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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 ?

mdewey
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Latent
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    You scarcely need jargon here: when you kill people for any reason at any age of their lives, you lower the average age of death, whence you lower the life expectancy. I will not comment on the ethical nature of the alleged statement: that speaks for itself. – whuber Oct 30 '20 at 18:44
  • Right @whuber but basically if the mean is 82 and you add n times the value 82 to the mean, it won't change it. So on average, you do not affect the life expectancy (regardless of the statement ) – Latent Oct 30 '20 at 19:15
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    That's incorrect. The mean is 82 *because there are plenty of people who live beyond 82* to balance out those who die earlier. When you remove the former, you lower the mean. – whuber Oct 30 '20 at 19:17
  • @whuber here we get into the idea of "e82" which is the life expectancy at age 82, in my country it's around 7.7 years,i.e - given you reached the age of 82, you have on average 7.7 more years to live. How do i show in a formal way that the "lost" of years is not zero due to adding 82 to a sample with mean 82. – Latent Oct 30 '20 at 19:42
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    The math is simple: it's a matter of addition and multiplication. Maybe it would help to contemplate an extreme example. Suppose there is a country in which nine out of every ten people die at birth and the other one lives to age 800. At birth, the expected duration of life therefore is 80 years. Now a disease settles permanently over the land that kills anyone who reaches the age of 80. Of the next ten children born, nine will die quickly and the tenth can expect to die at age 80, for an average of just 8 years. – whuber Oct 30 '20 at 19:45
  • I believe the concept of a life table addresses such issues as the life expectancy conditional on having attained a certain age, https://en.wikipedia.org/wiki/Life_table – Christoph Hanck Nov 24 '20 at 13:01

4 Answers4

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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.

Visualisation of Condition life expectancy

LBogaardt
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  • But the person how died at the age of 82 (not from covid) also had 10 years (on average) to live, so what are the differences? The statement suggests that since there is no change in the average life of death, then covid-19 is not (as itself) a cause of death but an excuse of "reason of death" ( and I'm not advocating the statement) – Latent Oct 31 '20 at 11:21
  • This line of reasoning misses one fundamental fact: Those who die from COVID are NOT representative in general of the people in their age group. Those who died were already very frail, weak and/or ill before contracting COVID. These probabilities only apply to people aged 82 on average, not to those who are by definition outliers. Meaning that those who died did NOT lose any QALYs. Your GIF only applies in the scenario where an AVERAGE 82 year old contracted COVID and died. In fact 75+ y/olds have a 92%+ chance of survival if they contract COVID. Those who survive are the averages ones. – Rstew Jun 06 '21 at 15:52
  • You're complicating things unnecessarily. Obviously my answer is a simplification of reality, but it is the minimum you need to answer the OP's question (i.e. _conditional_ probabilities in combination with _variance_ in the age of death). Also, those who died of Covid, though frail, certaintly lost QALYs. If Covid causes them to die even a single day earlier than otherwise would have happened, that's a huge cost at population level (i.e. how much would 1 day extra with a loved-one be worth to you?). – LBogaardt Jul 02 '21 at 14:05
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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.

