Yeah, the 1/8th multiplier sounded hard to believe. A 1⁄2 multiplier based on demographic correction sounds a lot more plausible, and it’s nice to have confirmation that someone else actually did the math. Thanks for finding/sharing it!
I should flag that I didn’t do the math for age correction. I only got this from another Diamond cruise study where the age correction provided a smaller update (and I didn’t really like other things about that study).
So, I think it could be valuable to investigate this claim more:
Projecting the Diamond Princess mortality rate onto the age structure of the U.S. population, the death rate among people infected with Covid-19 would be 0.125%.
(But even if this point was right, there’s still South Korea to explain.)
Reading the Ioannidis article, it seems to say that he did his own calculations, and he doesn’t show them. Okay.
I’m curious about this, so I’m going to try a ballparking estimate myself.
Tl;dr I intially arrived at a result that suggested 0.125% was way off, but then found better info on the cruise ship’s age distribution and had to revise my judgment. I now find it debatable whether 0.125% is defensible or not, but it’s not “way off.” My own estimate would be more in the ballpark of 0.3%, but I don’t anymore consider the cruise ship to be evidence for IFR estimates at 0.5% or higher.
Update March 24th: In the couple of days, 3 new patients who had tested positive on the Diamond Princess have died. In addition, the Wikipedia article has been edited to list another death that previously hadn’t been included. So total deaths per confirmed cases on the Diamond Princess are now 11 / 700 instead of 7 / 700. All my calculations below are based on the older, outdated numbers. To get the most updated estimates, just multiply the results below by 11⁄7.
---
Note that I have never done age adjustments for anything, so I have no idea what the proper methdology would be. I’m just curious to see if 0.125% is potentially reasonable rather than (as my current intuition suggests) very dubious.
A total of 634 people tested positive among 3,063 tests as at 20 February 2020. Of 634 cases, a total of 313 cases were female and six were aged 0–19 years, 152 were aged 20–59 years and 476 were 60 years and older.
At the end of the outbreak, roughly 700 people had tested positive. I’m going to assume that the 66 patients not yet in the above statistics fall into age categories in the same proportion. So a bit more than two thirds of the 66 patients get added to the 476 figure for people aged 60 and older.
With this adjustment, we have 700 diagnosed cases, of which an estimated 525 patients were aged 60 and older. Of those 700 diagnosed cases, 7 people died. 525 out of 700 corresponds to 75%. (I’m going to mostly ignore the death risk for people below age 60 for the analysis below, because it will be negligible given that people older than that anyway make up the majority share.)
Eyeballing this, let’s go with 22% of the population at age 60 or older.
75 divided by 22 is roughly 3.4, so this naively suggests that the cruise ship’s demographic was roughly 3.4 times more susceptible to dying from SARS-CoV-2. If I divide the observed IFR of 1% by 3.4, I get 0.3%. Why does Ioannidis get 0.125% instead of 0.3?
Moreover, it seems to me that 0.3% must be an underestimate because I assume that even though the cruise ship population is substantially older on average than the US population, I would think that this effect will disappear (or even reverse) at the extremes, once we look at the percentage of exceptionally old people (e.g., aged 80 and above, age 85 and above, etc.). Because Covid-19 is particularly fatal for the very oldest people, I expect the 0.3% figure to contain a substantial degree of overcorrection. Especially also because elderly people with the most severe pre-existing health conditions are likely heavily underrepresented on cruise ships. This effect could be really quite significant: It’s not even totally obvious that a downward adjustment of the 1% IFR observed on the Diamond Princess is warranted. It’s probably warranted, but depending on how strongly cruise ship passengers are pre-selected against having unusually bad health, and depending on how strongly pre-existing health conditions affect someone’s survival prospect for Covid-19, it’s conceivable that the 1% figure doesn’t need to be downward adjusted at all.
To conclude, I don’t understand how age adjustments for SARS-Cov-2 infections on the Diamond Princess can drive down the estimated IFR substantially below 0.5%. 0.5% seems closer to a lower bound to me than anything else. (Of course, those are point estimates. I don’t have strong views on whether 0.125% is outside some appropriate confidence interval, but my impression was that 0.125% was Ioannidis’s point estimate, and interpreted as such, it seems clearly much too low!)
UPDATE: Oh I see. I found an age table that I had overlooked initially. It turns out cruises are really popular for people at age 70-79 (there are about 20% more people of that age than 60-69, whereas it’s the other way around for US demographics). This distribution makes Ioannidis’s figures look more plausible, though the difference doesn’t seem large enough to fully bridge the gap between 0.3% and 0.125%, especially because the 80-89 bracket seems to be represented proportionally again. Still, I don’t anymore think that 0.125% is horribly off.
