# Covid-19 in Northamptonshire #2: a summary of mortality data from March to December 2020

**Nick Petford and Jackie Campbell, University of Northampton**

In August 2020 we published a blog summarising the mortality rates in Northamptonshire due to Covid-19 using publicly available data from the UK government’s Office for National Statistics (ONS). The objective was two-fold. First, to record and classify regional and sub-regional variations at a statistically significant level. Second, to present the initial results of a mathematical (SEIR) model of disease spread in the county. In addition, we used estimates of theoretical recovery rates derived from the SEIR model to estimate the range in crucial fraction of the susceptible population who would require vaccination as a function of the basic reproduction number *R*.

In this second contribution we have scrutinised the official published mortality data to December 6 (week 49), 2010, extending our previous analysis by 21 weeks. The results are presented against a backdrop of a second national lockdown in England (November 5 to December 2) that proceeded the introduction of regional Tiers brought in to reduce the reported rise infection rates since the summer. We have updated the longitudinal data for Northamptonshire and compared it to rates across the East Midlands and nationally. We also compare the data at the start of the infection in March, with rates from week 41 onwards, tentatively marking the onset of a ‘second wave’ of Covid-19 fatalities in the UK. Finally, we show how infection rates from testing can differ significantly from reported values if false positives and negatives are factored in.

# The National picture

ONS mortality data for Covid-19 for the year to December 6, 2020 are shown in Fig. 1 (green line). All deaths (blue) along with the five-year average are also shown, for comparison. The spring mortality data define a clear pattern of very steep increase in weeks 13–17, followed by a slower decline back to the background average by week 23. From week 41, all deaths, that include a contribution from Covid-19, begin to diverge from the five-year average, albeit at a much slower rate than in the spring. We comment on the relative rates of increase later.

Fig. 1. Deaths from all causes (2020 total deaths) compared to the five-year average in England showing the spring impact of Covid-19. Reported deaths involving Covid-19 shown in green (source ONS).

# Regional level

Regional and local trends are shown in Fig 2. The East Midlands rate (that includes Northamptonshire) mirrors the national picture, with the spring peak maximum in week 16 and an upturn from week 40.

Fig. 2. Covid-19 deaths to week 49, comparing England with the East Midlands and Northamptonshire.

# Northamptonshire

Compared in this way, the overall trend in Northamptonshire is much like the national and regional picture. Since week 28, total deaths have remained low and unlike the East Midlands there does not (yet) appear to be a significant rise in mortality from week 40 onwards. At its height, (weeks 13–27), Covid-19 deaths accounted for just over one quarter (27%) of the total number recorded (2557). Looking at the most recent data, mortality rates, while increasing slightly from week 43 (cumulatively 8% of all deaths), are not comparable in magnitude or severity to the first wave in the spring.

When broken down by district, Northampton, the most populous area, has recorded the highest percentage of deaths in the county, currently at 37% of the total (Fig. 3).

Fig. 3. Percentage of Covid-19 deaths by location in Northamptonshire for the period March to November 2020.

# By Unitary

Fig. 4. shows the Covid-19 mortality rate per 100,000 for East and North Northamptonshire by proposed Unitary boundary (as of April 1, 2021). This takes account of different population numbers and the higher rates in West Northants during the spring peak (weeks 12–15), reflect the dominance of Northampton in the data set (see our first blog on the topic here highlighting the effect of uneven population density in the county).

Fig. 4. Comparison of Covid-19 deaths (per 100,000 population) between the proposed new authorities. The average rate of change over time follows a broadly similar pattern, but with some local variation.

# Comparing Covid-19 spring rates with winter 2020

A key characteristic of novel pandemic spread in human (and animal) populations is an exponential increase in death rates during the initial phase (Kermack & McKendrick, 1927). Moreover, the initial exponential growth rate of an epidemic is closely related to the basic reproduction number and is a measure of its severity (Ma, 2020). Fig. 5. compares the first eight weeks of infection in England (weeks 10–17) with the most recent eight weeks from November and December (weeks 40–47), coinciding with the start of the second national lockdown, plotted on a weekly scale from 1–8. It is clear the shapes of the curves for both periods are quite different. In particular, the steep (exponential) rise seen in the spring data, for both England and Northamptonshire, is not there in the most recent data. Instead, the ‘second wave’ in mortality is characterised by linear growth. It is possible to quantify this contrast between different phases of the pandemic using some simple mathematics. The mortality rate during the initial exponential phase in England (weeks 10–15) and Northamptonshire (weeks 12–16) grew at approximately 20% and 12% respectively. Similar high growth rates during weeks 40–47 would have resulted in a national death toll that exceeded the first wave by many tens of thousands. The reasons behind these different trends needs further research. It could be that the November lock down, combined with a smaller pool of vulnerable individuals (the average age of death to Covid-19 is 82.4 years), both kept mortality rates lower than they might otherwise have been.

(a)

(b)

Fig. 5. Plots comparing mortality rates during the initial spring 2020 phase (blue line, wave 1) with deaths later in the year (from week 40, red line) over the same time interval. (a). Trend for England. The spring exponential growth rate is approximately 20%. By contrast, the autumn/winter phase is linear (r2 = 0.98). (b). The same analysis applied to Northamptonshire. The sub region mirrors the national trend. Growth rate in the spring exponential phase was 12%. The linear phase has a regression coefficient of 0.94.

# Test results Northamptonshire: how reliable?

Since out first blog, testing on a national scale has stepped up significantly, and now stands at more than 1 in 10 in England. In Northamptonshire, 15,538 positive cases have been reported up until 30 November. The growth in positive cases since September 14 is shown in Fig. 6.