LuckyPal
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  • This is so incredibly wrong. Your answer assumes that COVID kills average individuals. "Average" meaning generally fit and healthy people that had no prior health related complications. We know now for already a year that only the weakest, illest, frailest and oldest individuals succumb to COVID. Those people are not representative of their age group. This can be seen when you factor in that ~92% of 75+ y/olds survive a COVID infection. For the majority of COVID deaths, the average years of life lost due to COVID was less than 1. In other words, they only had months if not weeks to live. – Rstew Jun 06 '21 at 16:04
  • @Rstew you make a strong assumption, too, that is only the "strong" among the old (i.e., those with many years of expected live) survive COVID and the "weak" die. My answer, which is actually the PNAS-publication that I cite from, does not assume that only "generally fit and healthy people that had no prior health related complications", but that the people who die are representative for their age group. The authors justify this assumption by their finding that "the age gradient we see to date suggests that the risk factors for COVID-19 are similar to those for all causes of death". – LuckyPal Jun 07 '21 at 07:20
  • @Rstew to add, I agree that the estimated loss of 11.7 years of remaining life expectancy might be too high. However, I am certainly no expert on this field and I would be glad to receive recommendations from you for recent scientific publications that have considered factors such as the general illness of the patients using population-level data. And I think it is important that the intention of this analysis was not to alarm but to put Covid into perspective and conclude "it is important to know that we as a society have been through such mortality crises before". – LuckyPal Jun 07 '21 at 07:27
  • My assumption that only the weakest die from COVID is a well known fact. No government, institution or scientist disputes this (as far as I'm aware). Look at any data showing underlying or pre-existing conditions for those who died with/from the disease. You also state now that you think 11.7 years "might be too high", so why go with it in your answer then? 11.7 is ~23 times more than 6 months, which seems to be a far more reasonable figures given the data. – Rstew Jun 08 '21 at 08:20
  • Another thing I'd like to point out is that during all of COVID, we've only seen decontextualised alarmism/fear mongering from the media. There were very rarely parallels drawn between COVID figures and comparable flu figures. To make it all seem like we're in a dire situation. When in reality, almost all figures when corrected from the required variables, are almost identical to those of the swine flu in 2009/10. This lack of nuance in general has made people frightened of their life, despite the fact that we have seen the same thing prior and everyone was okay with it. – Rstew Jun 08 '21 at 08:23
  • @Rstew you seem to not have read the publication that I have cited from. They specifically make a comparison to other epidemics. Further, please do not write about a "well known fact" without support from appropriate scientific publications. And finally, I will not adjust the derived estimate from a PNAS publication just based on my gut feeling. – LuckyPal Jun 08 '21 at 08:58
  • LuckyPal, You're asking me to provide a scientific paper of what? To show that only the frail, weak and/or co-morbid died due to COVID? https://www.cdc.gov/mmwr/volumes/69/wr/mm6913e2.htm this is a report by the CDC in the early days. 94% of deaths were caused partially by at least one underlying condition. Look at the COVID deaths data by age group and you'll see it only affects the 75+ age group more significantly. This is quite literally no different when compared to H1N1, the only difference is, we were never shown this data when that pandemic occurred. – Rstew Jun 08 '21 at 18:37
  • @Rstew to cite from your link: "persons with underlying health conditions such as diabetes mellitus, chronic lung disease, and cardiovascular disease, appear to be at higher risk [...] It is not yet known whether the severity [...] of underlying health conditions affects the risk for severe disease associated with COVID-19. Many of these underlying health conditions are common in the United States" This neither contradicts the PNAS paper from my answer nor supports your statement that these patients had only weeks to live. Your argument is simply an opinion. I am out of this discussion. – LuckyPal Jun 08 '21 at 19:01
  • "Among 122,653 U.S. COVID-19 cases reported to CDC as of March 28, 2020, 5.8% patients had data available pertaining to underlying health conditions or potential risk factors; among these patients, higher percentages of patients with underlying conditions were admitted to the hospital and to an ICU than patients without reported underlying conditions." So you're going to ignore the literal paragraph right above the line you just quoted? What you quoted is as a result of this report being early days, it is now truly a well known fact that if you have underlying conditions, you're vulnerable. – Rstew Jun 08 '21 at 20:34
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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.

Sextus Empiricus
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  • Very interesting. So, First, Do we see an increase in the death rate of those ages in areas affected with covid-19? And second, If we do see a correlation between death rate increase and covid-19, can we assume that covid-19 did contribute more fatalities to the over-all "normal death" that we already included in the life expectancy calculations – Latent Oct 31 '20 at 10:57
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    @Latent those two points can be seen in 'excess mortality' (a higher mortality than the expected mortality based on the past), and the excess mortality correlates with places that have a high incidence of covid-19 so you can be pretty sure that this excess mortality is due to covid-19. – Sextus Empiricus Oct 31 '20 at 11:46
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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?

Acccumulation
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