Comparing INLA and OpenBUGS for hierarchical Poisson modeling in disease mapping

Area of Science:

• Biostatistics
• Computational Statistics
• Spatial Epidemiology

Background:

• Bayesian inference is crucial for complex statistical modeling.
• The R package INLA provides a computationally efficient alternative to traditional Markov Chain Monte Carlo (MCMC) methods.
• Disease mapping commonly utilizes Poisson data models for spatial analysis.

Purpose of the Study:

• To compare the performance of the R package INLA against the MCMC approach using the BRugs package (calling OpenBUGS).
• To evaluate the accuracy of parameter estimation, particularly for random effects and model fit, in disease mapping applications.
• To identify conditions under which INLA can provide comparable results to OpenBUGS.

Main Methods:

• Comparative analysis of INLA and MCMC (via BRugs/OpenBUGS) using a Poisson data model.
• Simulation study to assess estimation accuracy for fixed and random effects.
• Evaluation of model goodness-of-fit measures under default and adjusted settings.

Main Results:

• INLA provides computationally efficient Bayesian inference, yielding nearly identical estimates for fixed parameters compared to OpenBUGS.
• Under default settings, INLA shows limitations in accurately recovering estimates for random effects and their precisions.
• Model goodness-of-fit measures also differed between INLA and OpenBUGS with default settings.
• Adjusting INLA's settings in the simulation study allowed for recovery of estimates comparable to OpenBUGS.

Conclusions:

• INLA is a computationally efficient tool for Bayesian inference, particularly for disease mapping.
• Careful consideration and adjustment of default settings are necessary for INLA to achieve comparable accuracy to MCMC methods (OpenBUGS) for random effects and model fit.
• INLA's efficiency makes it a valuable alternative, but users must be aware of its performance characteristics under different settings.