Anonymised linelists of reported COVID-19-related deaths between the 1st of January and 30th of June 2020 were provided by Public Health England (PHE). COVID-19-related deaths were considered to include those with COVID-19 recorded as an underlying cause, or where COVID-19 was mentioned as a contributing factor but not specified as cause of death. These two categories included a total of 52,560 reported deaths in England which occurred between 2020-01-05 and 2020-06-28. Counts were then aggregated by lower-tier local authority (LTLA), week of death (counted from Wednesday 1st January) and 10-year age group. Aggregation by week was chosen in order to avoid excessive zero or low counts and potential day-of-week reporting effects, and to obtain a smoother representation of the epidemic curve. Records which did not have a LTLA provided (n = 74) were excluded. Local authority shapefiles and single-age population estimates were obtained from the Office for National Statistics (ONS) (10, 11) and matched to the aggregated death data.
LTLAs can be classified into one of four geographical categories: London borough (10.3% of total LTLAs), metropolitan district (11.5%), non-metropolitan district (60.3%) and unitary authority (17.9%). The former two categories capture the major urban areas of the country (including Birmingham, Liverpool, Manchester, Sheffield, Leeds and Newcastle) with high connectivity both nationally and internationally, while the latter capture predominantly rural areas and smaller towns or cities.
PCR-confirmed pre-P2 and post-P2 cases (i.e. COVID-19 infections identified through both pillar 1 and pillar 2 surveillance) were obtained from the same source and aggregated to the same spatial and temporal resolution. Finally, estimates of infection prevalence in England were obtained from the ONS COVID-19 infection survey pilot (12) which was initiated in May 2020. These are presented as an estimated percentage (plus 95% confidence interval based on the survey sample size) of the population who would test positive via PCR for COVID-19 during rolling fortnightly intervals.
For the remainder of the paper, infections confirmed with a positive PCR test and recorded in official case data prior to the expansion of symptomatic community testing on the 18th of May will be referred to as pre-P2 cases, and infections confirmed following expansion of testing will be referred to as post-P2 cases. It is noted that, due to piloting of pillar 2 testing among high-risk groups, a proportion of pre-P2 cases will have been detected via the pillar 2 route. We conservatively define the surveillance policy change from the point at which pillar 2 was fully available to all symptomatic individuals - assuming that case data from this point most accurately reflect the increased coverage of the expanded system - and define the terminology according to this distinction. We will also introduce the concept of predicted-P1+P2 cases, meaning the predicted infections which would have been PCR-confirmed in the hypothetical scenario in which symptomatic community testing had been in place since the beginning of the epidemic (January 2020). These predicted-P1+P2 cases form a subset of total symptomatic cases, conditional on the additional criteria that the case must be both symptomatic and seek and obtain a confirmatory positive test result. Lateral flow devices were not introduced for asymptomatic testing until later in the year (3) and therefore are not considered here. All references to deaths imply COVID-19-related deaths, i.e., those where either PCR-confirmed or clinically diagnosed COVID-19 infection is recorded on the death certificate.
Bayesian mixed effects models for deaths per week and per LTLA were fitted using integrated nested Laplace approximation (INLA), implemented via the R package R-INLA (13, 14).
To facilitate comparison in observed deaths across local authorities with different population age distributions, age-adjusted expected deaths, E, were calculated for each LTLA to serve as an offset in models. Expected counts were based on age-specific weekly mortality rates averaged over the observed time period and over the country as a whole. See Supplementary materials for details. Weekly reported deaths in LTLAi were assumed to follow a negative binomial distribution, with log link function, offset by log (Ei).
In addition to age, two population level characteristics were considered as risk factors for case fatality: level of deprivation and distribution of ethnicity. The Index of Multiple Deprivation (IMD) score is defined as a relative measure of deprivation between Lower Super Output Areas (LSOAs) and incorporates a range of social, economic and health factors (15). IMD scores were aggregated to the median across all LSOAs in each LTLA and categorised by quintiles. To account for the heterogeneous distribution of ethnicity across the country, the percentage of minority ethnic groups in each LTLA population (relative to white as the national majority) was calculated according to estimates from the most recent census (16).
The temporal dependence in the data was modelled using a combination of random effects with random walk (RW) correlation structures (17). A second-order random walk (RW2) on the number of weeks since the first observed death (the “epidemic” week) was intended to capture the shifted epidemic curve in each LA. Additionally, a first-order random walk (RW1) on calendar week was included to capture any overall deviations from these epidemic trends (potentially as a result of policy and behavioural change). As such, the number of deaths in any one LTLA during one week are a priori assumed to be correlated with the number of deaths across the prior two weeks. Models in which the second-order RW on epidemic week was fitted separately within each of the four geography categories were also considered.
