a "PLHIV attending" denominator of 68,300 and unmet treatment need of 4100 adults (95% CI: 3000 to 5500) for Gaborone health facilities. The facility-based "PLHIV attending" denominator was less-sensitive to fluctuations in district population size assumptions. New indicators provided more consistent targets for HIV service provision, but are limited by ART data quality. This challenge will increase as treatment coverage reaches high levels and treatment gaps are smaller.

Estimating county-level vaccination coverage using small area estimation with the National Immunization Survey-Child

The National Immunization Survey-Child (NIS-Child) provides annual vaccination coverage estimates in the United States for children aged 19 through 35 months, nationally, for each state, and for select local areas and territories. There is a need for vaccination coverage estimates for smaller geographic areas to support local authority planning and identify counties with potentially low vaccination coverage for possible further intervention. We describe small area estimation methods using 2008-2018 NIS-Child data to generate county-level estimates for children up to two years of age born 2007-2011 and 2012-2016. We applied an empirical best linear unbiased prediction method to combine direct estimates of vaccination coverage with model-based prediction using county-level predictors regarding health and demographic characteristics. We review the predictors commonly selected for the small area models and note multiple predictors related to barriers to vaccination.

Estimating regional unemployment with mobile network data for Functional Urban Areas in Germany

The ongoing growth of cities due to better job opportunities is leading to increased labour-related commuter flows in several countries. On the one hand, an increasing number of people commute and move to the cities, but on the other hand, the labour market indicates higher unemployment rates in urban areas than in the surrounding areas. We investigate this phenomenon on regional level by an alternative definition of unemployment rates in which commuting behaviour is integrated. We combine data from the Labour Force Survey with dynamic mobile network data by small area models for the federal state North Rhine-Westphalia in Germany. From a methodical perspective, we use a transformed Fay–Herriot model with bias correction for the estimation of unemployment rates and propose a parametric bootstrap for the mean squared error estimation that includes the bias correction. The performance of the proposed methodology is evaluated in a case study based on official data and in model-based simulations. The results in the application show that unemployment rates (adjusted by commuters) in German cities are lower than traditional official unemployment rates indicate.

An empirical study of hierarchical Bayes small area estimators using different priors for model variances

In this paper, we study hierarchical Bayes (HB) estimators based on different priors for small area estimation. In particular, we use inverse gamma and flat priors for variance components in the HB small area models of You and Chapman (2006) and You (2021). We evaluate the HB estimators through a simulation study and real data analysis. Our results indicate that using the inverse gamma prior for the variance components in the HB models can be very effective.

Validation of a small-area model for estimation of smoking prevalence at a subnational level.

Small-area estimation methods are an alternative to direct survey-based estimates in cases where a survey's sample size does not suffice to ensure representativeness. Nevertheless, the information yielded by small-area estimation methods must be validated. The objective of this study was thus to validate a small-area model. The prevalence of smokers, ex-smokers, and never smokers by sex and age group (15-34, 35-54, 55-64, 65-74, ≥75 years) was calculated in two Spanish Autonomous Regions (ARs) by applying a weighted ratio estimator (direct estimator) to data from representative surveys. These estimates were compared against those obtained with a small-area model applied to another survey, specifically the Spanish National Health Survey, which did not guarantee representativeness for these two ARs by sex and age. To evaluate the concordance of the estimates, we calculated the intraclass correlation coefficient (ICC) and the 95% confidence intervals of the differences between estimates. To assess the precision of the estimates, the coefficients of variation were obtained. In all cases, the ICC was ≥0.87, indicating good concordance between the direct and small-area model estimates. Slightly more than eight in ten 95% confidence intervals for the differences between estimates included zero. In all cases, the coefficient of variation of the small-area model was <30%, indicating a good degree of precision in the estimates. The small-area model applied to national survey data yields valid estimates of smoking prevalence by sex and age group at the AR level. These models could thus be applied to a single year's data from a national survey, which does not guarantee regional representativeness, to characterize various risk factors in a population at a subnational level.

