How actuaries get the Covid numbers right.


By Andrew Pijper & Jonathan Pearson-Stuttard for


COVID-19 Actuaries Response Group – Learn. Share. Educate. Influence.



The actuarial consultancy and analytics firm Lane Clark & Peacock (LCP) has developed a COVID-19 Tracker to help improve and better tailor measures to break the chain of transmission of the virus, slow or prevent exponential growth in cases, and reduce the impacts of the pandemic on lives lost, the health system and wider society.  The tracker aims to be as close to real-time as the PHE daily data, but as comprehensive as the ONS approach. Combining both datasets and using established actuarial methods provides a more rounded estimate of current new infection rates.  In this Bulletin we provide an overview of the methods, high level findings and an analysis of the impact of the tier-based system in December 2020.


The LCP Covid-19 Tracker has been developed to help improve and better tailor measures to break the chain of transmission of the virus, slow or prevent exponential growth in cases, and reduce the impact of the pandemic on lives lost, the health system and wider society.  Now that testing capacity has reached around half a million tests each day, the data is much more granular. This allows approaches to control the virus to move from ‘one size fits all’ to more tailored and local measures, such as the tiered system introduced in Autumn 2020.

However, efforts until very recently are hampered because around one in three who have COVID-19 have no symptoms and hence will not request a test under the NHS Test & Trace programme reported in daily test data. This then tends not to capture positive but asymptomatic individuals, or which lags behind the real-time situation by days or weeks.  Using two sets of official test data and established actuarial methods to integrate and analyse both data sets, the LCP Covid-19 Tracker provides an up-to-date estimate of the true prevalence of the virus nationally and locally. This is crucial information for those seeking to establish timely and proportionate interventions to control the virus.

Areas with the least stringent restrictions – specifically, those placed in Tier 1 at some point in December – saw the sharpest rise, with new infections rising by 9.0% per day on average;
• areas that remained in Tier 2 through December saw an average daily growth rate of 6.5%;
• areas that started in Tier 2 before being moved to Tier 3 on 26 December saw an average daily
growth rate of 4.8%;
• areas that started out in Tier 3 had a lower average daily growth rate of 3.1%;
• the divergence between the second and third groups coincides almost exactly with the period after 26 December when they were in different tiers.

Data sources and methods

Currently there are two main sources of COVID-19 case estimates:

  • The daily testing data released by Public Health England (PHE) on the UK Government dashboard. This reflects the number of positive tests in those who have requested a test due to having symptoms.
  • The Office for National Statistics (ONS) infection survey, which estimates the incidence and prevalence of infection in the community by testing a random sample of the population. This data is usually published weekly with a time lag of 6-12 days.

The PHE data is split by date of specimen test and by lower-tier local authority.  The most recent days of data will be incomplete and are revised upwards as days pass.  This leads to the concept of a time-lag between the date of the COVID-19 test being taken by an individual (specimen date) and the date that the result of that COVID-19 test is recorded (reporting date).  The LCP COVID-19 tracker records the recent time-lags by region and uses these to project the ultimate number of positive tests on each specimen date using the Chain Ladder method, an actuarial technique commonly used in insurance contexts to estimate claims that have been incurred but not yet reported.

The PHE figures can vary materially over the course of the week, with the number of positive tests on Sunday typically around 40% lower than those on Monday.  This weekly shape makes it difficult to elicit a trend from the data without substantial smoothing, eg using a seven-day rolling average, which reduces the currency of the findings.  The LCP COVID-19 tracker makes an adjustment for this weekly shape, allowing direct comparison of figures from recent days.

The ONS data is based on a survey that tests a random sample of the population (irrespective of whether they have COVID-19 symptoms) in order to obtain an estimate of the true prevalence of COVID-19 in the community at any one time.  This results in case estimates that are often up to twice as high as the number of positive tests in the PHE data.  The ONS estimates both the rate of new infections (incidence) and the proportion of the population who currently have COVID-19 (prevalence), although the former has been suspended recently, whilst the ONS reappraises the model used to determine its estimates.

