A multivariate statistical approach to predict COVID-19 count data with epidemiological interpretation and uncertainty quantification

For the analysis of COVID-19 pandemic data, we propose Bayesian multinomial and Dirichlet-multinomial autoregressive models for time-series of counts of patients in mutually exclusive and exhaustive observational categories, defined according to the severity of the patient status and the required treatment. Categories include hospitalized in regular wards (H) and in intensive care units (ICU), together with deceased (D) and recovered (R). These models explicitly formulate assumptions on the transition probabilities between these categories across time, thanks to a flexible formulation based on parameters that a priori follow normal distributions, possibly truncated to incorporate specific hypotheses having an epidemiological interpretation. The posterior distribution of model parameters and the transition matrices are estimated by a Markov chain Monte Carlo algorithm that also provides predictions and allows us to compute the reproduction number (Formula presented.). All estimates and predictions are endowed with an accuracy measure obtained thanks to the Bayesian approach. We present results concerning data collected during the first wave of the pandemic in Italy and Lombardy and study the effect of nonpharmaceutical interventions. Suitable discrepancy measures defined to check and compare models show that the Dirichlet-multinomial model has an adequate fit and provides good predictive performance in particular for H and ICU patients.