Development and assessment of a robust Bayesian hierarchical model for small-area health data

Thesis Abstract

Effective analysis of small-area health data is critical for local health policy formulation and resource allocation, yet challenges persist due to data sparsity, heterogeneity, and potential outliers, which compromise the reliability of traditional statistical models. This study aims to develop and rigorously assess a robust Bayesian hierarchical model tailored for small-area health datasets, addressing the limitations of existing approaches by incorporating mechanisms to handle data anomalies and heteroscedasticity. The specific objectives are to formulate a hierarchical Bayesian framework that integrates spatial and temporal correlations, evaluate its robustness against outliers through simulated and real-world data, and compare its performance with classical hierarchical models and non-Bayesian approaches. The research adopts a quantitative, methodological approach, employing a combination of simulation studies and empirical analysis. The population of the study comprises small geographical units, such as districts or neighborhoods, within a metropolitan region, with a sample size of approximately 150 small areas selected based on data availability and relevance to health outcome measures such as disease prevalence, hospitalization rates, and mortality figures. Data collection involved secondary compilation from municipal health records, census data, and geographic information systems (GIS), ensuring comprehensive coverage of pertinent covariates, including socioeconomic status, healthcare access, and environmental factors. The model development phase involves constructing a Bayesian hierarchical structure rooted in the spatial theory of conditional autoregressive (CAR) models, supplemented by the Generalized Pareto distribution to enhance robustness against outliers in observed data. The analytical framework employs Markov Chain Monte Carlo (MCMC) techniques, specifically Gibbs sampling, to estimate posterior distributions, with model fit and convergence assessed through diagnostics such as trace plots, Gelman-Rubin statistics, and Deviance Information Criterion (DIC). Validation involves extensive simulations to examine the model’s sensitivity to outliers and heterogeneity, complemented by empirical evaluation using the collected health data. Comparative analyses with traditional Bayesian hierarchical models, such as Besag-York-Mollié (BYM), and frequentist approaches like generalized linear mixed models (GLMM), are conducted based on criteria including mean squared error (MSE), predictive accuracy, and robustness indices. Expected findings indicate that the proposed model yields significantly improved estimates of small-area health metrics, with enhanced resilience to data anomalies and better capturing of spatial and temporal dependence structures. The incorporation of the robust distribution is anticipated to reduce bias and variance in estimates, especially in areas with sparse or aberrant data. The model’s superior performance is expected to facilitate more accurate and reliable local health assessments, guiding targeted interventions and policy decisions. This research contributes to the existing knowledge by introducing a novel Bayesian hierarchical approach that integrates robustness measures for small-area epidemiological data, filling gaps related to outlier sensitivity and heterogeneity. The findings will demonstrate the practicality of applying advanced Bayesian techniques in public health surveillance, particularly in resource-limited settings where data quality issues are prevalent. Additionally, the study offers practical guidelines for implementing robust Bayesian models in health research and policymaking. Concluding, the study underscores the importance of robust Bayesian methodologies in improving small-area health data analysis, recommending their adoption in health planning and disease monitoring frameworks. Future research directions include extending the model to incorporate temporal dynamics and exploring its applicability to other health domains such as infectious disease modeling and environmental health risk assessment. This work ultimately aims to enhance the precision and reliability of epidemiological insights at the local level, contributing to more equitable and effective health interventions.