A small area model to assess temporal trends and sub-national disparities in healthcare quality

Monitoring subnational healthcare quality is important for identifying and addressing geographic inequities. Yet, health facility surveys are rarely powered to support the generation of estimates at more local levels. With this study, we propose an analytical approach for estimating both temporal and subnational patterns of healthcare quality indicators from health facility survey data. This method uses random effects to account for differences between survey instruments; space-time processes to leverage correlations in space and time; and covariates to incorporate auxiliary information. We applied this method for three countries in which at least four health facility surveys had been conducted since 1999 – Kenya, Senegal, and Tanzania – and estimated measures of sick-child care quality per WHO Service Availability and Readiness Assessment (SARA) guidelines at programmatic subnational level, between 1999 and 2020. Model performance metrics indicated good out-of-sample predictive validity, illustrating the potential utility of geospatial statistical models for health facility data. This method offers a way to jointly estimate indicators of healthcare quality over space and time, which could then provide insights to decision-makers and health service program managers.

Small area estimation of inequality measures using mixtures of Beta

Abstract Economic inequalities referring to specific regions are crucial in deepening spatial heterogeneity. Income surveys are generally planned to produce reliable estimates at countries or macroregion levels, thus we implement a small area model for a set of inequality measures (Gini, Relative Theil, and Atkinson indexes) to obtain reliable microregion estimates. Considering that inequality estimators are unit-interval defined with skewed and heavy-tailed distributions, we propose a Bayesian hierarchical model at the area level involving a Beta mixture. An application on EU-SILC data is carried out and a design-based simulation is performed. Our model outperforms in terms of bias, coverage, and error the standard Beta regression model. Moreover, we extend the analysis of inequality estimators by deriving their approximate variance functions.

The Small Area Estimation of Economic Security: A Proposal

The objective of this work is to propose a small area estimation strategy for an economic security indicator. In the last decade the interest for the measurement of economic security or insecurity has grown constantly, especially since the financial crisis of 2008 and the pandemic period. In this work, economic security is measures through a longitudinal indicator that compares levels of equivalized household income over time. To solve a small area estimation problem, due to possible sample sizes too low in some areas, a small area estimation strategy is suggested to obtain reliable estimates of the indicator of interest. We consider small area models specified at area level. Besides the basic Fay-Herriot area-level model, we propose to consider some longitudinal extensions, including time-specific random effects following an AR(1) process or an MA(1) process. A simulation study based on EU-SILC data shows that all the small area models considered provide a significant efficiency gain with respect to the Horvitz-Thompson estimator, especially the small area model with MA(1) specification for random effects.

Small-area models to assess the geographical distribution of tobacco consumption by sex and age in Spain.

Complete and accurate data on smoking prevalence at a local level would enable health authorities to plan context-dependent smoking interventions. However, national health surveys do not generally provide direct estimates of smoking prevalence by sex and age groups at the subnational level. This study uses a small-area model-based methodology to obtain precise estimations of smoking prevalence by sex, age group and region, from a population-based survey. The areas targeted for analysis consisted of 180 groups based on a combination of sex, age group (15-34, 35-54, 55-64, 65-74, and ≥75 years), and Autonomous Region. Data on tobacco use came from the 2017 Spanish National Health Survey (2017 SNHS). In each of the 180 groups, we estimated the prevalence of smokers (S), ex-smokers (ExS) and never smokers (NS), as well as their coefficients of variation (CV), using a weighted ratio estimator (direct estimator) and a multinomial logistic model with random area effects. When smoking prevalence was estimated using the small-area model, the precision of direct estimates improved; the CV of S and ExS decreased on average by 26%, and those of NS by 25%. The range of S prevalence was 11-46% in men and 4-37% in women, excluding the group aged ≥75 years. This study proposes a methodology for obtaining reliable estimates of smoking prevalence in groups or areas not covered in the survey design. The model applied is a good alternative for enhancing the precision of estimates at a detailed level, at a much lower cost than that involved in conducting large-scale surveys. This method could be easily integrated into routine data processing of population health surveys. Having such estimates directly after completing a health survey would help characterize the tobacco epidemic and/or any other risk factor more precisely.

Small-area models to assess the geographic distribution of second-hand smoke exposure by sex and age in Spain

1. Tobacco. World Health Organization. 2002. https://www.who.int/news-room/.... Google Scholar

Hierarchical Bayes Measurement Error Small Area Model for Estimation of Disaggregated Level Workers Mobility Pattern in India

Hierarchical Bayes Measurement Error Small Area Model for Estimation of Disaggregated Level Workers Mobility Pattern in India