Small Area Estimation Methods Research Articles

Disparity of Imputed Data from Small Area Estimate Approaches – A Case Study on Diabetes Prevalence at the County Level in the U.S.

This paper assesses concordance and inconsistency among three small area estimation methods that are currently providing county-level health indicators in the United States. The three methods are multi-level logistic regression, spatial logistic regression, and spatial Poison regression, all proposed since 2010. Diabetes prevalence is estimated for each county in the continental United States from the 2012 sample of Behavioral Risk Factor Surveillance System. The mapping results show that all three methods displayed elevated diabetes prevalence in the South. While the Pearson correlation coefficients among three model-based estimates were all above 0.60, the highest one was 0.80 between the multilevel and spatial logistic methods. While point estimates are apparently different among the three small area estimate methods, their top and bottom of quintile distributions are fairly consistent based on Bangdiwala’s B-statistic, suggesting that outputs from each method would support consistent policy making in terms of identifying top and bottom percent counties.

The Use of the Robust GREG Estimator to Estimate Small Trade Firms

In the face of dynamic changes in the economy, there is a growing demand for multivariate statistics for cross‑classified domains. In economic statistics, this demand poses a particular challenge owing to the unique character of the population of enterprises, which is what motivates the search for estimation methods that can exploit administrative sources to a greater extent. The adoption of new solutions in this area is expected to increase the scope of statistical outputs and improve the efficiency of estimates. The purpose of the presented study is to test the application of the robust GREG estimator based on the LS method and least median of squares regression to estimate characteristics of small trade firms operating in 2012. The estimation process is supported with delayed variables from administrative registers used as auxiliary variables. The paper refers to small area estimation methods. The variables of interest are estimated at the low level of aggregation represented by cross‑section province and NUTS 2.

New methods for small area estimation with linkage uncertainty

In official statistics, interest for data integration has been increasingly growing, due to the need of extracting information from different sources. However, the effects of these procedures on the validity of the resulting statistical analyses has been disregarded for a long time. In recent years, it has been largely recognized that linkage is not an error-free procedure and linkage errors, as false links and/or missed links, can invalidate the reliability of estimates in standard statistical models. In this paper we consider the general problem of making inference using data that have been probabilistically linked and we explore the effect of potential linkage errors on the production of small area estimates. We describe the existing methods and propose and compare new approaches both from a classical and from a Bayesian perspective. We perform a simulation study to assess pros and cons of each proposed method; our simulation scheme aims at reproducing a realistic context both for small area estimation and record linkage procedures.

Small area estimation of proportions with different levels of auxiliary data.

Binary data are often of interest in many small areas of applications. The use of standard small area estimation methods based on linear mixed models becomes problematic for such data. An empirical plug-in predictor (EPP) under a unit-level generalized linear mixed model with logit link function is often used for the estimation of a small area proportion. However, this EPP requires the availability of unit-level population information for auxiliary data that may not be always accessible. As a consequence, in many practical situations, this EPP approach cannot be applied. Based on the level of auxiliary information available, different small area predictors for estimation of proportions are proposed. Analytic and bootstrap approaches to estimating the mean squared error of the proposed small area predictors are also developed. Monte Carlo simulations based on both simulated and real data show that the proposed small area predictors work well for generating the small area estimates of proportions and represent a practical alternative to the above approach. The developed predictor is applied to generate estimates of the proportions of indebted farm households at district-level using debt investment survey data from India.

Analysis of area level and unit level models for small area estimation in forest inventories assisted with LiDAR auxiliary information