The LCP COVID-19 tracker combines the PHE and ONS data to provide live estimates of new daily cases and current prevalence across England – including asymptomatic cases that would typically not be picked up by the PHE testing – on recent dates where ONS surveillance data is not yet available.  These estimates are based on the current pattern of PHE testing data and past relationships between PHE testing data and ONS surveillance data.  More detail on the methodology used is available here.

The tracker complements the ZOE tracker developed by King’s College London and the Health Science company, ZOE. Based largely on self-reported symptoms from more than 4 million contributors, the Zoe tracker is widely used and uses information from the COVID-19 symptom study app to provide up-to-date estimates of symptomatic cases.

Strengths and limitations

The LCP tracker relies heavily on the ratio of recent PHE case figures to recent ONS case estimates, and assumes that this ratio remains constant over the period of time between consecutive ONS data releases (usually one week).  This ratio remained between 60% and 71% from 26 October to 22 November, and typically moved by around 4% from one week to the next during this period.

This generally resulted in the LCP tracker giving reliable case estimates during the period when the ONS figures were being released weekly.

For example, their latest release on 4 December estimated 25,700 cases in the week to 22 November; the initial LCP estimate for this date, using data available to 24 November, was 29,682 cases (this has since been revised down to c23,000 cases as more data has become available).  The table below shows what the LCP tracker initially estimated on 24 November for the most recent 5 days of ONS estimates, which were published on 4 December.

18 November 19 November 20 November 21 November 22 November
LCP estimate on
24 November 2020
34,827 32,379 30,869 30,092 29,682
ONS estimate on
4 December 2020
31,300 29,800 28,400 27,000 25,700


This shows that, while the initial estimates were not spot on (in this case they were a little high), the LCP tracker was able to give a reliable indication of both the trend and the approximate level of infections ten days before official ONS figures became available.

However, as mentioned above, the ONS have suspended their incidence estimates since the 4 December release while they reassess the methods used to produce the figures.  As a result, the LCP tracker is now projecting the ratio between PHE and ONS incidence figures over a much longer timeframe, increasing the level of uncertainty in the LCP estimates.  The ONS intends to resume publishing incidence figures in January.

Around both Christmas and the New Year, the LCP COVID-19 tracker showed a brief dip in cases, followed by a steep rise in the following days.  This was likely caused by a slowdown in testing on public holidays, which was caught up in the subsequent working days, showing artificially low cases on the former and artificially high cases on the latter.  Owing to a lack of data, the LCP tracker currently makes no adjustments for public holidays or other sudden hiatuses in the testing system.  However, with the next public holidays not until April, this is unlikely to be a problem in the coming few months.


As would be expected given we know approximately one in three who have COVID-19 are asymptomatic, the tracker has consistently estimated higher rates of new daily cases than the PHE estimates. We found that the November lockdown period reduced the daily incidence rate by approximately 30%, d from 28,000 daily cases on 4th November to around 20,000 daily cases by 2nd December.  That reduction in cases, however, was undone within 8 days, with an estimated 29,000 daily cases on 10th December.

We refined the tracker to enable local authority estimates given that the national picture tends to aggregate large variations across the country. The areas that had the highest COVID-19 prevalence before the November lockdown saw the largest declines through November, while those with much lower rates such as London and the South-East did not experience much decline during November and then saw the most rapid increase in cases through December.

We saw a substantial and sustained increase in new cases through December and the Christmas period with estimates of more than 80,000 new COVID-19 cases on 8 of 9 days around New Year.

Analysis of the tier system

After the lifting of the November lockdown, there was significant regional variation in case infection rates, with cases in different parts of the country growing at different rates.  This was partly due to the new strain of the virus first identified in Kent, which contributed to the rapid increase in infection rates in southern and eastern parts of the country.  Our analysis suggests, however, that the restrictions, or tier, that a given area was in still had a large impact on the variation in growth rates across the country.

The table and chart on the following page groups the English Local Authorities into seven distinct groups, based on the strength and duration of the restrictions in force since the end of the November lockdown.  This classification follows a loose geographical pattern, with 4 of the 7 groups in northern and western parts of the country, and the other 3 in the southern and eastern parts of the country that were primarily impacted by the new strain.  The map in the appendix shows the geographical areas covered by each of the seven groups.

