Small Area Estimation Research Articles

Artificial intelligence to predict estimates of physical activity in small geographic areas

Abstract Background Artificial intelligence (AI) predictive models have been used to estimate the risk of a certain outcome occurring, using all available variables. Methods Using AI methods we have developed a small area estimation (SAE) technique to estimate the prevalence of leisure-time physical activity (LTPA), or who practices 150 minutes of LTPA per week, in small areas, in Belo Horizonte, Brazil, between 2009 and 2018, by the usage of k-means clustering. The VIGITEL, national telephone survey of Risk Factors for non-communicable diseases, was the main source. We applied available data to estimate prevalence of LTPA in 3300 census tracts, aggregated in 150 Primary Health Care (PHC) areas. The prevalence of PA was analyzed between two time periods, due to the low number of census tract interviews. With the available data, we estimate vulnerability clusters, derived from a Health Vulnerability Index (IVS), for the city of Belo Horizonte, according to socioeconomic, sanitation and health indicators, which measure the percentage of the population living in areas of vulnerability in the city. The index main purpose is to support public policy implementation. Results Nine clusters were identified according to the Silhouette coefficient analysis, i.e.: low (LO-0, LO-1), medium (ME-0, ME-1), high (HI-0, HI-1, HI-2) and very high) vulnerability (VH-0, VH-1. The prevalence of physical activity ranged from 23.7% (worst prevalence), in area of high vulnerability cluster (VH-1) to 45.5% in a low-risk cluster (LO-1) in period from 2009 to 2014. The prevalence of physical activity increased to 31.4% (high vulnerability cluster) to 52.81% (low-risk cluster) from 2014 to 2018. Conclusions The use of AI to estimate the prevalence of physical activity in small areas proved to be effective and highlighted important differences in the city. Thus, national surveys, with a small number of interviews per census sector, can be used to predict risks and health outcomes for small areas. Key messages • The study highlights the importance of using artificial intelligence to predict estimates of risk factors for chronic non-communicable diseases in small geographic areas. • The study showed less physical activity (PA) in areas of greater vulnerability. This can support health promotion policies and programs that encourage PA.

Small area estimators in a simulation test

The Finnish National Forest Inventory produces municipality level results either with an indirect model-based K nearest neighbor estimator or a direct design-based post-stratification estimator. Design-based approach is unbiased, but not always feasible due to low number of field plots. The K nearest neighbor estimator is lacking an analytical estimator for the variance. A composite estimator combining the indirect and direct estimates could be an attractive solution. In this article, estimators for small-area estimation are analyzed in a simulation experiment with varying size small areas and quality auxiliary data. The potential of estimators is assessed based on the true standard errors and RMSEs in the simulation experiment. Direct estimators and composite estimators work reasonably well with varying quality models, but the performance of indirect estimators is dependent on the quality of the model used. The performance of different estimators also depends on the size of the small areas. Linear models in which the weight of plots outside the target domain is smaller than those within the target domain, performed better than an unweighted model, suggesting that localizing the models for the small areas is beneficial. EBLUP approach also performed well, both in connection of a KNN model and a linear model.

Small Area Estimation of Household Economic Indicators under Unit-Level Generalized Additive Models for Location, Scale and Shape

Abstract We propose a small area estimation model based on Generalized Additive Models for Location, Scale and Shape (SAE-GAMLSS) for the estimation of household economic indicators. SAE-GAMLSS relax the exponential family distributional assumption and allow each distributional parameter to depend on covariates. A bootstrap approach to estimate the MSE is proposed. The SAE-GAMLSS estimator shows a largely better performance than the well-known Empirical Best Linear Unbiased Predictor (EBLUP) under various simulated scenarios. Per-capita consumption of Italian and foreign households in Italian regions, in urban and rural areas, is estimated using SAE-GAMLSS. Results show that the well-known Italian North–South divide does not hold for foreigners.

Does Local Area Social Mobility Affect Political Alienation?

