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There's been some discussion on Twitter regarding whether a BBC article is misleading or not. The article says:

Researchers estimate that 25 deaths in a population of some 12 million children in England gives a broad, overall mortality rate of 2 per million children.

And has an infographic as well that says:

2 in a million: absolute risk of death from Covid-19 in children

I'm somewhat familiar with notions like CFR and IFR... but on a quick google search "absolute risk of death" is also a phrase that seems to appear often in papers... but I couldn't find a definition for it. (The use of "motility rate" from a given cause in the first quote, on the other hand, is matching the Wikipedia definition. So that one is uncontentious in pure technical terms.) How is this latter notion of "absolute risk of death" usually defined for infectious diseases?

There is one site that defines (in the broadest terms) "absolute risk is the likelihood of an event occurring under specific conditions"... but what are those conditions usually assumed to be for infectious diseases?

(N.B. there a somewhat related Reuters fact check on absolute vs. relative risk reduction regarding vaccines. It seems that "anti-vaxxers" have been been pushing ARR instead of RRR, which might explain why some in the "opposing camp" are now allergic to any "absolute risk" measures regarding covid...)

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Absolute risk is just "events/population". "# of deaths in a population" is an absolute risk. I don't see any other more complex way to define or describe it, it's one of the simplest summary measures there is. It differs from "case" or "infections" measures in that the denominator is the whole population. If you pluck a name out of a registry of UK children, what's the probability that the name you plucked belongs to someone who died: that's your absolute risk.

Despite being simple, absolute risks can be both useful and misleading like any statistic, depending on how you phrase it and if you realize what is being said. To take something a bit less political, consider Ebola. The absolute risk of death from Ebola for someone in the UK is somewhere very close to zero. Something reasonable to take from this information might be "if I'm living in the UK, Ebola shouldn't be causing me immediate worry that I'm going to drop dead". Taking a bunch of extra countermeasures to avoid getting Ebola would be a waste of time. Something not reasonable to take from this statistic would be "Ebola is safe" or "if an Ebola outbreak occurs, we shouldn't try to prevent its spread".

In the context of the Twitter discussion, the problem is that the news has mostly been talking about case or infection rates of death. It sounds like "2 in a million" refers to "a million children with COVID" rather than "a million children in the population". It's only misleading by that implied (incorrect) context.

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The short Wikipedia article linked from Bryan Krause's answer seems not to get much google juice perhaps because it's verys short, but it does have a source: A dictionary of epidemiology (OUP), which says

absolute risk (AR) The probability of an event (usually adverse, but it may also be beneficial) in a closed population over a specified time interval. The number of events in a group divided by the total number of subjects in that group. This usage presumes the population is a cohort. AR is not a synonym of attributable fraction, excess risk, or risk difference.

(That OUP dictionary is also citing 5 previous works for the def.)

So it seems reasonable that if "death from covid" is the event, the population in the denominator need not have Covid for AR purposes.

Nature Scitable also defines AR as

[...] the probability that an individual will develop a particular condition, such as a disease or some other outcome [...]

Having said that, by looking at a few other sources (1 2 3 4), it seems that "absolute risk" is more commonly used to report just the probability of catching the disease rather than the combined event of catching and dying from it. To exemplify,

Absolute risk is the simple rate of disease among a population (e.g., 75 per 100,000 population per year among the exposed or 25 per 100,000 per year among the nonexposed).

On the other hand, there is one other UK study that reports absolute risk of death from a Covid variant, but also reported relative risk:

The increased hazard ratio between 1.32 and 2.04, higher than for other variants, translates to a 32% to 104% increased risk of death, with the most probable hazard ratio estimate of 1.64, or a 64% increased risk of death. The absolute risk of death in this group of community identified participants, however, remains relatively low.

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    "The above quote" used "increased risk", not unqualified "risk" -- it's a different meaning.
    – Armand
    Aug 25 at 8:06
  • @Armand: fair enough.
    – Fizz
    Aug 25 at 8:09

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