Level of restrictions Broad geographical description(*) Population (millions) New cases per 100,000 on 2 Dec 2020 New cases per 100,000 on 5 Jan 2020 Average daily growth in new cases Wider region
Tier 1 at some point Remote rural areas 0.9 6.4 119.4 9.0%  



North and West

Tier 2 continuously from 2 December to 30 December Liverpool & hilly areas 6.6 20.1 169.4 6.5%
Tier 2 on 2 December; moved into Tier 3 on 26 December Somerset, Gloucestershire, Northamptonshire & Cheshire 3.2 25.7 128.4 4.8%
Tier 3 on 2 December; still in Tier 3 on 30 December Bristol, Midlands & populous North 20.9 44.1 122.6 3.1%
Tier 2 on 2 December; moved into Tier 4 on 26 December Rural Southeast & East 6.6 19.2 146.1 6.2%  


South and East

Tier 2 on 2 December; moved into Tier 4 on 20 December London & surrounding areas 15.0 40.6 217.2 5.1%
Tier 3 on 2 December; moved into Tier 4 on 20 December Kent & Slough 2.0 87.6 198.1 2.4%

*These geographical descriptions aim to cover the vast majority of areas within each group, although some groups contain local areas that do not exactly fit the description, owing to the way the restrictions were implemented.  The precise areas are shown in the appendix.

Of the seven groups, the group with the least stringent restrictions – specifically, those areas that were placed in Tier 1 at some point in December (the Isle of Wight, Cornwall and the Isles of Scilly, and Herefordshire) – saw the sharpest rise in infections, with new cases rising by 9.0% per day on average.

Of the three other northern and western groups, areas that remained in Tier 2 from 2nd December to 30th December saw the highest rise in cases, with an average daily growth rate of 6.5%; areas that started in Tier 2 before being moved to Tier 3 on 26th December saw an average daily growth rate of 4.8%, with the divergence between these two groups coinciding almost exactly with the period after 26 December when they were in different tiers.  Areas that started out in Tier 3 had a lower average daily growth rate of 3.1%.

The same relationship between severity of restrictions and growth in cases is evident across the three southern and eastern groups.  Of areas that started out in Tier 2, those that were moved to Tier 4 on 26th December saw an average daily growth rate of 6.2%, while areas that were moved on 20th December saw an average daily growth rate of 5.1%, with the divergence again coming towards the end of the month.  The county of Kent, which overall faced the toughest restrictions of any part of the country, saw the lowest growth rate of all seven groups, at 2.4% per day.


This analysis shows that, after stratifying by local authorities with large portions of cases attributable to the new strain in southern and eastern areas, there was a clear correlation between the level of tiering and the rate of growth, with switches to higher tiers being followed almost immediately by reduced growth in new cases.  Furthermore, the mixing of households over the Christmas period is highly likely to have contributed to the rate of growth of COVID-19 at the very end of this period (end of December onwards).  While the emergence of new, more infectious variants has affected (and will continue to affect) growth rates, many of the approaches that we have known for some time to be effective in controlling the virus remain valid.

We conclude, therefore, that there was a strong inverse correlation between the rate of growth of COVID-19 cases and the tier-level restrictions in the local area.  Stronger social distancing restrictions sustained for longer periods are consistently more effective at controlling the growth of the virus.

As the vaccine roll-out programme gathers pace, this analysis and ongoing estimates will add to the body of evidence to inform national and local decision-makers when tailoring the interventions required to safely exit the national lockdown and move back to a local tier-based system.

21 January 2021

Appendix: map of the seven groups

About henry tapper

Founder of the Pension PlayPen,, partner of Stella, father of Olly . I am the Pension Plowman
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2 Responses to How actuaries get the Covid numbers right.

  1. John Mather says:

    Maybe if the authorities concentrated on outcomes rather than documenting the train wreck they might make a difference. Try listening to Larry Brilliant, his achievements with smallpox are exceptional

    Does documenting train wrecks remind you of the way the consultants look at DB schemes? Absolutely right but no *** use

  2. peter says:

    hi andrew we went to uni together 🙂

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