While existing research has considered how individual-level social mobility experiences affect a person’s political outlook, less attention has been paid to how historic levels of social mobility in local areas influence political attitudes and political behaviour. We link individual-level data from the UK Household Longitudinal Study to small area estimates of social class mobility derived from the decennial census. We find that living in a low absolute social mobility area was associated with a higher probability of voting ‘Leave’ in the 2016 UK European Union membership referendum. However, we find no evidence that historical social mobility rates in the local area predict abstention in general elections or attitudinal indicators of political alienation. Given declining rates of upwards mobility, and increasing levels of downwards mobility, our results have important implications for understanding geographies of political discontent.

Special issue SMA: big data and alternative data sources for small area estimation

Special issue SMA: big data and alternative data sources for small area estimation

Exploring Veteran Mental Health Disparities: A Comparative Analysis of Rural and Urban Communities in the Midwest of the United States.

Veterans face unique mental health challenges influenced by their service experiences and post-military transitions into civilian life. Geographic location also plays an integral role in impacting veterans' outcomes and access to proper care. The purpose of this case study is to examine disparities between rural and urban veterans in the Midwest using data collected from the 2022 Behavioral Risk Factor Surveillance System (BRFSS). Self-reported bad mental health days among veterans in rural and urban regions across twelve Midwestern states were analyzed through direct rate estimation and small area estimation techniques utilizing RStudio software. Higher rates of poor mental health days were ultimately observed among urban veterans in most states through both analyses. The results of the direct rate analysis revealed 13.5% of veterans reporting 14 + poor mental health days per month versus 9.5% in rural areas. Likewise, the results of the small area analysis demonstrated 12.2% of veterans reporting 14 + days of poor mental health days per month in urban areas versus 9.8% in rural areas. This highlights the significance of environmental stressors and social determinants of health in differentially impacting mental health outcomes. Thus, tailored interventions utilizing interdisciplinary teams are needed to meet the unique barriers for veterans in different geographic contexts. Despite the cross-sectional nature of the study and reliance on self-reported data, this case study provides valuable insights for mental health disparities among Midwest veterans. Creating a more equitable and accessible mental health landscape for veterans will require targeted and collaborative approaches.

Abstract A015: Small area-estimation for low mammography screening: Geographic and racial disparities in mammography screening, 2015 – 2022

Abstract Background: Mammography screening is associated with at least a 20% reduction in breast cancer mortality. However, there are racial/ethnic differences in breast cancer mortality. For example, non-Hispanic Black (NHB) women are significantly more likely to die of breast cancer than non-Hispanic White (NHW) women. Few studies have reported small-area estimates for mammography screening among the entire US population; differences by race were either not examined or resulted in mixed findings. The American Cancer Society (ACS) and the United States Preventive Services Taskforce (USPSTF) recommend regular mammography screening from age 40 through 74 years. The current study aims to identify areas of up-to-date mammography screening and to elucidate whether mammography screening varied by geographical location, race, or ethnicity. Methods: Mammography screening within the past 12 months was retrieved from the 2015-2022 Behavioral Risk Factor Surveillance System data. The study population consisted of adult women aged 40 and older residing within the United States. 2020 US census tract population estimates were used to generate gender (all women), race/ethnicity (NHB, NHW, non-Hispanic Asian, and Hispanic/Latina), income, and age group weights for each US census tract. Synthetic estimates of mammography screening uptake at the census tract were conducted using our novel PARIS model (Probability of mammography screening within the past year, given age, race/ethnicity, income, and state) using a multilevel logistic regression model. Regional differences in mammography screening by US Census Bureau regions and divisions were examined. Results: Up-to-date mammography among all women in the sample was 55.98% (SD = 2.07; F (3, 72429) = 2886.81, p < .0001). Mammography screening examined by race indicated the greatest screening rates among non-Hispanic Black women (M = 60.78, SD = 3.11) and least among Asian women (M = 48.68, SD = 3.15). Among four US Census Bureau regions, the West region had the lowest rates of mammography screening among women (M = 54.74, SD = 1.85) while the South region had the highest rates (M = 56.55, SD = 2.18; F(3, 72429) = 2886.81, p < .0001). After further parsing geographical units, the West Pacific region, among the 9 US Census Bureau divisions, had the lowest mammography screening (M = 54.53, SD = 1.81) while the East South Central division had the highest rates of mammography screening (M = 56.94, SD = 2.10; F(8, 72429) = 1360.60, p < .0001).Conclusion: Using novel geospatial methods, the current study elucidated significant differences in mammography screening by race and place. These results suggest that Black women and women living in the South have higher up-to-date mammography screening compared to other women. Thus, the existing inequities in breast cancer outcomes may be explained by differences in the cancer care continuum (delays in follow-up care, treatment, and breast cancer survival). Further examination of the interplay between screening uptake, late-stage diagnosis, and death is needed. Citation Format: Sydney P. Howard, Justin X. Moore, Elinita Pollard, Ryan Johnson, Lovoria Williams, Adebola Adegboyega, Jie Chen, Jorge Cortes, Aimee James. Small area-estimation for low mammography screening: Geographic and racial disparities in mammography screening, 2015 – 2022 [abstract]. In: Proceedings of the 17th AACR Conference on the Science of Cancer Health Disparities in Racial/Ethnic Minorities and the Medically Underserved; 2024 Sep 21-24; Los Angeles, CA. Philadelphia (PA): AACR; Cancer Epidemiol Biomarkers Prev 2024;33(9 Suppl):Abstract nr A015.

