Skew-elliptical spatial random effect modeling for areal data with application to mapping health utilization rates

Area of Science:

• Biostatistics
• Spatial Epidemiology
• Health Services Research

Background:

• Areal data analysis often uses mixed models with spatially correlated random effects.
• Latent Gaussian Markov random fields are common for spatial smoothing but can be restrictive due to Gaussian assumptions, especially with outliers or discontinuities.
• Non-Gaussian spatial random effects models offer a more flexible alternative for such scenarios.

Purpose of the Study:

• To develop a robust statistical model for smoothing small-area health service utilization rates, addressing limitations of Gaussian spatial models.
• To incorporate non-Gaussian spatial random effects, specifically developing a formulation for skew-elliptical areal spatial models.
• To generalize the Gaussian conditional autoregressive model to accommodate non-Gaussian spatial random effects with flexible tail behavior.

Main Methods:

• Developed a novel non-Gaussian spatial model for areal data, generalizing the Gaussian conditional autoregressive model.
• Formulated skew-elliptical areal spatial models to allow for asymmetric marginal distributions and flexible tail behavior.
• Implemented the proposed models using Bayesian software (WinBUGS) for computational manageability.

Main Results:

• The proposed non-Gaussian spatial models demonstrated flexibility and computational feasibility.
• Simulations and analysis of acute coronary syndrome revascularization rates in Quebec showed the performance of the new methods.
• Comparisons indicated advantages over commonly used Gaussian and other non-Gaussian spatial prior formulations.

Conclusions:

• The developed non-Gaussian skew-elliptical areal spatial models provide a robust and flexible approach for analyzing health service utilization rates with spatial dependence.
• These models are particularly useful in the presence of outliers or discontinuities in spatial surfaces.
• The methods are computationally manageable and applicable to real-world health service research, such as mapping geographic variations in treatment.