Bayesian spatio-temporal analysis of the COVID-19 pandemic in Catalonia

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The COVID-19 pandemic posed an unprecedented challenge to public health systems around the world and motivated the need for comprehensive epidemiological measures to monitor and respond effectively to the outbreak. The analysis of small units of space and time, where decisions often need to be made, is generally characterised by presenting high variability and noise, and traditional approaches may struggle to provide accurate estimates(1). Using spatial and spatio-temporal disease mapping models, we can overcome many of these challenges by borrowing strength from spatial and temporal neighbours, allowing us to obtain reliable estimates for these small units and to uncover and understand the patterns of disease spread across space and time(2). The objective of this study was to investigate the spatio-temporal evolution of the incidence of reported COVID-19 cases and hospitalisations in the different basic health areas (ABS) of Catalonia during the pandemic period. The effect of ABS demographic and socio-economic factors on COVID-19 cases and hospitalisations was also assessed, along with the effect of the percentage of vaccinated population

 An ecological study of administrative data was carried out to model the incidence of COVID-19 cases and hospitalisations by basic health areas (ABS) in Catalonia (Figure 1).

Figure 1. Map of the study territory, Catalonia. The territory is divided into 373 basic health areas (ABS), which are grouped into 7 different health regions, each represented by a different colour

Spatial, temporal and spatio-temporal incidence trends were described using estimation methods that allow to borrow strength from neighbouring areas and time points. We used the Bayesian hierarchical spatio-temporal framework to model the weekly observed counts of COVID-19 cases/hospitalisations, Yit , as follows:

Yitit~Poisson(Eitθit)

logθit =α+βittit

 where α quantifies the global risk;  βi is the spatial effect; γt and ωt are the temporally structured and unstructured random effects, respectively; and δit models the spatio-temporal interaction random effect. With this formulation, the maximum likelihood (ML) estimator of θit is given by  θit=Yit/Eit corresponding to the age and sex standardised incidence ratio (SIR). Thus, the estimated θit is a smooth estimate of the SIR and can be interpreted as the area and week specific relative risk (RR), with respect to the global territory of Catalonia for the whole period. Furthermore, an exploratory analysis was conducted to identify potential ABS factors associated with the incidence of cases and hospitalisations. We included the available socio-demographic covariates and the cumulative percentage of full vaccination in the past week to the model as fixed effects.

To model the spatio-temporal random effects we considered the set of non-parametric models proposed by Knorr-Held(3), and the best model in terms of the Deviance Information Criterion (DIC) and the Widely Applicable Information Criterion (WAIC) was selected. Finally, the spatial effect was modelled using the reparametrisation of the classical Besag York Mollié model to avoid identifability problems. The unstructured temporal effect was not included in the model, and the structured temporal effect was modelled by assuming a first-order random walk that imposes a dependence on the previous week. For the spatio-temporal interaction effect, the type II proposed by Knorr-Held worked better on our data. The models were fitted using the Integrated Nested Laplace Approximation (INLA).

 All code was developed using the free statistical software R in the version 4.3.0(4) with special attention to the package R-INLA(5). All implemented code used in this study is publicly available online at: https://github.com/pasahe/Bayesian-spatio-temporal-analysis-of-COVID-19-in-Catalonia

During the study period, a cumulative total of 2,685,568 COVID-19 cases and 144,550 hospitalisations were reported in Catalonia, representing a 35% and a 1.89% of the total population. In Fig. 2b and d the evolution of weekly cases and hospitalisation rates (×100,000 population) in Catalonia over the whole study period is represented. The vertical dotted lines represent the start of each of the six waves, which were very different in shape, especially for cases. Considering all the pandemic period, the proportion of the total population infected ranged from a minimum of 26% in some areas to a maximum of 46% in others, while the proportion of the total population hospitalised ranged from 0.5% to 3.5%

Figure 2. COVID-19 cases and hospitalisation weekly rates and cumulative distribution by basic health areas (ABS). (a) Map of the total cumulative incidence percentage of COVID-19 cases over the whole study period for each ABS. (b) Raw rate (×100,000 population) of COVID-19 cases in Catalonia per week. (c) Map of the total cumulative incidence percentage of COVID-19 hospitalisations over the whole study period for each ABS. (d) Raw rate (×100,000 population) of COVID-19 hospitalisations in Catalonia per week.

We have identified the spatial, temporal and spatio-temporal trends of the Covid-19 pandemic in Catalonia. Clustered cold and hot spots in space, time and spatio-temporal dimension were identified for both cases and hospitalisations (Fig. 3). The lack/excess of risk for each area, compared to the general population on average over the whole population is represented in Fig.3a and b (spatial RR). The lack/excess of risk for the general population of one week compared to the average for the whole period is represented in Fig. 3c and d (temporal RR). Finally, how areas deviate from the overall temporal trend of the general population at many different points in time is represented in Fig. 3e and f (spatio-temporal RR).

Figure 3. COVID-19 cases and hospitalisation weekly rates and cumulative distribution by basic health areas (ABS). (a) Map of the total cumulative incidence percentage of COVID-19 cases over the whole study period for each ABS. (b) Raw rate (×100,000 population) of COVID-19 cases in Catalonia per week. (c) Map of the total cumulative incidence percentage of COVID-19 hospitalisations over the whole study period for each ABS. (d) Raw rate (×100,000 population) of COVID-19 hospitalisations in Catalonia per week.

Furthermore, we showed that urban areas had a higher risk of COVID-19 cases and hospitalisations compared to rural areas, while socio-economic deprivation of the area was a risk factor for higher hospitalisations rates. Finally, an increase in the cumulative percentage of complete vaccination in the previous week was associated with a significant reduction in the risk of cases and hospitalisations of the area.

 In this study we explored the COVID-19 pandemic across the territory of Catalonia at a small area level, describing the spatial, temporal and spatio-temporal trends of the disease. We also provided insight into some of the factors associated with COVID-19, showing that urban areas have a higher risk of COVID-19 cases and hospitalisations compared to rural areas, while socio-economic deprivation of the area was a risk factor for hospitalisations. Bayesian hierarchical modelling was found to be very useful for this task, providing a fexible and robust framework. This study contributes to the literature exploring the spatio-temporal pattern and factors associated with COVID-19 in small area-level studies in other regions of the world.

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Bayesian Inference
Mathematics and Computing > Statistics > Statistical Theory and Methods > Bayesian Inference
Biostatistics
Mathematics and Computing > Statistics > Applied Statistics > Biostatistics
Epidemiology
Life Sciences > Health Sciences > Biomedical Research > Epidemiology
COVID19
Life Sciences > Health Sciences > Clinical Medicine > Diseases > Infectious Diseases > COVID19

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