Forest inventories require estimates and measures of uncertainty for subpopulations such as management units. These units often times hold a small sample size, so they should be regarded as small areas. When auxiliary information is available, different small area estimation methods have been proposed to obtain reliable estimates for small areas. Unit level empirical best linear unbiased predictors (EBLUP) based on plot or grid unit level models have been studied more thoroughly than area level EBLUPs, where the modelling occurs at the management unit scale. Area level EBLUPs do not require a precise plot positioning and allow the use of variable radius plots, thus reducing fieldwork costs. However, their performance has not been examined thoroughly. We compared unit level and area level EBLUPs, using LiDAR auxiliary information collected for inventorying 98,104 ha coastal coniferous forest. Unit level models were consistently more accurate than area level EBLUPs, and area level EBLUPs were consistently more accurate than field estimates except for large management units that held a large sample. For stand density, volume, basal area, quadratic mean diameter, mean height and Lorey’s height, root mean squared errors (rmses) of estimates obtained using area level EBLUPs were, on average, 1.43, 2.83, 2.09, 1.40, 1.32 and 1.64 times larger than those based on unit level estimates, respectively. Similarly, direct field estimates had rmses that were, on average, 1.37, 1.45, 1.17, 1.17, 1.26, and 1.38 times larger than rmses of area level EBLUPs. Therefore, area level models can lead to substantial gains in accuracy compared to direct estimates, and unit level models lead to very important gains in accuracy compared to area level models, potentially justifying the additional costs of obtaining accurate field plot coordinates.

Hierarchical Bayesian models for small area estimation of county-level private forest landowner population

The National Woodland Owner Survey (NWOS), administered by the USDA Forest Service, provides estimates of private forest ownership characteristics and owners’ attitudes and behaviors at a national, regional, and state levels. Due to sample sizes prescribed for inference at the state level, there are insufficient data to support county-level estimates. However, county-level estimates of NWOS variables are desired because ownership programs and education initiatives often occur at the county level and such information could help tailor these efforts to better match county-specific needs and demographics. Here, we present and assess methods to estimate the number of private forest ownerships at the county level for two states, Montana and New Jersey. To assess model performance, true population parameters were derived from cadastral and remote sensing data. Two small area estimation (SAE) models, the Fay-Herriot (FH) and the FH with conditional autoregressive random effects (FHCAR), improved estimated county-level population mean squared error (MSE) over that achieved by direct estimates. The proposed SAE models use covariates to improve accuracy and precision of county-level estimates. Results show total forest area, and 2010 decennial census population density covariates explained a significant portion of variability in county-level population size. These and other results suggest that the proposed SAE methods yield a statistically robust approach to deliver reliable estimates of private ownership population size and could be extended to additional important NWOS variables at the county level.

Estimation of Mean Population in Small Area with Spatial Best Linear Unbiased Prediction Method

Survey is aimed at estimating population parameters such as the total as well as the mean of an area with a large sample size. One approach in estimating population parameters are obtained through direct estimation methods. However, there is a problem when the direct estimation is used for a small area, which will cause a large standard error. This problem was addressed by developing a method of parameter estimation known as the Small Area Estimation (SAE) method. In this paper, we will describe the procedure to find the mean population estimate in a small area using Spatial Best Linear Unbiased Prediction (Spatial BLUP) method that follows Simultaneously Autoregressive (SAR) model. In general, this procedure begins with the definition of an area-level model. Then, the area-level model is expanded by the addition of spatial effect into the random effects of the area. In the end, the spatial model of the area level is used as the basis for estimating the mean population in small areas.

Applications of Small Area Estimation to Generalization With Subclassification by Propensity Scores

Policymakers have grown increasingly interested in how experimental results may generalize to a larger population. However, recently developed propensity score–based methods are limited by small sample sizes, where the experimental study is generalized to a population that is at least 20 times larger. This is particularly problematic for methods such as subclassification by propensity score, where limited sample sizes lead to sparse strata. This article explores the potential of small area estimation methods to improve the precision of estimators in sparse strata using population data as a source of auxiliary information to borrow strength. Results from simulation studies identify the conditions under which small area estimators outperform conventional estimators and the limitations of this application to causal generalization studies.

Variation in life expectancy and mortality by cause among neighbourhoods in King County, WA, USA, 1990–2014: a census tract-level analysis for the Global Burden of Disease Study 2015