Models without any specified spatial structure were compared to those with independent and identically-distributed (IID) random effects per LTLA, and with a combination of IID and structured, conditional auto-regressive effects (as described by Besag, York and Mollié (18), hereafter referred to as BYM), parameterised with a mixing parameter 𝜙 between the two (19). The latter allowed assessment of the contribution of local spatial correlation to the fit of the model, relative to purely random (IID) variation.
Six models were fitted and compared:
(A) Baseline Observed deaths ~ log(E) (offset) + Overall epidemic trend (RW2) + calendar week trend (RW1) + covariates (IMD, % minority); no spatial structure.
(B) A + geography-dependent epidemic trends
(C) A + IID spatial structure
(D) B + IID spatial structure
(E) A + BYM spatial structure
(F) B + BYM spatial structure
The distributions of structured random effects (spatial and temporal) were fit with penalised complexity priors on the precision and BYM mixing parameters (20), and fixed effects fit with weakly-informative gaussian priors centred at zero. A more detailed specification of all models can be found in the supplementary materials.
All analyses were performed in R version 3.6.3 (2020-02-29). All code used to run these analyses have been made available at https://doi.org/10.5281/zenodo.5763664.
Models were compared using WAIC (21) and log score (22). Pearson residuals between fitted values and observed were averaged per LTLA and mapped as a visualisation of the spatial structure unexplained by each model. Posterior samples (n = 1,000) were drawn to explore the uncertainty in predictions and aggregated over LTLAs to give total trajectories over time.
Comparison to post-P2 cases
It was assumed that post-P2 cases (swabbed from 18th May onwards) were reflective of the higher coverage surveillance and less obscured by capacity constraints. A fixed lag of one week between date of swabbing and date of death was applied to infer predicted-P1+P2 cases from modelled deaths in the primary analysis, while a sensitivity analysis was conducted assuming two- and three-week lags. This choice was informed by the swab-death delay distribution observed in this dataset (median 6 days, IQR 8 days), while also considering an external report from the COVID Clinical Information Network (CO-CIN) (23) which suggested an overall longer and more varied distribution (median 13 days, IQR 14 days) between onset of symptoms and death. The possibility was considered that the lag between testing and death may have been shorter early in the epidemic, with cases predominantly being tested in a hospital setting when symptoms were already severe. However, the available data on swabbing and death dates did not suggest a difference between pre- and post-P2 cases (median 6 days pre-P2 and 7 days post-P2, with equal quartiles of 3-11 days), and therefore one fixed lag was assumed for the entire period. It was assumed that variation over this period of time in the ratio of post-P2 cases to deaths would be predominantly a result of varying completeness of observation of cases, rather than of a difference in underlying case-fatality risk.
The approach taken to infer predicted-P1+P2 cases from reported deaths consisted of three steps. First, smoothed trajectories of deaths per week and per LTLA, corrected for spatial heterogeneity in case-fatality risk factors, were obtained from the fitted model (1,000 posterior samples predicted at averaged covariate values with non-age-stratified population offset). An LTLA-level ratio of cases per covid-related death (post-P2 case per death ratio, CPDR) was then estimated for every week beyond the 18th May and for each posterior sample, lagging the modelled death counts by one week (two and three weeks for the sensitivity analysis) and comparing to post-P2 cases. CPDRs were summarised over all post-P2 weeks to obtain a median and IQR for each LTLA, which were then used to scale up the posterior samples over the whole time period. This yielded an estimate of the magnitude of cases giving rise to those deaths, which would have been detected under expanded surveillance.
Inferring infection and rate of detection
The previous steps yield estimated local trajectories of COVID-19 infections which would have been detected through combined hospital and community-based symptomatic testing, had such capacity been available throughout the first epidemic wave. However, post-P2 cases detected under expanded surveillance remain a subset of the total number of infections. The ONS COVID-19 infection survey pilot (12) suggested that per fortnight between the 27th April and 24th May around 0.25% of the population of England would have tested positive for COVID-19, with this percentage steadily decreasing to 0.03% by the beginning of July. To investigate the gap between total infection incidence and detected cases, these data were combined with post-P2 case counts over the same period to infer a rate of detection under expanded surveillance (see Supplementary Materials D). This rate of detection was then applied to the entire trajectories of predicted-P1+P2 cases to estimate the number of infections represented by those detected cases. Observed pre- and post-P2 counts could then be compared to these estimated infections to infer the percentage of infections detected over time and within each LTLA.