3.1 About the infections data
The main dataset that is used in this paper is from the official UK Government data dashboard, https://coronavirus.data.gov.uk. Here we focus on cases of Covid-19 infection rather than deaths because only the infection data are available at weekly intervals and at a neighbourhood scale in England, allowing geographical and temporal patterns in the data to be considered. However, a data set giving the number of deaths due to Covid for each of the months from March 2020 to January 2021 was published at the same neighbourhood scale at the end of February 2021, as this research was being completed, having not previously been updated since August 2020 (ONS, 2021). We use these data to underscore that what is seen in the infection data is evident in the morality data too.
The neighbourhood geography is the Middle Level Super Output Areas (MSOAs). These are the third tier of the Census geography for England and Wales; third when aggregating upwards from the smallest, which are Output Areas. They represent a formal, administrative specification of neighbourhood but they are not arbitrary. They were designed with the criteria of broadly equal population size, socio-economic homogeneity based on accommodation type and tenure, and spatial compactness of the zones (Cockings et al., 2011). Matching them to the Office for National Statistics mid-2019 population estimates suggests an average population size of 8,605 in English major towns and cities, with an interquartile range from 7,154 to 9,640 persons.[3]
The infections data tally, by date reported, the number of individuals who had at least one positive Covid-19 test result, over that and the preceding six days. The data used in this paper span the week to March 21, 2020 to the week to February 19, 2021. The data include only pillar 1 cases until 2 July, from when pillar 2 cases also are included. Pillar 1 cases are “diagnostic tests done in Public Health England labs and hospitals for health and care workers and patients who are seriously ill” (Full Fact, 2020). Pillar 2 cases “are also diagnostic tests but done by commercial partners for the wider population. These tests are done at regional test sites, mobile testing units, satellite test centres and via home tests.”
Not everyone who has the disease is tested or necessarily displays symptoms so the numbers are underestimates of the true prevalence of the disease within the population. Especially this will be true prior to the beginning of July 2020 when it is, in effect, a count of the number hospitalised by Covid-19. The undercount is compounded throughout the study period by the suppression of the exact number in any MSOAs that had 0 to 2 cases that week. For this study, these are treated as zero values but they could be one or two.
A further problem is that test results are necessarily a function of testing – of where people are being tested and their ability to access a test. The availability of tests has changed over time. The 7-day average numbers of tests at the beginning of the months from May 2020 to February 2021 were 67,512 (May), 92,716 (June), 112,001 (July), 154,151 (August), 187,287 (September), 255,302 (October), 284,306 (November), 311,602 (December), 425,064 (January), and 6444,440 (February) (https://coronavirus.data.gov.uk/details/testing/). Although the increase is a response to the second wave of the disease, it also reflects increased capacity to test, which, in turn, allows for more positive diagnoses. That testing capacity has been constrained for some of the period of this study, with the British Medical Journal publishing a briefing in September entitled What’s going wrong with testing in the UK? (Wise, 2020). It is possible that the relative resilience of London to growing numbers of cases during the initial emergence of the second wave in England – from the end of September / early October, 2020 – was in part caused by insufficient testing. However, the nature of the regional economy and the type of jobs that are more easily adapted to home working may also be a factor (Harris & Cheshire, 2020).
Not everyone who has been in close contact with an infected person has necessarily been tested. On-going problems with the track-and-trace system (Triggle, Schraer & Kemp, 2020) meant about half of those who have been in contact with an infected person had not been contacted, so could harbour the disease with neither symptoms nor knowledge. There have also been changes to the data, first to harmonise them and to remove duplicates, and, secondly, to more accurately assign people to their current residential address. This raised the numbers around Universities as students were located to their term-time address, which may differ from the one on their NHS record because the latter can be a parental address if they are registered to a GP ‘back home’.
Nevertheless, the analysis assumes that tests follow symptoms, as well as the identification of known clusters of the disease, and that, therefore, the data track the disease’s spread amongst the population sufficiently well to be broadly representative of who has been infected and where they live. They are neither a random sample nor a complete census of all those who have been infected each week. However, they are the official source of infection data in the UK, used to inform public health policy and to guide preventative measures such as national and local lockdowns. We do not dispute the possibility of bias but note that the most likely systematic problem is an undercount of those who could be infected but either can least afford to socially isolate from out-of-home employment for the quarantine period required, or to travel to access a test. If such a bias exists, then it is likely to downplay the infection rate amongst BAME groups because of the intersections of ethnicity and social disadvantage, which means differences in exposure between BAME groups and the White British will be underestimated in the analysis.
3.2 Geography of the study
The study is confined to English major towns and cities, as defined in the ONS file of December 2015.[4] This is based on the built-up areas geography developed following the 2011 Census (ONS, 2013). Rural and semi-urban areas are not considered, partly because of their greater population sparsity that, all things being equal, reduces person-to-person contact and therefore the transmission of Covid-19. Much of the South West region of England, for example, has had consistently lower rates of infection throughout the pandemic and is mainly rural.
However, the main reason is demographic, informed by the ethnic geography of the country. Whereas many English towns and cities are ethnically diverse, more rural areas are typically not, containing far fewer of the BAME than White population. According to the 2011 Census, 61 per cent of the White British population resides outside the major towns and cities. The next largest percentage is equal for the White Other and Mixed ethnicity groups, of whom 30 per cent do not reside in these towns and cities. For the Black Caribbean and Black African groups, it is only 11 per cent. Nationally, lower Covid-19 infection and death rates amongst the White British population reflect rural-urban patterns of living. To compare ‘white’ rural hamlets with multicultural urban settlements is problematic; they are very different types of places. Consequently, we prefer the direct comparison, asking whether differential rates of exposure remain evident between different ethnic groups, within urban settlements.