Health outcomes are known to vary at both the country and local levels, but trends in mortality across a detailed and comprehensive set of causes have not been previously described at a very local level. Life expectancy in King County, WA, USA, is in the 95th percentile among all counties in the USA. However, little is known about how life expectancy and mortality from different causes of death vary at a local, neighbourhood level within this county. In this analysis, we estimated life expectancy and cause-specific mortality within King County to describe spatial trends, quantify disparities in mortality, and assess the contribution of each cause of death to overall disparities in all-cause mortality. We applied established so-called garbage code redistribution algorithms and small area estimation methods to death registration data for King County to estimate life expectancy, cause-specific mortality rates, and years of life lost (YLL) rates from 152 causes of death for 397 census tracts from Jan 1, 1990, to Dec 31, 2014. We used the cause list developed for the Global Burden of Disease 2015 study for this analysis. Deaths were tabulated by age group, sex, census tract, and cause of death. We used Bayesian mixed-effects regression models to estimate mortality overall and from each cause. Between 1990 and 2014, life expectancy in King County increased by 5·4 years (95% uncertainty interval [UI] 5·0-5·7) among men (from 74·0 years [73·7-74·3] to 79·3 years [79·1-79·6]) and by 3·4 years (3·0-3·7) among women (from 80·0 years [79·7-80·2] to 83·3 years [83·1-83·5]). In 2014, life expectancy ranged from 68·4 years (95% UI 66·9-70·1) to 86·7 years (85·0-88·2) for men and from 73·6 years (71·6-75·5) to 88·4 years (86·9-89·9) for women among census tracts within King County. Rates of YLL by cause also varied substantially among census tracts for each cause of death. Geographical areas with relatively high and relatively low YLL rates differed by cause. In general, causes of death responsible for more YLLs overall also contributed more significantly to geographical inequality within King County. However, certain causes contributed more to inequality than to overall YLLs. This census tract-level analysis of life expectancy and cause-specific YLL rates highlights important differences in health among neighbourhoods in King County that are masked by county-level estimates. Efforts to improve population health in King County should focus on reducing geographical inequality, by targeting those health conditions that contribute the most to overall YLLs and to inequality. This analysis should be replicated in other locations to more fully describe fine-grained local-level variation in population health and contribute to efforts to improve health while reducing inequalities. John W Stanton and Theresa E Gillespie.

Robust Mean-Squared Error Estimation for Poverty Estimates Based on the Method of Elbers, Lanjouw and Lanjouw

Summary The method of Elbers, Lanjouw and Lanjouw (ELL) is the small area estimation method developed by the World Bank for poverty mapping and is widely used in developing countries. However, it has been criticized because of its assumption of negligible between-area variability when used to calculate small area poverty estimates. In particular, the mean-squared errors (MSEs) of these estimates are significantly underestimated when this between-area variability cannot be adequately explained by the model covariates. A method of MSE estimation for ELL-type estimates is proposed which is robust to significant unexplained between-area variability. Simulation results show that the method proposed performs better than standard ELL MSE estimators when the area homogeneity assumption is violated. An application to a Bangladesh poverty mapping study provides some empirical evidence for this robustness.

Comparing Airborne Laser Scanning, and Image-Based Point Clouds by Semi-Global Matching and Enhanced Automatic Terrain Extraction to Estimate Forest Timber Volume

Information pertaining to forest timber volume is crucial for sustainable forest management. Remotely-sensed data have been incorporated into operational forest inventories to serve the need for ever more diverse and detailed forest statistics and to produce spatially explicit data products. In this study, data derived from airborne laser scanning and image-based point clouds were compared using three volume estimation methods to aid wall-to-wall mapping of forest timber volume. Estimates of forest height and tree density metrics derived from remotely-sensed data are used as explanatory variables, and forest timber volumes based on sample field plots are used as response variables. When compared to data derived from image-based point clouds, airborne laser scanning produced slightly more accurate estimates of timber volume, with a root mean square error (RMSE) of 26.3% using multiple linear regression. In comparison, RMSEs for volume estimates derived from image-based point clouds were 28.3% and 29.0%, respectively, using Semi-Global Matching and enhanced Automatic Terrain Extraction methods. Multiple linear regression was the best-performing parameter estimation method when compared to k-Nearest Neighbour and Support Vector Machine. In many countries, aerial imagery is acquired and updated on regular cycles of 1–5 years when compared to more costly, once-off airborne laser scanning surveys. This study demonstrates point clouds generated from such aerial imagery can be used to enhance the estimation of forest parameters at a stand and forest compartment level-scale using small area estimation methods while at the same time achieving sampling error reduction and improving accuracy at the forest enterprise-level scale.

