Evaluation of predictive capability of Bayesian spatio-temporal models for Covid-19 spread

Abstract

Abstract Background Bayesian models have been applied throughout the Covid-19 pandemic especially to model time series of case counts or deaths. Fewer examples exist of spatio-temporal modeling, even though the spatial spread of disease is a crucial factor in public health monitoring. The predictive capabilities of infectious disease models is also important. Methods In this study, the ability of Bayesian hierarchical models to recover different parts of the variation in disease counts is the focus. It is clear that different measures provide different views of behavior when models are fitted prospectively. Over a series of time horizons one step predictions have been generated and compared for different models (for case counts and death counts). These Bayesian SIR models were fitted using MCMC at 28 time horizons to mimic prospective prediction. A range of goodness of prediction measures were analyzed across the different time horizons. Results A particularly important result is that the peak intensity of case load is often under-estimated, while random spikes in case load can be mimicked using time dependent random effects. It is also clear that during the early wave of the pandemic simpler model forms are favored, but subsequently lagged spatial dependence models for cases are favored, even if the sophisticated models perform better overall. Discussion The models fitted mimic the situation where at a given time the history of the process is known but the future must be predicted based on the current evolution which has been observed. Using an overall ‘best’ model for prediction based on retrospective fitting of the complete pandemic waves is an assumption. However it is also clear that this case count model is well favored over other forms. During the first wave a simpler time series model predicts case counts better for counties than a spatially dependent one. The picture is more varied for morality. Conclusions From a predictive point of view it is clear that spatio-temporal models applied to county level Covid-19 data within the US vary in how well they fit over time and also how well they predict future events. At different times, SIR case count models and also mortality models with cumulative counts perform better in terms of prediction. A fundamental result is that predictive capability of models varies over time and using the same model could lead to poor predictive performance. In addition it is clear that models addressing the spatial context for case counts (i.e. with lagged neighborhood terms) and cumulative case counts for mortality data are clearly better at modeling spatio-temporal data which is commonly available for the Covid-19 pandemic in different areas of the globe.

Keywords

• Covid-19
• Pandemic
• Spatio-temporal
• Bayesian hierarchical modeling (BHM)
• MASE
• MAE