Spatial correlation in Bayesian logistic regression with misclassification

Standard logistic regression assumes that the outcome is measured perfectly. In practice, this is often not the case, which could lead to biased estimates if not accounted for. This study presents Bayesian logistic regression with adjustment for misclassification of the outcome applied to data with spatial correlation. The models assessed include a fixed effects model, an independent random effects model, and models with spatially correlated random effects modelled using conditional autoregressive prior distributions (ICAR and ICAR(ρ)). Performance of these models was evaluated in a simulation study. Parameters were estimated by Markov Chain Monte Carlo methods, using slice sampling to improve convergence. The results demonstrated that adjustment for misclassification must be included to produce unbiased regression estimates. With strong correlation the ICAR model performed best. With weak or moderate correlation the ICAR(ρ) performed best. With unknown spatial correlation the recommended model would be the ICAR(ρ), assuming convergence can be obtained.