A method for small-area estimation of population mortality in settings affected by crises

Background Populations affected by crises (armed conflict, food insecurity, natural disasters) are poorly covered by demographic surveillance. As such, crisis-wide estimation of population mortality is extremely challenging, resulting in a lack of evidence to inform humanitarian response and conflict resolution. Methods We describe here a ‘small-area estimation’ method to circumvent these data gaps and quantify both total and excess (i.e. crisis-attributable) death rates and tolls, both overall and for granular geographic (e.g. district) and time (e.g. month) strata. The method is based on analysis of data previously collected by national and humanitarian actors, including ground survey observations of mortality, displacement-adjusted population denominators and datasets of variables that may predict the death rate. We describe the six sequential steps required for the method’s implementation and illustrate its recent application in Somalia, South Sudan and northeast Nigeria, based on a generic set of analysis scripts. Results Descriptive analysis of ground survey data reveals informative patterns, e.g. concerning the contribution of injuries to overall mortality, or household net migration. Despite some data sparsity, for each crisis that we have applied the method to thus far, available predictor data allow the specification of reasonably predictive mixed effects models of crude and under 5 years death rate, validated using cross-validation. Assumptions about values of the predictors in the absence of a crisis provide counterfactual and excess mortality estimates. Conclusions The method enables retrospective estimation of crisis-attributable mortality with considerable geographic and period stratification, and can therefore contribute to better understanding and historical memorialisation of the public health effects of crises. We discuss key limitations and areas for further development.

Assessment of health and social security agency participants proportion using hierarchical bayesian small area estimation

Data on the number of health insurance participants at the subdistrict level is crucial since it is strongly correlated with the availability of health service centers in the areas. This study’s primary purpose is to predict the proportion of health and social security participants of a state-owned company named Badan Penyelenggara Jaminan Sosial Kesehatan (BPJS) in eleven subdistricts in Padang, Indonesia. The direct, ordinary least square, and hierarchical Bayesian for small area estimation (HB-SAE) methods were employed in obtaining the best estimator for the BPJS participants in these small areas. This study found that the HB-SAE method resulted in better estimation than two other methods since it has the smallest standard deviation value. The auxiliary variable age (percentage of individuals more than 50 years old) and the percentage of health complaints have a significant effect on the proportion of the number of BPJS participants based on the HB-SAE method.

Small-Area Estimation for the USDA Forest Service, National Woodland Owner Survey: Creating a Fine-Scale Land Cover and Ownership Layer to Support County-Level Population Estimates

Small area estimation is a powerful modeling technique in which ancillary data can be utilized to “borrow” additional information, effectively increasing sample sizes in small spatial, temporal, or categorical domains. Though more commonly applied to biophysical variables within the study of forest inventory analyses, small area estimation can also be implemented in the context of understanding social values, behaviors, and trends among types of forest landowners within small domains. Here, we demonstrate a method for deriving a continuous fine-scale land cover and ownership layer for the state of Delaware, United States, and an application of that ancillary layer to facilitate small-area estimation of several variables from the USDA Forest Service’s National Woodland Owner Survey. Utilizing a proprietary parcel layer alongside the National Land Cover Database, we constructed a continuous layer with 10-meter resolution depicting land cover and land ownership classes. We found that the National Woodland Owner Survey state-level estimations of total acreage and total ownerships by ownership class were generally within one standard error of the population values calculated from the raster layer, which supported the direct calculation of several population-level summary variables at the county levels. Subsequently, we compare design-based and model-based methods of predicting commercial harvesting by family forest ownerships in Delaware in which forest ownership acreage, taken from the parcel map, was utilized to inform the model-based approach. Results show general agreement between the two modes, indicating that a small area estimation approach can be utilized successfully in this context and shows promise for other variables, especially if additional variables, e.g., United States Census Bureau data, are also incorporated.

