Laplace approximation for conditional autoregressive models for spatial data of diseases.

Area of Science:

• Spatial statistics
• Biostatistics
• Computational epidemiology

Background:

• Conditional autoregressive (CAR) distributions, particularly intrinsic CAR (ICAR), are vital for analyzing spatial autocorrelation in disease risk assessment.
• Bayesian methods like Markov chain Monte Carlo (MCMC) and integrated nested Laplace approximation (INLA) are commonly used for ICAR models but can face convergence issues.

Purpose of the Study:

• To introduce and evaluate the use of Template Model Builder (TMB) for maximum likelihood estimation (MLE) of ICAR model parameters.
• To compare the computational speed and performance of TMB against MCMC and INLA for disease mapping.

Main Methods:

• Implemented ICAR models using Laplace approximation within Template Model Builder (TMB) for efficient maximum likelihood estimation.
• Integrated latent spatial variables in TMB for rapid computation of marginal likelihood functions.
• Compared runtime and parameter estimation accuracy of TMB with MCMC and INLA using three human disease datasets from the UK and US.

Main Results:

• Maximum likelihood estimates from TMB were comparable to those obtained using MCMC and INLA.
• TMB demonstrated substantial speed improvements, being 100-200 times faster than MCMC and nine times faster than INLA.
• The TMB approach successfully integrated out latent spatial variables for faster marginal likelihood calculations.

Conclusions:

• Template Model Builder (TMB) provides a computationally efficient and accurate alternative for fitting ICAR models.
• The TMB implementation offers significant performance advantages over traditional Bayesian methods for spatial disease risk analysis.
• This study validates TMB as a powerful tool for handling complex spatial statistical models in epidemiology.