Does Covid raise everyone’s relative risk of dying by a similar amount? More evidence.

In a popular blog published on March 21st (which seems a lifetime ago), I argued that the estimated mortality rate of people whilst infected with Covid-19 was very similar to the average risk that people of the same age experienced over a whole year. Both Covid and annual background risk vary hugely within age-groups, with most of the lethal risk being held by people who are already frail. An additional bold assumption that this average property held at the individual level would lead to a very simple interpretation: Covid could be considered as packing what amounts to your current annual risk into a few weeks. This is an additional risk, of course, and certainly does not mean that these deaths would have occurred anyway in the following year (although some would have).

Another interpretations is to think of Covid increasing an individual’s short-term risk by a common multiplicative factor, whatever their current baseline risk. An exception might be health-care workers, who appear to have higher risk, possibly through increased exposure.

We can now start using real data to investigate this hypothesis. The Office for National Statistics (ONS) now provide a weekly update on death registrations for England and Wales that mention Covid, which are reported in broad age bands. Currently available data (released on April 7th) runs only to deaths registered up to the end of Week 13 (ending March 27th), during which a total of 539 deaths involving Covid had been registered by March 27th, with the age-sex breakdown shown in the Table at the end of this blog. Note that this is the count of registrations during this week in England and Wales — far more deaths from Covid actually occurred in this week but were registered later.

Using population figures provided by ONS, we can work out the death rate per 100,000 people in each age band, both for deaths involving Covid and non-Covid. These are plotted in the graphic below on a logarithmic scale, together with the average weekly death rate taken from standard life-tables. Parallel trajectories indicate proportional risks.

The weekly death rates per 100,000 people of different ages. Non-Covid and additional Covid death rates are for deaths registered in Week 13 for England and Wales, and are provided for age-groups 15–44, 45–64, 65–74, 74–84, 85+, which are plotted at 30, 55, 70, 80 and 90.

It is remarkable how closely the observed Covid-mortality rates follow a straight line. This means the population Covid risk increases exponentially with age, in parallel with the normal age-specific risk, and so Covid might be considered as multiplying those risks over a short period.

Another, and extremely simple, way of looking at this data is to consider the proportion of all registered deaths that are Covid-related, also shown in the Table at the end. This is displayed in the image below, and shows that there is no systematic relationship with age. Around 3.8% of all female deaths registered in Week 13 were Covid-related, regardless of age, and around 5.8% of male deaths (the low rates for 15–44 are only based on 14 deaths, and so are still compatible with a constant proportion). So males have around a 50% higher mortality rate.

Observed proportions of all deaths registered in England and Wales in Week 13 that involved Covid-19, with 95% confidence intervals for the underlying risk. For both men and women, the proportions do not depend systematically on age-group, in that the observed irregularity can be explained by chance variation (X2 = 9.6, 8 df, P=0.30).

We would expect the population mortality rate to follow a similar age-trajectory as the infection mortality rate, if infections were fairly uniformly spread across age groups, and this may be more realistic early on in the epidemic before shielding measures for vulnerable people began. The ages of those who test positive is a poor test of this, as in the UK those being tested are overwhelmingly those entering hospital, who will tend to be older. However, some support for a uniform spread of infection comes from Germany, who have conducted a much more extensive testing programme.

So evidence on the first 500+ registered Covid deaths strongly supports the idea of lethality rising exponentially with age. If generalised to the individual level, this would mean that Covid essentially gave a member of the general public a short burst of extreme relative risk, dramatically increasing whatever risk they normally faced.

Further data from ONS, arriving each Tuesday at 9.30am, will enable this hypothesis to be tested and refined, possibly stratifying for ethnicity as well as sex.

Data for England and Wales underlying the graphs: mortality data from ONS Weekly mortality report for Week 13, England and Wales population data from ONS.

WintonCentre

The Winton Centre for Risk and Evidence Communication is…

WintonCentre

The Winton Centre for Risk and Evidence Communication is hosted within the Department of Pure Mathematics and Mathematical Statistics in the University of Cambridge. Transparent evidence designed to inform, not to persuade.

David Spiegelhalter

Written by

Statistician, communicator about evidence, risk, probability, chance, uncertainty, etc. Chair, Winton Centre for Risk and Evidence Communication, Cambridge.

WintonCentre

The Winton Centre for Risk and Evidence Communication is hosted within the Department of Pure Mathematics and Mathematical Statistics in the University of Cambridge. Transparent evidence designed to inform, not to persuade.

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