Model-Based Prediction for Small Domains Using Covariates: A Comparison of Four Methods

Abstract We consider methods for model-based small area estimation when the number of areas with sampled data is a small fraction of the total areas for which estimates are required. Abundant auxiliary information is available from the survey for all the sampled areas. Further, through an external source, there is information for all areas. The goal is to use auxiliary variables to predict the outcome of interest for all areas. We compare areal-level random forests and LASSO approaches to a frequentist forward variable selection approach and a Bayesian shrinkage method using a horseshoe prior. Further, to measure the uncertainty of estimates obtained from random forests and the LASSO, we propose a modification of the split conformal procedure that relaxes the assumption of exchangeable data. We show that the proposed method yields intervals with the correct coverage rate and this is confirmed through a simulation study. This work is motivated by Ghanaian data available from the sixth Ghana Living Standards Survey (GLSS) and the 2010 Population and Housing Census, in the Greater Accra Metropolitan Area (GAMA) region, which comprises eight districts that are further divided into enumeration areas (EAs). We estimate the areal mean household log consumption using both datasets. The outcome variable is measured only in the GLSS for 3 percent of all the EAs (136 out of 5019) and 174 potential covariates are available in both datasets. In the application, among the four modeling methods considered, the Bayesian shrinkage performed the best in terms of bias, mean squared error (MSE), and prediction interval coverages and scores, as assessed through a cross-validation study. We find substantial between-area variation with the estimated log consumption showing a 1.3-fold variation across the GAMA region. The western areas are the poorest while the Accra Metropolitan Area district has the richest areas.

Small Area Estimation of Maluku and Papua Island Child Poverty Levels in 2023

Child welfare issues such as child poverty pose a challenge for Indonesia. The provinces in Maluku and Papua have the highest rates of child poverty. Data on child poverty at regencies/municipalities level is needed to address this issue through targeted policies. The direct estimations have a Relative Standard Error (RSE) value of more than 25 percent, necessitating the use of an indirect method, Small Area Estimation (SAE). This study aims to compare the results of indirect estimates of the percentage of children aged 0-17 living in poverty at the regencies/municipalities level in Maluku and Papua using SAE Empirical Best Linear Unbiased Prediction (EBLUP) and Hierarchical Bayes Beta (HB Beta) methods. Susenas KOR March 2023 data is used to produce direct estimates, while Podes 2021 data is used to form auxiliary variables. The results indicate that the SAE HB Beta method provides estimates with better RSE compared to SAE EBLUP. All regencies/municipalities in the Maluku and Papua have a fairly good level of accuracy.

