Bayesian Inference for Disease Mapping: Comparing INLA and MCMC
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Using maps to illustrate the distribution of a particular disease in geographical regions of interest is disease mapping. Disease mapping data falls within the framework of hierarchical model with counts in regions which are geographically near exhibiting residual spatial dependence. One can use this dependence to account for risk summaries in a disease mapping studies, by smoothening it across "contiguous" regions and this makes the Bayesian approach ideal for statistical inference in this studies. Popular among the methods used in Bayesian inference is Markov Chain Monte Carlo (MCMC). Though this method is popular, it is not without challenges. One of its challenges is the extensive simulation required to evaluate the convergence of the posterior samples with the process taking quite a long time. Lately, integrated nested Laplace approximations (INLA) has been introduced as an alternative method for Bayesian inference and the quest is to compare the performance of these methods. In using MCMC to estimate the parameters of interest, two different approaches were used in drawing the samples. One was by the implementation of an appropriate MCMC sampler and the other was by the use of the OpenBUGS software. It is worth emphasizing that both approaches resulted in approximately the same estimates and for the purposes of the comparative study of the two software packages in this research, the MCMC estimates were determined by the use of the OpenBUGS software.Carroll and others (2015) published a paper comparing the performance of OpenBUGS andINLA as methods applied in Bayesian inference with spatial random effects. These softwarepackages were compared in their ability to estimate parameters accurately. Concentrating onlow count scenarios, they concluded that the default settings of INLA ought to be altered when performing Bayesian inference with spatial random effects. They went further to claim that OpenBUGS outperformed INLA in the estimation of the precision parameters of the spatial random effects. With the aim of reproducing the results found in their paper and also compare the performance of OpenBUGS and INLA in parameter estimation, data was generated from six models which had different combinations of covariates and spatial random effects. After estimating the parameters of interest, it was realized that though both software packages failed to recover the true values of the precision parameters of the random effects at low observed counts, INLA outperformed OpenBUGS. It was also realized that INLA performs better when the observed counts of the model are high. This phenomenon can be attributed to the fact that if the posterior distribution is approximately normally distributed, posterior marginals are accurately computed using Laplace approximations and this condition is satisfied with the advent of observed high counts. Last but not least, no significant difference was observed between the estimates by INLA in its default settings (that is its simplified Laplace strategy) and when the default settings were altered to its full Laplace strategy. By these observations, our conclusion is that the assertion by the paper might be misleading.