Fig. 6. Total positive cases by week (14/09/20 to 30/11/20). Source: Public Health Northamptonshire.

However, despite the steep rise in positive cases from October onwards, this is not (yet) translating in to excess deaths the way it did in the spring (see Fig. 5). This may be due to the demographics of the test population (age, sex and ethnicity). If most positive outcomes are in younger people (< 60 years, and female), then the risk of mortality is relatively low. However, an additional, more controversial reason, might be that the test results are not a true reflection of the actual incidence rate in the population. We explore this idea in more detail below.

No medical test is ever 100% accurate. Errors can arise because of sensitivity issues with the test equipment, contamination and human error. More fundamentally, the test itself presents a dilemma to do with the probabilities of cause and effect. To understand this better, let’s suppose you have had a medical test for a disease, the result of which comes back positive. How likely is it that you *really *have the disease? This seems a ridiculous proposition. You’ve been tested and it came back positive. Well, let’s see.

There are two measures that are important for clinical tests: the true positive rate (or sensitivity) is the percentage of those that have the disease who test positive and the true negative rate (or specificity) is the percentage of those without the disease who test negative. The true positive and true negative rates for a test are determined by experimental and clinical testing and are predictable. For the RT-PCR Covid-19 test, the analytical sensitivity of the test equipment is estimated at 95%. However, the operational false positive rate in UK swab tests is estimated currently at between 0.8 and 4.0% (Surkova et al., 2020). Moreover, the actual numbers of positive and negative tests are dependent on the underlying disease rate or pretest probability — how many of those coming for tests actually have the disease. And, of course you don’t know that for certain — otherwise you wouldn’t need the test….

What we are usually interested in is the number of wrong results — the false negatives (people who have the disease but test negative) and false positives (people who don’t have the disease but test positive). This is because these lead to inappropriate actions — in the case of Covid-19, false negatives can go on to infect others without restrictions, and false positives must quarantine when they don’t need to. And, of course, testing results contribute to general policy regarding regional tiers and lockdowns etc. It is counter-intuitive, but, even though the true positive and negative rates are fixed, the false rates vary depending on the true proportion of positive cases (the disease prevalence) in those coming for the tests.

Let’s have a look to see how this works. At the beginning of December 2020, the Office for National Statistics estimated that approximately 1% of the population of England had Covid-19. This is estimated from a random sample of people, not people with Covid-19 symptoms. If you used a test with 95% true positive and negative rates on a random group of 10,000 people, then this group would be expected to have 100 Covid-19 cases (1% of 10,000). The test will be positive for 95 of these 100 (true positive rate of 95% of the 100 with Covid-19). This leaves 5 people with Covid-19 who test negative. There are thus 9,900 of the group who don’t have Covid-19. A 95% true negative rate for the test means that 95% of 9,900=9,405 will have a true negative test result, leaving 9,900–9,405=495 who therefore had a false positive. This is summarised below in Table 1.

Table 1. Effect of the risk of having Covid-19 on the numbers of true and false positive test outcomes

Table 1 also shows those calculations where the chance of the people being tested having Covid-19 is higher than a random sample. This is the situation where people being tested have symptoms of Covid-19 (community testing) or are at particularly high risk (e.g. in hospitals or care homes). The percentage risks are for illustration purposes only but highlights nicely the problem with interpreting the results of Covid-19 tests. When the disease prevalence in the test group is the same as the false positive rate (the 5% chance of having Covid-19 in Table 1), then the number of false positives is equal to the number of true positives. So, if you received a positive test results, it only has a 50% chance of being accurate. However, if you take the same test as part of a group of 10,000 with a higher chance of being positive (say 10%) then 450 will have false positives compared to 950 true positives. Here, if you had a positive test it would be 68% accurate — with a 32% chance that you were, in fact, disease free. So, the higher the infection rate in the group being tested, the more confident you can be that a positive test result means you *really do* have Covid-19.

# References

Kermack, WO, McKendrick AG. (1927). A contribution to the mathematical theory of epidemics. *Proc Royal Soc Math Phys Eng Sci.* **115**: 700–721.

Ma, J (2020). Estimating epidemic exponential growth rate and basic reproduction number. *Infectious Disease Modelling* **5**: 129–141. https://doi.org/10.1016/j.idm.2019.12.009

Surkova, E, Nikolayevskyy, V, Drobniewski, F. (2020). False-positive Covid-19 results: hidden problems and costs. *The Lancet*, https://doi.org/10.1016/S2213-2600(20)30453-7

https://www.ons.gov.uk/datasets/weekly-deaths-local-authority/editions/time-series/versions/9

# Biography

Nick is vice chancellor of the University of Northampton. Although a geologist by training he has published several medical-related research articles on topics malaria prevention, mathematical modelling of blood flow in stroke victims and the three-dimensional structure of animal skin. He is also Chair of Northamptonshire Health and Wellbeing Board, one of over 100 statutory bodies responsible for developing integrated health and social care strategies and reducing health inequalities. View ORCID Profile

Jackie** **initially qualified as a physicist before working as a researcher into the processes of pain and pain relief at the Pain Relief Institute in Liverpool. She has worked in the healthcare sector of higher education since 1987 and is the part-time Professor of Neurophysiology at the University of Northampton and is Chair of the NIHR East Midlands Research Design Service Regional Advisory Board. She is a chartered statistician, has served as the statistician member of an NHS Research Ethics Committee and teaches statistics and research methods to doctoral level. She is a reviewer for many major funding bodies and academic journals, including membership of the statistical review panel for The Lancet group. View ORCID Profile