On indirect estimation of small area parameters under ranked set sampling

In investigations of domains under post-stratified random sampling, it is difficult to get an acceptable precision for domain-specific estimates due to low sample sizes. Small area estimate, a popular technique that has been widely used over the past few decades, involves indirect estimating using the auxiliary data from the entire population. In this article, we utilize a ranked set sampling (RSS) technique to achieve a greater level of precision in area-specific estimations under the assumption that ranking the smaller sets is simple, inexpensive, and flawless. RSS optimizes sample size for a fixed degree of precision or increases precision for a fixed sample size. We create direct estimators for population total under homogeneous, ratio, and regression models that are area specific. To evaluate the effectiveness and application of the suggested RSS technique, data from the Pakistan Demographic Health Survey (PDHS 2017–18) and Iris flower data are used. The effectiveness of the RSS mechanism is supported by both theoretical characteristics and Bootstrapped tests.

Using Small Area Estimation to Produce Reliable Transportation Statistics: The Case of Household Trips Estimation at the Census Tract Level

Using Small Area Estimation to Produce Reliable Transportation Statistics: The Case of Household Trips Estimation at the Census Tract Level

Handling Out‐of‐Sample Areas to Estimate the Unemployment Rate at Local Labour Market Areas in Italy

SummaryUnemployment rate estimates for small areas are used to efficiently support the distribution of services and the allocation of resources, grants and funding. A Fay–Herriot type model is the most used tool to obtain these estimates. Under this approach out‐of‐sample areas require some synthetic estimates. As the geographical context is extremely important for analysing local economies, in this paper, we allow for area random effects to be spatially correlated. The spatial model parameters are estimated by a marginal likelihood method and are used to predict in‐sample as well as out‐of‐sample areas. Extensive simulation experiments are used to assess the impact of the auto‐regression parameter and of the rate of out‐of‐sample areas on the performance of this approach. The paper concludes with an illustrative application on real data from the Italian Labour Force Survey in which the estimation of the unemployment rate in each Local Labour Market Area is addressed.

Empirical best predictors under multivariate Fay-Herriot models and their numerical approximation

Small area estimation of multivariable non-linear domain indicators using aggregated data is addressed. By assuming that the target vector follows a multivariate Fay-Herriot model, empirical best predictors of domain parameters that are arbitrary Lebesgue-measurable functions of multiple target variables are derived. In this context, Monte Carlo and Gauss-Hermite quadrature methods for integral approximation are discussed. A parametric bootstrap algorithm for mean squared error estimation is presented. Simulation experiments are conducted to study the behaviour of the introduced methodology. Moreover, an illustrative application to real data from the Spanish labour force survey is provided. In this example, province-level unemployment rates, crossed by age classes and sex, are estimated.

측정오차 공변량을 고려한 포아송 소지역 모델의 준모수적 계층적 베이즈 추정

In the sample survey, it is impossible to obtain sufficient samples in relatively small areas, which makes it difficult to estimate accurate statistics for small areas. For this reason, various studies on small area estimation are constantly being conducted, and in particular, the Fay-Herriot (1979) model has been expanded to various forms as one of the most widely used small area estimation models. In this study, we developed a semiparametric regression model based on a radial basis function that can consider nonlinear relationships between the resulting variables and covariates, extended from the model considering the measurement error of the covariate in the Poisson distribution proposed by Nam, Hwang(2021). Also, parameter estimation and model fit were performed through hierarchical Bayesian estimation using Gibbs sampling and Metropolis-Hastings algorithm among Markov chain Monte Carlo techniques. Simulations were conducted under various conditions to confirm the suitability of the model developed in this study, and the excellence of the developed model was further verified through empirical analysis using data from the 8th Korean longitudinal study of aging.