On prediction of population and subpopulation characteristics for future periods

ABSTRACTThe estimation or prediction of population characteristics based on the sample information is the key issue in survey sampling. If the sample sizes in subpopulations (domains) are large enough, similar methods as used for the whole population can be used to estimate or to predict subpopulations characteristics as well. To estimate or to predict characteristics of domains with small or even zero sample sizes, small area estimation methods “borrowing strength” from other subpopulations or time periods are widely used. We extend this problem and study methods of prediction of future population and subpopulations’ characteristics based on the longitudinal data.

Non-parametric Small Area Models Using Shape-Constrained PenalizedB-Splines

SummaryFor the estimation of spruce timber reserves in individual forest districts of the German federal state Rhineland-Palatinate, small area methods are applied. A model using stock values of the state forest inventory and a canopy height model derived by airborne laser scanning is used to provide adequate estimates. Since the interaction between the variables is non-linear and must fulfil further constraints, a new spline-based small area estimation method is proposed, formulated as a quadratic programming problem. This method enables providing realistic estimates via including specialized constraints which are especially important in practice as well as more stable estimates. The applicability of the new method and the related mean-squared-error estimators is shown in a simulation study. Further, spruce timber reserves in Rhineland-Palatinate are estimated by using the new approach compared with already existing methods.

Inequalities in Life Expectancy Among US Counties, 1980 to 2014

ImportanceExamining life expectancy by county allows for tracking geographic disparities over time and assessing factors related to these disparities. This information is potentially useful for policy makers, clinicians, and researchers seeking to reduce disparities and increase longevity.ObjectiveTo estimate annual life tables by county from 1980 to 2014; describe trends in geographic inequalities in life expectancy and age-specific risk of death; and assess the proportion of variation in life expectancy explained by variation in socioeconomic and race/ethnicity factors, behavioral and metabolic risk factors, and health care factors.Design, Setting, and ParticipantsAnnual county-level life tables were constructed using small area estimation methods from deidentified death records from the National Center for Health Statistics (NCHS), and population counts from the US Census Bureau, NCHS, and the Human Mortality Database. Measures of geographic inequality in life expectancy and age-specific mortality risk were calculated. Principal component analysis and ordinary least squares regression were used to examine the county-level association between life expectancy and socioeconomic and race/ethnicity factors, behavioral and metabolic risk factors, and health care factors.ExposuresCounty of residence.Main Outcomes and MeasuresLife expectancy at birth and age-specific mortality risk.ResultsCounties were combined as needed to create stable units of analysis over the period 1980 to 2014, reducing the number of areas analyzed from 3142 to 3110. In 2014, life expectancy at birth for both sexes combined was 79.1 (95% uncertainty interval [UI], 79.0-79.1) years overall, but differed by 20.1 (95% UI, 19.1-21.3) years between the counties with the lowest and highest life expectancy. Absolute geographic inequality in life expectancy increased between 1980 and 2014. Over the same period, absolute geographic inequality in the risk of death decreased among children and adolescents, but increased among older adults. Socioeconomic and race/ethnicity factors, behavioral and metabolic risk factors, and health care factors explained 60%, 74%, and 27% of county-level variation in life expectancy, respectively. Combined, these factors explained 74% of this variation. Most of the association between socioeconomic and race/ethnicity factors and life expectancy was mediated through behavioral and metabolic risk factors.Conclusions and RelevanceGeographic disparities in life expectancy among US counties are large and increasing. Much of the variation in life expectancy among counties can be explained by a combination of socioeconomic and race/ethnicity factors, behavioral and metabolic risk factors, and health care factors. Policy action targeting socioeconomic factors and behavioral and metabolic risk factors may help reverse the trend of increasing disparities in life expectancy in the United States.