In total, 109 English towns and cities are included in the study. The smallest is Walsall, with a mid-2019 estimated population of 65,928. The largest is London, with a population of 8,924,265. Because London is so much larger than the other settlements – its population is over 35 times greater than the average of 250,479 and approaching eight times greater than the second largest settlement, Birmingham, with 1,153,804 – it is split into its 32 local authorities for the analysis: the 32 London Boroughs, with the City of London merged with Westminster. This gives a total of 140 urban ‘places’.
3.3 Method of estimating the relative exposure of ethnic groups to neighbourhoods of Covid-19 infection
For the analysis, an index of exposure is formed to measure how much members of the various ethnic groups are exposed, by residence, to neighbourhoods of Covid-19 infection for each week of the study period. This index is based on the residuals from a Bayesian Poisson model, which are used to identify neighbourhoods that have more or less than the expected number of Covid-19 cases, relative to: (a) the overall infection rate that week; or, (b), also relative to the town or city in which the neighbourhood is situated.
The underlying model is,
![](https://myfiles.space/user_files/58677_ec8811c6b4185256/58677_custom_files/img1617103361.png)
These control variables are the ratio of care home beds in the MSOA to the adult population, the percentage of the adult population aged 18 to 21, and the percentage aged 22 to 35. The first two of these variables are included to control for two distinct types of setting where infection rates have been unusually high for at least some of the pandemic but where the inhabitants of those settings do not necessarily reflect the population characteristics of the wider neighbourhood. These are care homes and student halls of residence.
The third variable, the percentage of the adult population aged 22 to 35, is included because of a period, after the first national lockdown, when infection cases were growing amongst younger adults, and because BAME groups are, on average, younger than the White British. There is a risk that this control ends-up understating the exposure of BAME groups to infected neighbourhoods if controlling for age also partially controls for ethnicity. However, we judge this preferable to potentially confusing an age effect with an ethnic one. From an analytical point of view, if observed differences remain between the ethnic groups despite potentially biasing those differences downwards then that strengthens the argument that those differences are of substantive interest.
The control variables are standardised into z-values in the model (units of standard deviation from their mean). No further variables are included in the model because its purpose is not to explain the variations in the infection rates but to identify them, at the neighbourhood and town/city/London Borough scales. It is adopted to enable a multilevel approach that permits the differences between the urban places to be separated from the differences within them. It is, in effect, a null model, albeit one that controls for a few distinct circumstances that are unusual and would otherwise ‘inflate’ the number of cases in their MSOA.
Returning to Equation 1, is the number of the adult population in the MSOA and is an offset (it has a prescribed coefficient of one) that gives the log of the conditional rate of infection. This is seen by re-arranging the equation,
![](https://myfiles.space/user_files/58677_ec8811c6b4185256/58677_custom_files/img1617103458.png)
The multilevel model is formed by extending the underlying model to include two sets of random intercept terms, allowing for extra-Poisson variation at the MSOA level and for differences between the towns/cities/London Boroughs:
They measure the intra-place (within) and inter-place (between) differences, respectively. It is these that are used to form the index of exposure, measuring how exposed the average member of each ethnic group is to neighbourhoods with higher or lower than the expected infection rate.
The index is based on that used in studies of segregation where,
![](https://myfiles.space/user_files/58677_ec8811c6b4185256/58677_custom_files/img1617103865.png)
The modification we make is that pi becomes the probability of selecting, from a Normal distribution, a value lower than the MSOA’s deviance from its expected infection rate for the week. This means that if most of an ethnic group is living in MSOAs where the infection rate is higher than expected then the index will tend towards one, getting closer to one the greater the deviance from expectation. If most are living in neighbourhoods where the infection rate is lower than expected, it will tend towards zero. If the group is spread amongst neighbourhoods where those with higher infection rates balance out those with lower, then the index value will be 0.5.
The model is fitted 49 times, once for each week of the pandemic included in the study. It follows that the index of exposure is calculated weekly too. Adding-in the subscript, t , to denote time gives,
![](https://myfiles.space/user_files/58677_ec8811c6b4185256/58677_custom_files/img1617104026.png)
This shows that the modelled rate varies weekly as do the random intercepts but not the control variables because the population size, demographic profile and number of care homes beds are assumed to be constant for the study period. The regression coefficients could also be assumed to be time invariant, calculated once for the whole period and fixed at those values. However, such an assumption would be misplaced so their coefficients are permitted to vary too.
Although estimating their effect size is not the purpose of the model, their changing values are of passing interest and are shown in Figure 1. The number of care home beds per adult population had the greatest impact on increasing neighbourhood infection rates as the first national lockdown ended, in May 2020 (the periods of national lockdown are indicated in the figure with light grey shading). This is when concern about the lack of protection afforded to care home residents and their staff was of considerable media interest. Greater percentages of those aged 18-21 generally has a negative effect on the infection rates but not in the first week of October, in particular, when it had the strongest effect on increasing infection rates. This is when students returned from their homes to their term-time addresses after a delay in the start of the University term. The effect of populations aged 22-35 on infections is greatest after the first lockdown had ended and through the summer when pubs and restaurants had partially reopened and more people had returned to their workplaces.
The models are fitted as a Bayesian model using the brms package for R (Bürkner, 2017, 2018), which provides an interface to Stan (Stan Development Team, 2019). Results takes the form of draws from a Bayesian posterior distribution for the parameters of interest that are then summarised by their mean value.