Small data estimation for binary variables with big data: A comparison of calibrated nearest neighbour and hierarchical Bayes methods of estimation

A recent application in machine learning has introduced a novel approach, complemented by big data sources, aimed at providing precise estimates for small geographical areas. This method employs a dual strategy: (a) hybrid estimation, involving the integration of big data sources with imputed values derived from K nearest neighbours (KNN) to address missing target variable values from the big data source; and (b) calibration of the collective sum of small area estimates to an independent yet efficient national total. Evaluating its efficacy using simulated data from the 2016 Australian population census, the calibrated KNN (CKNN) method demonstrated superior performance compared to the Fay-Herriot method based on area-level covariates. This paper enhances the comparative analysis by contrasting the CKNN method with a hierarchical Bayes method using the logit-normal model (LN) relevant for binary data. Broadly speaking, the LN method can be viewed as the Bayesian equivalent of Battese-Harter-Fuller (BHF) method, which incorporates unit-level covariates. Our results demonstrate the CKNN method’s superiority over the LN method. However, the application of hybrid estimation to the LN method significantly diminishes this superiority. Although CKNN estimates maintain better precision, they are not as accurate as the estimates from the hybridized LN method.

Prevalence of asymptomatic malaria at the communal level in Burkina Faso: an application of the small area estimation approach

BackgroundIn malaria-endemic countries, asymptomatic carriers of plasmodium represent an important reservoir for malaria transmission. Estimating the burden at a fine scale and identifying areas at high risk of asymptomatic carriage are important to guide malaria control strategies. This study aimed to estimate the prevalence of asymptomatic carriage at the communal level in Burkina Faso, the smallest geographical entity from which a local development policy can be driven.MethodsThe data used in this study came from several open sources: the 2018 Multiple Indicator Cluster Survey on Malaria and the 2019 general census of the population data and environmental. The analysis involved a total of 5489 children under 5 from the malaria survey and 293,715 children under 5 from the census. The Elbers Langjouw and Langjouw (ELL) approach is used to estimate the prevalence. This approach consists of including data from several sources (mainly census and survey data) in a statistical model to obtain predictive indicators at a sub-geographical level, which are not measured in the population census. The method achieves this by finding correlations between common census variables and survey data.FindingsThe findings suggest that the spatial distribution of the prevalence of asymptomatic carriage is very heterogeneous across the communes. It varies from a minimum of 5.1% (95% CI 3.6–6.5) in the commune of Bobo-Dioulasso to a maximum of 41.4% (95% CI 33.5–49.4) in the commune of Djigoué. Of the 341 communes, 208 (61%) had prevalences above the national average of 20.3% (95% CI 18.8–21.2).ContributionsThis analysis provided commune-level estimates of the prevalence of asymptomatic carriage of plasmodium in Burkina Faso. The results of this analysis should help to improve planning of malaria control at the communal level in Burkina Faso.

Gauging Airbnb review sentiments and critical key-topics by small area estimation

In literature, several researchers have discovered that the reviews written about Airbnb accommodation tend to be extremely positive than those published on other famous platforms, consequently, many negative experiences remain untracked. Leaving negative experiences underrepresented hampers hosts’ ability to improve their services. To overcome this gap, we employ Small Area Estimation to quantify negative sentiment in Airbnb reviews and the relative critical topics that characterize them. Our methodology involves a two-step process: first, we employ sentiment analysis and topic modeling to identify negative sentiment and critical issues, followed by the application of a mixed effect random forest model to provide a granular analysis of Airbnb reviews in small sub-populations in the context of small area estimation. We focus on domains of the city of Rome defined by geographical areas and the presence of hosts and Superhosts. Our findings reveal nuanced sentiment variations and critical topic proportions that traditional methods often overlook.

Designing the Australian Cancer Atlas: visualizing geostatistical model uncertainty for multiple audiences.

The Australian Cancer Atlas (ACA) aims to provide small-area estimates of cancer incidence and survival in Australia to help identify and address geographical health disparities. We report on the 21-month user-centered design study to visualize the data, in particular, the visualization of the estimate uncertainty for multiple audiences. The preliminary phases included a scoping study, literature review, and target audience focus groups. Several methods were used to reach the wide target audience. The design and development stage included digital prototyping in parallel with Bayesian model development. Feedback was sought from multiple workshops, audience focus groups, and regular meetings throughout with an expert external advisory group. The initial scoping identified 4 target audience groups: the general public, researchers, health practitioners, and policy makers. These target groups were consulted throughout the project to ensure the developed model and uncertainty visualizations were effective for communication. In this paper, we detail ACA features and design iterations, including the 3 complementary ways in which uncertainty is communicated: the wave plot, the v-plot, and color transparency. We reflect on the methods, design iterations, decision-making process, and document lessons learned for future atlases. The ACA has been hugely successful since launching in 2018. It has received over 62000 individual users from over 100 countries and across all target audiences. It has been replicated in other countries and the second version of the ACA was launched in May 2024. This paper provides rich documentation for future projects.