Self-reported general health, physical distress, mental distress, and activity limitation by US county, 1995-2012

BackgroundMetrics based on self-reports of health status have been proposed for tracking population health and making comparisons among different populations. While these metrics have been used in the US to explore disparities by sex, race/ethnicity, and socioeconomic position, less is known about how self-reported health varies geographically. This study aimed to describe county-level trends in the prevalence of poor self-reported health and to assess the face validity of these estimates.MethodsWe applied validated small area estimation methods to Behavioral Risk Factor Surveillance System data to estimate annual county-level prevalence of four measures of poor self-reported health (low general health, frequent physical distress, frequent mental distress, and frequent activity limitation) from 1995 and 2012. We compared these measures of poor self-reported health to other population health indicators, including risk factor prevalence (smoking, physical inactivity, and obesity), chronic condition prevalence (hypertension and diabetes), and life expectancy.ResultsWe found substantial geographic disparities in poor self-reported health. Counties in parts of South Dakota, eastern Kentucky and western West Virginia, along the Texas-Mexico border, along the southern half of the Mississippi river, and in southern Alabama generally experienced the highest levels of poor self-reported health. At the county level, there was a strong positive correlation among the four measures of poor self-reported health and between the prevalence of poor self-reported health and the prevalence of risk factors and chronic conditions. There was a strong negative correlation between prevalence of poor self-reported health and life expectancy. Nonetheless, counties with similar levels of poor self-reported health experienced life expectancies that varied by several years. Changes over time in life expectancy were only weakly correlated with changes in the prevalence of poor self-reported health.ConclusionsThis analysis adds to the growing body of literature documenting large geographic disparities in health outcomes in the United States. Health metrics based on self-reports of health status can and should be used to complement other measures of population health, such as life expectancy, to identify high need areas, efficiently allocate resources, and monitor geographic disparities.

US County-Level Trends in Mortality Rates for Major Causes of Death, 1980-2014

County-level patterns in mortality rates by cause have not been systematically described but are potentially useful for public health officials, clinicians, and researchers seeking to improve health and reduce geographic disparities. To demonstrate the use of a novel method for county-level estimation and to estimate annual mortality rates by US county for 21 mutually exclusive causes of death from 1980 through 2014. Redistribution methods for garbage codes (implausible or insufficiently specific cause of death codes) and small area estimation methods (statistical methods for estimating rates in small subpopulations) were applied to death registration data from the National Vital Statistics System to estimate annual county-level mortality rates for 21 causes of death. These estimates were raked (scaled along multiple dimensions) to ensure consistency between causes and with existing national-level estimates. Geographic patterns in the age-standardized mortality rates in 2014 and in the change in the age-standardized mortality rates between 1980 and 2014 for the 10 highest-burden causes were determined. County of residence. Cause-specific age-standardized mortality rates. A total of 80 412 524 deaths were recorded from January 1, 1980, through December 31, 2014, in the United States. Of these, 19.4 million deaths were assigned garbage codes. Mortality rates were analyzed for 3110 counties or groups of counties. Large between-county disparities were evident for every cause, with the gap in age-standardized mortality rates between counties in the 90th and 10th percentiles varying from 14.0 deaths per 100 000 population (cirrhosis and chronic liver diseases) to 147.0 deaths per 100 000 population (cardiovascular diseases). Geographic regions with elevated mortality rates differed among causes: for example, cardiovascular disease mortality tended to be highest along the southern half of the Mississippi River, while mortality rates from self-harm and interpersonal violence were elevated in southwestern counties, and mortality rates from chronic respiratory disease were highest in counties in eastern Kentucky and western West Virginia. Counties also varied widely in terms of the change in cause-specific mortality rates between 1980 and 2014. For most causes (eg, neoplasms, neurological disorders, and self-harm and interpersonal violence), both increases and decreases in county-level mortality rates were observed. In this analysis of US cause-specific county-level mortality rates from 1980 through 2014, there were large between-county differences for every cause of death, although geographic patterns varied substantially by cause of death. The approach to county-level analyses with small area models used in this study has the potential to provide novel insights into US disease-specific mortality time trends and their differences across geographic regions.