Hierarchical Bayesian Small Area Estimation Using Weakly Informative Priors in Ecologically Homogeneous Areas of the Interior Western Forests

The U.S. Forest Inventory and Analysis Program (FIA) collects inventory data on and computes estimates for many forest attributes to monitor the status and trends of the nation's forests. Increasingly, FIA needs to produce estimates in small geographic and temporal regions. In this application, we implement area level hierarchical Bayesian (HB) small area estimators of several forest attributes for ecosubsections in the Interior West of the US. We use a remotely-sensed auxiliary variable, percent tree canopy cover, to predict response variables derived from ground-collected data such as basal area, biomass, tree count, and volume. We implement four area level HB estimators that borrow strength across ecological provinces and sections and consider prior information on the between-area variation of the response variables. We compare the performance of these HB estimators to the area level empirical best linear unbiased prediction (EBLUP) estimator and to the industry-standard post-stratified (PS) direct estimator. Results suggest that when borrowing strength to areas which are believed to be homogeneous (such as the ecosection level) and a weakly informative prior distribution is placed on the between-area variation parameter, we can reduce variance substantially compared the analogous EBLUP estimator and the PS estimator. Explorations of bias introduced with the HB estimators through comparison with the PS estimator indicates little to no addition of bias. These results illustrate the applicability and benefit of performing small area estimation of forest attributes in a HB framework, as they allow for more precise inference at the ecosubsection level.

United States Forest Service Use of Forest Inventory Data: Examples and Needs for Small Area Estimation

Forest Inventory and Analysis (FIA) data provides robust information for the United States Forest Service’s (USFS) mid-to-broad-scale planning and assessments, but ecological challenges (i.e., climate change, wildfire) necessitate increasingly strategic information without significantly increasing field sampling. Small area estimation (SAE) techniques could provide more precision supported by a rapidly growing suite of landscape-scale datasets. We present three Regional case studies demonstrating current FIA uses, how SAE techniques could enhance existing uses, and steps FIA could take to enable SAE applications that are user-friendly, comprehensive, and statistically appropriate. The Northern Region uses FIA data for planning and assessments, but SAE techniques could provide more specificity to guide vegetation management activities. State and transition simulation models (STSM) are run with FIA data in the Southwestern Region to predict effects of treatments and disturbances, but SAE could support model validation and more precision to identify treatable areas. The Southern Region used FIA to identify existing longleaf pine stands and evaluate condition, but SAE techniques within FIA tools would streamline analyses. Each case study demonstrates a desire to have FIA data on non-forested conditions and non-tree variables. Additional tools to measure statistical confidence would help maximize utility. FIA’s SAE techniques could add value to a widely used data set, if FIA can support key supplements to basic data and functionality.

Robust Estimation of the Theil Index and the Gini Coeffient for Small Areas

Small area estimation is receiving considerable attention due to the high demand for small area statistics. Small area estimators of means and totals have been widely studied in the literature. Moreover, in the last years also small area estimators of quantiles and poverty indicators have been studied. In contrast, small area estimators of inequality indicators, which are often used in socio-economic studies, have received less attention. In this article, we propose a robust method based on the M-quantile regression model for small area estimation of the Theil index and the Gini coefficient, two popular inequality measures. To estimate the mean squared error a non-parametric bootstrap is adopted. A robust approach is used because often inequality is measured using income or consumption data, which are often non-normal and affected by outliers. The proposed methodology is applied to income data to estimate the Theil index and the Gini coefficient for small domains in Tuscany (provinces by age groups), using survey and Census micro-data as auxiliary variables. In addition, a design-based simulation is carried out to study the behaviour of the proposed robust estimators. The performance of the bootstrap mean squared error estimator is also investigated in the simulation study.

Small area estimation of socioeconomic indicators for sampled and unsampled domains

Socioeconomic indicators play a crucial role in monitoring political actions over time and across regions. Income-based indicators such as the median income of sub-populations can provide information on the impact of measures, e.g., on poverty reduction. Regional information is usually published on an aggregated level. Due to small sample sizes, these regional aggregates are often associated with large standard errors or are missing if the region is unsampled or the estimate is simply not published. For example, if the median income of Hispanic or Latino Americans from the American Community Survey is of interest, some county-year combinations are not available. Therefore, a comparison of different counties or time-points is partly not possible. We propose a new predictor based on small area estimation techniques for aggregated data and bivariate modeling. This predictor provides empirical best predictions for the partially unavailable county-year combinations. We provide an analytical approximation to the mean squared error. The theoretical findings are backed up by a large-scale simulation study. Finally, we return to the problem of estimating the county-year estimates for the median income of Hispanic or Latino Americans and externally validate the estimates.