Mind the Income Gap: Behavior of Inequality Estimators from Complex Survey Small Samples

Income inequality measures are biased in small samples leading generally to an underestimation. After investigating the nature of the bias, we propose a bias-correction framework for a large class of inequality measures comprising Gini Index, Generalized Entropy and Atkinson families by accounting for complex survey designs. The proposed methodology is based on Taylor's expansions and Generalized Linearization Method, and does not require any parametric assumption on income distribution, being very flexible. Design-based performance evaluation of the suggested correction has been carried out using data taken from EU-SILC survey. Results show a noticeable bias reduction for all measures. A bootstrap variance estimation proposal and a distributional analysis follow in order to provide a comprehensive overview of the behavior of inequality estimators in small samples. Results about estimators distributions show increasing positive skewness and leptokurtosis at decreasing sample sizes, confirming the non-applicability of classical asymptotic results in small samples and suggesting the development of alternative methods of inference.Comment: 29 pages, 5 figures. Submitted for publicatio

Small Area Estimation of Inequality Measures using Mixtures of Betas

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 microregion estimates. Considering that inequality estimators are unit-interval defined with skewed and heavy-tailed distributions, we propose a Bayesian hierarchical model at 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.Comment: 28 pages, 7 figures, 2 tables, 2 pages of supplementary materia

Mapping poverty at multiple geographical scales

Poverty mapping is a powerful tool to study the geography of poverty. The choice of the spatial resolution is central as poverty measures defined at a coarser level may mask their heterogeneity at finer levels. We introduce a small area multi-scale approach integrating survey and remote sensing data that leverages information at different spatial resolutions and accounts for hierarchical dependencies, preserving estimates coherence. We map poverty rates by proposing a Bayesian Beta-based model equipped with a new benchmarking algorithm that accounts for the double-bounded support. A simulation study shows the effectiveness of our proposal and an application on Bangladesh is discussed.Comment: 22 pages, 7 figure

The R package tipsae: tools for mapping proportions and indicators on the unit interval

The tipsae package implements a set of small area estimation tools for mapping proportions and indicators defined on the unit interval. It provides for small area models defined at area level, including the classical Beta regression, Zero and/or One Inflated Beta and Flexible Beta ones, possibly accounting for spatial and/or temporal dependency structures. The models, developed within a Bayesian framework, are estimated through Stan language, allowing fast estimation and customized parallel computing. The additional features of the tipsae package, such as diagnostics, visualization and exporting functions as well as variance smoothing and benchmarking functions, improve the user experience through the entire process of estimation, validation and outcome presentation. A Shiny application with a user-friendly interface further eases the implementation of Bayesian models for small area analysis

Mind the income gap: bias correction of inequality estimators in small-sized samples

Income inequality estimators are biased in small samples, leading generally to an underestimation. This aspect deserves particular attention when estimating inequality in small domains. After investigating the nature of the bias, we propose a bias correction framework for a large class of inequality measures comprising Gini Index, Generalized Entropy and Atkinson index families by accounting for complex survey designs. The proposed methodology is based on Taylor’s expansions and does not require any parametric assumption on income distribution, being very flexible. Design-based performance evaluation of our proposal has been carried out using data taken from the EU-SILC survey, showing a noticeable bias reduction for all the measures. Lastly, a small area estimation exercise shows the risks of ignoring prior bias correction in a basic area-level model, determining model misspecification

Small area estimation of inequality measures using mixtures of betas

Economic inequalities referring to specific regions are crucial in deepening spatial heterogeneity. Income surveys are generally planned to produce reliable estimates at countries or macro region levels, thus we implement a small area model for a set of inequality measures (Gini, Relative Theil and Atkinson indexes) to obtain microregion estimates. Considering that inequality estimators are unit-interval defined with skewed and heavy-tailed distributions, we propose a Bayesian hierarchical model at 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

Extended beta models for poverty mapping. An application integrating survey and remote sensing data in Bangladesh

The paper targets the estimation of the poverty rate at the Upazila level in Bangladesh through the use of Demographic and Health Survey (DHS) data. Upazilas are administrative regions equivalent to counties or boroughs whose sample sizes are not large enough to provide reliable estimates or are even absent. We tackle this issue by proposing a small area estimation model complementing survey data with remote sensing information at the area level. We specify an Extended Beta mixed regression model within the Bayesian framework, allowing it to accommodate the peculiarities of sample data and to predict out-of-sample rates. In particular, it enables to include estimates equal to either 0 or 1 and to model the strong intra-cluster correlation. We aim at proposing a method that can be implemented by statistical offices as a routine. In this spirit, we consider a regularizing prior for coefficients rather than a model selection approach, to deal with a large number of auxiliary variables. We compare our methods with existing alternatives using a design-based simulation exercise and illustrate its potential with the motivating application

SCL-90 empirical factors predict post-surgery weight loss in bariatric patients over longer time periods

This longitudinal study examined how pre-intervention psychological health helps predict bariatric surgery (BS) success as percentage of expected body mass index loss (ëMIL) over shorter to longer periods

Monitoring Tacrolimus Concentrations in Whole Blood and Peripheral Blood Mononuclear Cells: Inter- and Intra-Patient Variability in a Cohort of Pediatric Patients

Tacrolimus (TAC) is a first-choice immunosuppressant for solid organ transplantation, characterized by high potential for drug-drug interactions, significant inter- and intra-patient variability, and narrow therapeutic index. Therapeutic drug monitoring (TDM) of TAC concentrations in whole blood (WB) is capable of reducing the incidence of adverse events. Since TAC acts within lymphocytes, its monitoring in peripheral blood mononuclear cells (PBMC) may represent a valid future alternative for TDM. Nevertheless, TAC intracellular concentrations and their variability are poorly described, particularly in the pediatric context. Therefore, our aim was describing TAC concentrations in WB and PBMC and their variability in a cohort of pediatric patients undergoing constant immunosuppressive maintenance therapy, after liver transplantation. TAC intra-PBMCs quantification was performed through a validated UHPLC–MS/MS assay over a period of 2–3 months. There were 27 patients included in this study. No significant TAC changes in intracellular concentrations were observed (p = 0.710), with a median percent change of −0.1% (IQR −22.4%–+46.9%) between timings: this intra-individual variability was similar to the one in WB, −2.9% (IQR −29.4–+42.1; p = 0.902). Among different patients, TAC weight-adjusted dose and age appeared to be significant predictors of TAC concentrations in WB and PBMC. Intra-individual seasonal variation of TAC concentrations in WB, but not in PBMC, have been observed. These data show that the intra-individual variability in TAC intracellular exposure is comparable to the one observed in WB. This opens the way for further studies aiming at the identification of therapeutic ranges for TAC intra-PBMC concentrations