The Spatial Fay-Herriot Model in Poverty Estimation

Abstract Counteracting poverty is one of the objectives of the European Commission clearly emphasized in the Europe 2020 strategy. Conducting appropriate social policy requires knowledge of the extent of this phenomenon. Such information is provided through surveys on living conditions conducted by, among others, the Central Statistical Office (CSO). Nevertheless, the sample size in these surveys allows for a precise estimation of poverty rate only at a very general level - the whole country and regions. Small sample size at the lower level of spatial aggregation results in a large variance of obtained estimates and hence lower reliability. To obtain information in sparsely represented territorial sections, methods of small area estimation are used. Through using the information from other sources, such as censuses and administrative registers, it is possible to estimate distribution parameters with smaller variance than in the case of direct estimation. This paper attempts to estimate the poverty rate at LAU 1 level of Poland. This estimation will be possible through the use of data from different sources describing the living conditions of households and the use of the Fay-Herriot model with spatial correlation. As a result, estimates for previously unpublished levels of aggregation will be obtained.

A small area estimation model of comorbidity for England

BackgroundCardiovascular disease, diabetes, and obesity as single health conditions are rising in prevalence, but a growing body of evidence suggests that individuals are increasingly experiencing two or more of these conditions at the same time. Previous research on comorbidity has focused on identifying the most common groupings of illnesses among elderly health-care users by use of hospital administrative data. Using small area estimation techniques, we developed a population-wide dataset of comorbidity of cardiovascular disease, diabetes, and obesity for England at the small area level. MethodsMatching data from the 2011 Health Survey for England and the 2011 Census in England and Wales, we proposed a new global optimisation (GO) survey calibration method for the estimation of small area estimates of comorbidity. Unlike previous small area estimation methods, the GO method is time efficient and always convergent, uses initial weights a priori for the small area distribution, and allows the user to confirm the best solution. Validation of the newly simulated data involved comparison of the fit (as measured by the relative difference of the sum of squared Z-scores, Z2rel<0) of the benchmark constraints and non-benchmark constraints with census data. FindingsValidation revealed a significant fit for the benchmark constraints, age and sex (Z2rel<0). Validation of the simulated non-benchmark constraint (health status) also revealed a significant fit (Z2rel<0). In the absence of small area data on comorbidity, the close fit of both the benchmark and non-benchmark constraints allowed us to assume that the simulated estimates of comorbidity were statistically robust. InterpretationWHO has identified increased rates of comorbidity as a major challenge for health policy. GO, a new approach to small area estimation, allows the prevalence of cardiovascular disease, diabetes, and obesity as both single and comorbid health conditions to be estimated at the small area level. The newly estimated data have the potential to highlight comorbidity hotspots across England and inform future health policy. FundingEconomic and Social Research Council Secondary Data Initiative (grant ES/K004433/).

A Methodological Approach to Small Area Estimation for the Behavioral Risk Factor Surveillance System

Public health researchers have used a class of statistical methods to calculate prevalence estimates for small geographic areas with few direct observations. Many researchers have used Behavioral Risk Factor Surveillance System (BRFSS) data as a basis for their models. The aims of this study were to 1) describe a new BRFSS small area estimation (SAE) method and 2) investigate the internal and external validity of the BRFSS SAEs it produced. The BRFSS SAE method uses 4 data sets (the BRFSS, the American Community Survey Public Use Microdata Sample, Nielsen Claritas population totals, and the Missouri Census Geographic Equivalency File) to build a single weighted data set. Our findings indicate that internal and external validity tests were successful across many estimates. The BRFSS SAE method is one of several methods that can be used to produce reliable prevalence estimates in small geographic areas.

Estimating pedestrian and cyclist activity at the neighborhood scale

In most parts of the U.S., data on bicycle and pedestrian activity at the neighborhood scale are sparse or non-existent, despite the importance of such data for local planning. Here, a simple small-area estimation method is used to pair travel survey with land use and census data to estimate cyclist and pedestrian activity for census tracts in the state of California. This method is an improvement on fixed per-capita estimates of activity based only on regional or statewide averages. These activity estimates are then used to calculate the intensity of road use by cyclists and pedestrians, and crash rates for these road users. For California, the intensity of pedestrian and cyclist road use in urban census tracts is double that found in suburban tracts, while use in suburban tracts is an order of magnitude greater than that found in rural tracts. Per-capita estimates would suggest substantially smaller differences between neighborhood types. On the safety side, although non-severe crashes involving cyclists and pedestrians are much more likely in more urban areas, severe crash rates for the non-motorized modes exhibit no clear spatial pattern. The method used is simple and easily replicable, potentially filling a critical need for bicycle and pedestrian planners.