key: cord-0871970-kmi0lu42
authors: Lee, Duncan; Robertson, Chris; Marques, Diogo
title: Quantifying the small-area spatio-temporal dynamics of the Covid-19 pandemic in Scotland during a period with limited testing capacity
date: 2021-04-10
journal: Spat Stat
DOI: 10.1016/j.spasta.2021.100508
sha: ccea8871fc394ca472cadca40869eb7cb66e42ae
doc_id: 871970
cord_uid: kmi0lu42

Modelling the small-area spatio-temporal dynamics of the Covid-19 pandemic is of major public health importance, because it allows health agencies to better understand how and why the virus spreads. However, in Scotland during the first wave of the pandemic testing capacity was severely limited, meaning that large numbers of infected people were not formally diagnosed as having the virus. As a result, data on confirmed cases are unlikely to represent the true infection rates, and due to the small numbers of positive tests these data are not available at the small-area level for confidentiality reasons. Therefore to estimate the small-area dynamics in Covid-19 incidence this paper analyses the spatio-temporal trends in telehealth data relating to Covid-19, because during the first wave of the pandemic the public were advised to call the national telehealth provider NHS 24 if they experienced symptoms of the virus. Specifically, we propose a multivariate spatio-temporal correlation model for modelling the proportions of calls classified as either relating to Covid-19 directly or having related symptoms, and provide software for fitting the model in a Bayesian setting using Markov chain Monte Carlo simulation. The model was developed in partnership with the national health agency Public Health Scotland, and here we use it to analyse the spatio-temporal dynamics of the first wave of the Covid-19 pandemic in Scotland between March and July 2020, specifically focusing on the spatial variation in the peak and the end of the first wave.

Italy in February 2020, and in Scotland, the focus of this paper, the first con- ing a small-area surveillance system for monitoring the spatio-temporal trend 25 in Covid-19 incidence is a vital tool in the fight against the virus, because 26 it allows public health agencies to monitor its spread and identify hot-spots 27 with high incidence, as well as providing vital clues as to how and why the The focus of this study is Covid-19 surveillance in Scotland, which is 30 currently in its second wave of infection since September 2020. During this 31 second wave the spatio-temporal spread of the pandemic can be measured 32 using data on positive tests at the small-area scale, which is due to Scot-33 land having a wide-spread testing programme during this period. This 34 programme allows any member of the public to book a test at https: 35 //www.gov.uk/get-coronavirus-test, and well over 15,000 tests are con-36 ducted each day. However, during the first wave of the pandemic between 37 March and July 2020 Covid-19 testing capacity was strictly limited to priority 38 groups, because there was a lack of infrastructure to allow large-scale test- to 1,900 in April 2020. Therefore in this first wave the public were not able 42 to access a diagnostic test to determine if they had the virus unless a test 43 was recommended by a doctor. Instead, anyone experiencing symptoms was 44 advised to phone the national telehealth service NHS 24 for medical advice, 45 and was then asked to self-isolate at home. As a result data on confirmed 46 Covid-19 cases will not provide a detailed picture of the spatio-temporal spread of the virus during this first wave, because only a very small fraction 48 of the actual cases were confirmed by a positive test.

Due to this massive under-reporting the aim of this paper is to use proxy 50 indicators of disease incidence to quantify the small-area spatio-temporal 51 dynamics of the Covid-19 pandemic in Scotland during its first wave of in-52 fections. Specifically, we aim to estimate both Scotland-wide and small-area 53 temporal trends in disease incidence, focusing on both the peak and the end 54 of this first wave. As people with symptoms during this first wave were ad-55 vised to phone NHS 24 for medical advice, we model data on the numbers 56 of NHS 24 calls categorised as Covid-19 or having related symptoms at the 57 small-area scale on a weekly basis. The model we developed was run by 58 analysts in Public Health Scotland (PHS) on this proxy measure of disease 59 incidence on a weekly basis during the first wave of the pandemic, allowing 60 them to better understand the spread of the virus and target public health 61 interventions appropriately at areas likely to exhibit the greatest risks.

Our model is a multivariate binomial spatio-temporal random effects 63 model, with inference in a Bayesian setting using Markov chain Monte Carlo 64 (MCMC) simulation. It jointly models the spatio-temporal variation in the calls categorised with related symptoms such as fever and difficulty breath-67 ing, the latter ensuring that potential local outbreaks are not missed due to 68 calls being misclassified. In developing this model the key methodological 69 challenge we address is the complex multivariate spatio-temporal structure 70 of the data, which means we need to capture spatial, temporal and between 71 call type correlations. as allowing for varying strengths of spatial correlation via the Leroux spa-84 tial correlation model (Leroux et al., 2000) . The NHS 24 telehealth data for 85 the first wave of the pandemic that we analyse are described in Section 2, 86 while our multivariate spatio-temporal model is presented in Section 3. Our 87 surveillance model is applied to the Scottish telehealth data in Section 4, 88 while Section 5 concludes the paper. Thus as the data exhibit spatio-temporal and between call type correlations 207 contaminated by noise due to small numbers, a multivariate spatio-temporal 

spatio-temporal variation in the estimated {θ ktj } provides a proxy measure of 238 the incidence of the virus in the absence of comprehensive testing data. We 

where ⊗ denotes a Kronecker product. The precision matrix is given by 273

(3) In what follows we now discuss the three components of the precision 274 matrix in turn. 

which is combined with the improper non-informative prior f (α) ∝ 1.

This specification corresponds to a tridiagonal matrix for D(α) with entries can be decomposed as

which is combined with the improper non-informative prior f (α 1 , α 2 ) ∝ 1.

This specification corresponds to the following sparse matrix for D(α) with for t = 1 1 + α 2 1 + α 2 2 for t = 2, . . . , N − 2 1 + α 2 where Y −ktj denotes all observations except for Y ktj . The best fitting model is 386 the one that maximises the LMPL, which is also achieved by the model with 387 an intrinsic CAR spatial structure and a second order autoregressive tempo-388 ral structure. However, in common with the DIC the differences between the 389 models by this measure are also small, being at most 1.3%

The residuals from all models were assessed for the presence of any re-391 maining spatial autocorrelation using a Moran's I permutation test sepa-392 rately for each year, and in all cases no significant autocorrelation remained.

The presence of residual temporal autocorrelation was also checked for each 394 model and PD, by determining whether the lag 1 autocorrelation coefficient 395 was significantly different from zero at the 5% level. We based on our assess- week thatθ kt1 was at its highest, which represents the peak of its first wave; 488 and (B) the first week after this peak thatθ kt1 was smaller than its value in to SE1 declined to lower levels than those attributed to Covid-19.

The overarching aim of this paper was to estimate the key dynamics of the 556 Covid-19 pandemic at a high spatio-temporal resolution in a retrospective 557 manner, which is why no predictive modelling of the proportions of calls 558 classified as Covid-19 or SE1 into the future was undertaken. However, the 559 temporally autoregressive nature of the models would make such prediction 560 straightforward via (6) or (7), and both the proportions {θ k,T +1,j } and counts 561 {Y k,T +1,j } could be predicted in this way, although for the latter {N k,T +1,j } 562 would also need to be predicted. Thus an area of future work will be to utilise 563 these MVST models to predict disease burden into the future, to allow NHS 564 managers to predict the amount of health care resources (e.g. hospital beds) 565 needed in the future.

Another area of future work would be to continue the development of 

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The authors declare they have no competing interests.