Retrospective estimation of respiratory virus covariances using Bayesian multivariate autoregressive models

Mair, Colette; Nickbakhsh, Sema; Reeve, Richard; McMenamin, Jim; Reynolds, Arlene; Gunson, Rory; Murcia, Pablo R; Matthews, Louise

Respiratory infections in humans are caused by a diverse community of co-circulating viral species including viruses that cause influenza and the common cold. Public health interventions such as vaccination programs typically focus on individual viral species. However, observational data suggest that the spread of one species may impact the dynamics of another. This finding would have important implications for the predicted impact of seasonal vaccines but currently lacks statistical support. The aim of this paper is to develop a statistical framework to identify non-independent viral dynamics. As Bayesian multivariate disease mapping models naturally encompass a between-disease covariance matrix, we extended this framework to model multivariate time series data accounting for within- and between-year dependencies. By inferring non-zero off-diagonal entries of the between-disease covariance matrix, we present a novel technique that successfully identifies significant viral interactions. We illustrate this framework using incidence data from five co-circulating respiratory viruses (adenovirus [AdV], coronavirus [Cov], human metapneumovirus [MPV], influenza B virus [IBV] and respiratory syncytial virus [RSV]) detected by routine diagnostics at the West of Scotland Specialist Virology Center (WoSSVC) between 2005 and 2013. We found a significant positive covariance between RSV \&MPV and a negative covariance between IBV \&AdV paving the way for future examination of biological or behavioural factors that may generate interactions between certain virus pairs.