Covid-19 and life expectancy A public figure in my home country said the following:
"The life expectancy in our country is 82 years. The average age of those who die of covid-19 is also about 82 years. Hence, on average, people do not die from covid-19 disease at all.
I am trying to construct a more formal explanation for why it is statistically wrong. The first thought is - The life expectancy is 82 at age 0, but at age 82 the life expectancy is probably larger, but again, not sure what is the formal jargon for this conditional life expectancy and how to prove / refute the statement.  Any ideas? some knowledge about life expectancy and covid-19 ? what is the accepted jargon of conditional life expectancy or life expectancy at age X ?
 A: Although it may be the case that life expectancy at birth is 82 years, someone who is already 82 years old certainly has a life expectancy of 82 or above. This is due to conditional probabilities in combination with variance in the age of death.
Take the simple case where 50% of the population dies at 72 and 50% dies at 92, then life expectancy at birth is 82 years. However, life expectancy at 82 is 92, giving you an additional 10 years.
In that case, if Covid causes you to die at 82, it has taken 10 years of your life.

Update: a visualisation to help make clear that variance in the age of death combined with selection on people who are still alive at age 82 results in an expected age of death larger than 82 (the mean of the orange area). If Covid would result in death at 82, some expected life years were indeed lost.

A: There is simple mistake in this argument: it wrongly treats life expectancy at birth and average age of death during an epidemic situation as interchangeable terms. They are not.
I was about to write a more complete explanation for this but then I stumbled across a perfectly fitting paper in the reputable journal PNAS: Goldstein, Joshua R. and Lee, Ronald D. 2020. Demographic perspectives on the mortality of COVID-19 and other epidemics. Proceedings of the National Academy of Sciences
https://www.pnas.org/content/117/36/22035
I think this is highly worth reading for being prepared for statements as the one in the question or "people are just dying with Covid, not from Covid". The authors write:

In the context of epidemic mortality, life expectancy at birth is a misleading indicator, because it implicitly assumes the epidemic is experienced each year over and over again as a person gets older. [...] what we really want to know is how a one-time epidemic affects the remaining life expectancy of the actual population.


We calculate [...] that the average person dying of COVID-19 had 11.7 y of remaining life expectancy [...]

The sentence continues and takes this into a population-level context (in the US):

[...] so if the epidemic kills an additional 1 million people,  it  will  result  in  a  loss  of  11.7  million  y  of  remaining  life expectancy. This represents a loss of less than 1/1,000th of the population’s remaining years to live.

So actually there is a considerable loss of life expectancy among the people who died from/with Covid19. However, it will probably (and hopefully) not heavily affect the current overall population's life expectancy.
A: In a stable population with a life expectancy of 82 years you will have the situation that on average people die at 82 years. The number of people that die is more or less constant every year and roughly 1/82 of the people die every year (although it does not need to be exactly 1/82, but it matches roughly).
So you might be indeed puzzled when covid-19 kills on average people of 82 years. If the average age of dying is the same, then is it not also the same like 'normal' death as in this stable population?
But the deaths due to covid-19 are an increase of the death rate (that happens to occur at 82 years on average, and that is possible because the stable population has people that are older than the life expectancy). And now we have an unstable population (so that is the difference, it is not the same as 'normal death'). The number of people that die has increased and more people die than the year before.
In the end you will always have different causes of death at different ages. And the age dependent death rates can increase and decrease. The death rate at the age of 82 is currently a few percent and not 100%, so there is still room to rise.
A: According to that logic, if COVID kills someone at 72, it's taken away 10 years, but if it kills someone at 92, it's given them an extra 10 years, which is absurd. Death can only take years away. You can't have an average years lost of zero, because that would require some to be negative.
Other comparisons:
A football player averages two goals per game. After they've scored two goals, the ref ejects them from the game. Has the ref cost the team any goals?
You're offered a game in an underground casino where you roll a die until you get a six. Every time you roll something else, you get a dollar. After rolling the die six times without ever getting a six, the government raids the casino. Has the government cost you any money?
You kill an 82 year old person. Have you committed murder?