Discussion of the 2023 Hansen Lecture: “Model Selection and Its Important Roles in Surveys”

Abstract The 31st Morris Hansen Lecture gave a broad overview of some fundamental issues regarding the roles of statistical models in surveys, with an emphasis on a method of model selection known as the fence. This discussion provides some general lecture remarks and expands on the possible applicability of the fence methods in small area estimation. Unit-level and area-level small area estimation modeling illustrations are provided. A general variable selection framework for small area estimation is presented, along with recent application studies and ideas for expansion to include the fence methods.

Mortality due to falls by county, age group, race, and ethnicity in the USA, 2000–19: a systematic analysis of health disparities

Fall-related mortality has increased rapidly over the past two decades in the USA, but the extent to which mortality varies across racial and ethnic populations, counties, and age groups is not well understood. The aim of this study was to estimate age-standardised mortality rates due to falls by racial and ethnic population, county, and age group over a 20-year period. Redistribution methods for insufficient cause of death codes and validated small-area estimation methods were applied to death registration data from the US National Vital Statistics System and population data from the US National Center for Health Statistics to estimate annual fall-related mortality. Estimates from 2000 to 2019 were stratified by county (n=3110) and five mutually exclusive racial and ethnic populations: American Indian or Alaska Native (AIAN), Asian or Pacific Islander (Asian), Black, Latino or Hispanic (Latino), and White. Estimates were corrected for misreporting of race and ethnicity on death certificates using published misclassification ratios. We masked (ie, did not display) estimates for county and racial and ethnic population combinations with a mean annual population of less than 1000. Age-standardised mortality is presented for all ages combined and for age groups 20-64 years (younger adults) and 65 years and older (older adults). Nationally, in 2019, the overall age-standardised fall-related mortality rate for the total population was 13·4 deaths per 100 000 population (95% uncertainty interval 13·3-13·6), an increase of 65·3% (61·9-68·8) from 8·1 deaths per 100 000 (8·0-8·3) in 2000, with the largest increases observed in older adults. Fall-related mortality at the national level was highest across all years in the AIAN population (in 2019, 15·9 deaths per 100 000 population [95% uncertainty interval 14·0-18·2]) and White population (14·8 deaths per 100 000 [14·6-15·0]), and was about half as high among the Latino (8·7 deaths per 100 000 [8·3-9·0]), Black (8·1 deaths per 100 000 [7·9-8·4]), and Asian (7·5 deaths per 100 000 [7·1-7·9]) populations. The disparities between racial and ethnic populations varied widely by age group, with mortality among younger adults highest for the AIAN population and mortality among older adults highest for the White population. The national-level patterns were observed broadly at the county level, although there was considerable spatial variation across ages and racial and ethnic populations. For younger adults, among almost all counties with unmasked estimates, there was higher mortality in the AIAN population than in all other racial and ethnic populations, while there were pockets of high mortality in the Latino population, particularly in the Mountain West region. For older adults, mortality was particularly high in the White population within clusters of counties across states including Florida, Minnesota, and Wisconsin. Age-standardised mortality due to falls increased over the study period for each racial and ethnic population and almost every county. Wide variation in mortality across geography, age, and race and ethnicity highlights areas and populations that might benefit most from efficacious fall prevention interventions as well as additional prevention research. US National Institutes of Health (Intramural Research Program, National Institute on Minority Health and Health Disparities; National Heart, Lung, and Blood Institute; Intramural Research Program, National Cancer Institute; National Institute on Aging; National Institute of Arthritis and Musculoskeletal and Skin Diseases; Office of Disease Prevention; and Office of Behavioral and Social Sciences Research).