In this post, I try to reproduce the mathematics that led the COVID Nature paper to conclude the COVID patients who die lose an average of 16 years of life.
First, let us place an upper bound for YLL (years of life lost) for people dying from a specific cause.
For a first estimate, we can assume that people live up to 100 years and all people who die have been born and their age is above zero. Thus, an upper bound for YLL would be 100*lives lost.
On second iteration we could look at how old people are at the moment of death. Thus, people dying aged 20 will lose 80 years per death.
We can then adjust the upper age to some realistic number. Lowering the life expectancy to 95, I was able to obtain a YLL of 14 years for Italy and 12.7 for Belgium. Still, the real life expectancy of Belgium is 81.6 and for Italy is 83.35. Thus, assuming the COVID patients would have lived to 95 seems unreasonable.
So, what went wrong in the article? I think the authors made an error of judgement as follows:
An 85 years old just died of COVID, in a country where the average life expectancy is 80, but, people aged 85 and alive will continue to live on average another 2 years.
The authors assume these 2 years to be the YLL. This is however wrong and not how YLL is generally calculated in the literature .
To make matters clear, I will propose a thought experiment:
Let us consider a disease X that does not exist. This disease will consist of marker people receive without any effect of their knowledge. The marker is assigned randomly by a computer based on their social security number or information from the telephone book.
Naturally, there should be no years of life lost to disease X. Thus, YLL_X=0.
People marked with the non-existent disease X will die in the same way as unmarked people. Some will die young, some will die old. Their average age at death will be the same as that of the general population and their life expectancy again identical to the unmarked population.
However, every individual who dies belongs to an age group that still has some years to live. If the average life expectancy at birth is 85, a child marked with X dying at birth will be accounted as a YLL of 85.
If 85 years olds in this population are expected to live to 90, a man dying at 85 will be accounted as having a YLL of 5 years.
Thus, if we apply this algorithm for calculating YLL to the disease X that doesn't exist, we get 15-19 years for various European populations. If we apply it to corona, we get 16 years.
A correct way to estimate YLL should yield zero for a disease that doesn't exist, like X.
The way I estimated the YLL in March 2020 was to look at the difference between the average age of the Corona deaths and the life expectancy of the general population. The result was 2 years.
I argued that this is an overestimate. Corona kills members of the general population who are more likely to be sick. Thus, unlike disease X, these people wouldn't, on average, reach the average life expectancy of the general population.
Thus, the YLL for Corona won't be the full 2 years I estimated in March last year, but the difference between their average age of death and their potential life expectancy as adjusted for their pre-existing conditions.
Thus, a 20 years old with terminal cancer who dies of Corona loses, perhaps, a few weeks of life and not 80 years.
It is however difficult to estimate the potential life expectancy of this heterogenous population as too many variables have to be taken into account. I guessed the 2 years YLL to be half Corona and half the other conditions. I think this guess is reasonable, but if someone would argue for a YLL 2 years, I wouldn't argue back.
The Nature paper, however argues for 16 years. That isn't something I can agree with.
One conclusion of the nature paper that I do agree with is that COVID-19 is between 2 and 9 times worse than the average flu. This is far more realistic than the 16 years of life lost. Corona has filled the hospitals worldwide and does appear to be a bad cold indeed. Twice as bad as usual is optimistic. I would have guessed three times.
Using the formula from the literature, we get the following results for YLL.
Italy
YLL_75=2
YLL_85=6
YLL_95=14
Belgium
YLL_75=2
YLL_85=3.9
YLL_95=12.7
YLL_75 is normally used when discussing the years of lost life in other illnesses or situations like war, traffic accidents, etc.
No comments:
Post a Comment