A Methodological Framework for Improved Precision and Efficiency

This thesis focuses on the development and application of advanced Bayesian hierarchical models with copula-based spatial effects to address complex issues in spatial epidemiology and socio-economic analysis. It presents two key studies: a bivariate Bayesian hierarchical model for disease mapping and the construction of a Longitudinal Index of Relative Socio-Economic Disadvantage (L-IRSD) in Australia.

The first study introduces a novel Bayesian hierarchical model for bivariate disease mapping, employing copula-based spatial effects to flexibly model spatial dependencies between multiple diseases. This model is examined on simulated datasets and applied to spatial epidemiological data from Australia, demonstrating its effectiveness in capturing complex, non-linear relationships and improving risk estimation in regions with sparse data. By incorporating copulas, the model decouples the marginal distributions from the dependence structure, providing more accurate and nuanced insights into disease risks and their spatial correlations. An R package has also been developed and made available on GitHub to facilitate the implementation of the copula-based model, enhancing its accessibility for future research and applications.

The second study constructs the L-IRSD to capture socio-economic disparities over time, enhancing traditional socio-economic indices like SEIFA (socio-economic indices for Australia) through incorporating a longitudinal perspective. Principal Component Analysis (PCA) is applied to create a temporally consistent measure of socio-economic status from multiple Australian censuses. The L-IRSD reveals shifts in socio-economic conditions across regions, highlighting persistent challenges and areas of improvement—crucial for effective policy-making and targeted interventions. Additionally, the L-IRSD serves as a valuable covariate in spatio-temporal small area estimation, allowing for more precise modelling of regional heterogeneity and dynamics.

Together, these contributions offer a robust methodological framework for addressing challenges in spatial epidemiology and socio-economic analysis. By integrating copula-based spatial modelling and longitudinal socio-economic indices, this research enhances the understanding of spatial and temporal dynamics in socio-economic inequalities, providing valuable insights for public health policy and resource allocation.

Mu Li is a PhD candidate in the School of Demography at ANU. His PhD project centres on the development of the advanced Bayesian hierarchical models for spatial data in small area estimation and the analysis of the social component indicators. He completed the Master of Actuarial Practice in the Research School of Finance, Actuarial Studies and Statistics in 2020 at ANU and has been participate as research assistant in the project “SPARSE: Smoking Prevalence for Australia with Reliable Small-area Estimation”.