Bayesian spatio-temporal joint disease mapping of Covid-19 cases and deaths in local authorities of England

Abstract

The overwhelming spatio-temporal nature of the spread of the ongoing Covid-19 pandemic demands urgent attention of data analysts and model developers. Modelling results obtained from analytical tool development are essential to understand the ongoing pandemic dynamics with a view to helping the public and policy makers. The pandemic has generated data on a huge number of interesting statistics such as the number of new cases, hospitalisations and deaths in many spatio-temporal resolutions for the analysts to investigate. The multivariate nature of these data sets, along with the inherent spatio-temporal dependencies, poses new challenges for modellers. This article proposes a two-stage hierarchical Bayesian model as a joint bivariate model for the number of cases and deaths observed weekly for the different local authority administrative regions in England. An adaptive model is proposed for the weekly Covid-19 death rates as part of the joint bivariate model. The adaptive model is able to detect possible step changes in death rates in neighbouring areas. The joint model is also used to evaluate the effects of several socio-economic and environmental covariates on the rates of cases and deaths. Inclusion of these covariates points to the presence of a north-south divide in both the case and death rates. Nitrogen dioxide, the only air pollution measure used in the model, is seen to be significantly positively associated with the number cases, even in the presence of the spatio-temporal random effects taking care of spatio-temporal dependencies present in the data. The proposed models provide excellent fits to the observed data and are seen to perform well for predicting the location specific number of deaths a week in advance. The structure of the models is very general and the same framework can be used for modelling other areally aggregated temporal statistics of the pandemics, e.g. the rate of hospitalisation.

Keywords: Bayesian space–time modelling; CAR; Covid-19 case rate; Covid-19 death rate; Ecological analysis; Temporal disease mapping.

Fig. 1

A map of the local authorities and nine administrative regions in England. Air pollution monitoring sites are shown as blue dots in the map. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 2

Boxplots of weekly death rates per 100,000 population. The boxplots are coloured according to the factor variable Course.

Fig. 3

Average SMR of covid deaths (top-left) and three relevant variables capturing socio-economic information.

Fig. 4

Graphical summaries of case rates.

Fig. 5

Pairwise scatter plots of the log SCMR values of covid cases and log SMR values for deaths along with various covariates. The variable price is on log to the base 10 scale, popden is on the log scale, NO${}_2$ is on the square-root scale, case smr and smr for death are on the log-scale. To avoid having to take log of zero the zero values of the SMR have been replaced by 0.05.

Fig. 6

Left panel: average NO${}_2$ levels in each LADCUA during the 36 weeks. Right panel: plot associating NO${}_2$ with covid case rates.

Fig. 7

Maps of observed and fitted average covid case and death rates.

Fig. 8

Highlighted borders where there are step changes in the death rates.

Fig. 9

Observations and forecasts for the number of deaths in week 46.

Fig. 10

Observed and fitted covid case and death rates by week.