Spatio-temporal dependence and model misspecification in infectious disease counts: A simulation study of inference and prediction

Abstract

Spatio-temporal dependence is inherent in infectious disease count data, yet applied analyses often ignore spatial and temporal correlation, leading to model misspecification and unreliable inference. This study uses simulation experiments calibrated to weekly COVID-19 surveillance across the twelve administrative regions of Albania to evaluate the impact of model choice on inference and prediction. Three scenarios were considered: (A) strong spatial and temporal dependence, (B) weak spatial but strong temporal dependence, and (C) strong spatial confounding between a spatial covariate and the latent spatial effect. A non-spatial Poisson generalized linear model (GLM), a time-only Poisson generalized additive model (GAM), and a Bayesian BYM2+RW1 latent Gaussian model fitted using integrated nested Laplace approximation (INLA) were compared using 100 Monte Carlo replicates per scenario. Performance was assessed using empirical bias, root mean squared error (RMSE), interval coverage, predictive RMSE, and spatial risk recovery. Under Scenarios A and B, the GLM and GAM exhibited poor interval coverage and substantially larger predictive errors despite relatively modest bias. The BYM2+RW1 model achieved near-nominal coverage, markedly improved predictive accuracy, and accurately recovered the latent spatial risk surface. Under strong spatial confounding, prediction remained robust, whereas estimation of spatial regression effects remained biased. These findings support Bayesian latent Gaussian spatio-temporal models as an appropriate default framework for disease mapping while highlighting the need for specialised methods when unbiased estimation of spatially structured covariate effects is the primary objective.