You found an age distribution for the infected population on the Diamond Princess, but you’re using it as if it’s the age distribution for everyone on the ship. Older people are more likely to get infected, so the infected population in the US will lean older as well—closer to the distribution on the ship. To do a good age adjustment we need to know the ages of the people on the ship who were not infected.
Older people are more likely to get infected, so the infected population in the US will lean older as well—closer to the distribution on the ship.
Interesting! Do you think this is established? I haven’t looked into this, but my guess would have been that the risk is similar because young people are less scared of the virus. But yeah, good point about further adjustments being needed to get the best estimate.
Hmm, maybe you’re right. The South Korean distribution of cases by age here suggests that it’s actually most common by far among people in their twenties, and the larger number of confirmed cases among older people is a statistical artifact resulting from test criteria. The data do look a bit suspicious though.
Right, I got that it was them doing the math correction not you. Still, they did the math and give an age breakdown of the passengers and a crude sanity check gives a number within about 30% of what they report.
Yeah, the 1/8th multiplier sounded hard to believe. A 1⁄2 multiplier based on demographic correction sounds a lot more plausible, and it’s nice to have confirmation that someone else actually did the math. Thanks for finding/sharing it!
I should flag that I didn’t do the math for age correction. I only got this from another Diamond cruise study where the age correction provided a smaller update (and I didn’t really like other things about that study).
So, I think it could be valuable to investigate this claim more:
(But even if this point was right, there’s still South Korea to explain.)
Reading the Ioannidis article, it seems to say that he did his own calculations, and he doesn’t show them. Okay.
I’m curious about this, so I’m going to try a ballparking estimate myself.
Tl;dr I intially arrived at a result that suggested 0.125% was way off, but then found better info on the cruise ship’s age distribution and had to revise my judgment. I now find it debatable whether 0.125% is defensible or not, but it’s not “way off.” My own estimate would be more in the ballpark of 0.3%, but I don’t anymore consider the cruise ship to be evidence for IFR estimates at 0.5% or higher.
Update March 24th: In the couple of days, 3 new patients who had tested positive on the Diamond Princess have died. In addition, the Wikipedia article has been edited to list another death that previously hadn’t been included. So total deaths per confirmed cases on the Diamond Princess are now 11 / 700 instead of 7 / 700. All my calculations below are based on the older, outdated numbers. To get the most updated estimates, just multiply the results below by 11⁄7.
---
Note that I have never done age adjustments for anything, so I have no idea what the proper methdology would be. I’m just curious to see if 0.125% is potentially reasonable rather than (as my current intuition suggests) very dubious.
From this paper, I found the following info:
At the end of the outbreak, roughly 700 people had tested positive. I’m going to assume that the 66 patients not yet in the above statistics fall into age categories in the same proportion. So a bit more than two thirds of the 66 patients get added to the 476 figure for people aged 60 and older.
With this adjustment, we have 700 diagnosed cases, of which an estimated 525 patients were aged 60 and older. Of those 700 diagnosed cases, 7 people died. 525 out of 700 corresponds to 75%. (I’m going to mostly ignore the death risk for people below age 60 for the analysis below, because it will be negligible given that people older than that anyway make up the majority share.)
This wikipedia article on US demographics says the following:
0–14 years: 18.62%
15–24 years: 13.12%
25–54 years: 39.29%
55–64 years: 12.94%
65 years and over: 16.03%
Eyeballing this, let’s go with 22% of the population at age 60 or older.
75 divided by 22 is roughly 3.4, so this naively suggests that the cruise ship’s demographic was roughly 3.4 times more susceptible to dying from SARS-CoV-2. If I divide the observed IFR of 1% by 3.4, I get 0.3%. Why does Ioannidis get 0.125% instead of 0.3?
Moreover, it seems to me that 0.3% must be an underestimate because I assume that even though the cruise ship population is substantially older on average than the US population, I would think that this effect will disappear (or even reverse) at the extremes, once we look at the percentage of exceptionally old people (e.g., aged 80 and above, age 85 and above, etc.). Because Covid-19 is particularly fatal for the very oldest people, I expect the 0.3% figure to contain a substantial degree of overcorrection. Especially also because elderly people with the most severe pre-existing health conditions are likely heavily underrepresented on cruise ships. This effect could be really quite significant: It’s not even totally obvious that a downward adjustment of the 1% IFR observed on the Diamond Princess is warranted. It’s probably warranted, but depending on how strongly cruise ship passengers are pre-selected against having unusually bad health, and depending on how strongly pre-existing health conditions affect someone’s survival prospect for Covid-19, it’s conceivable that the 1% figure doesn’t need to be downward adjusted at all.
To conclude, I don’t understand how age adjustments for SARS-Cov-2 infections on the Diamond Princess can drive down the estimated IFR substantially below 0.5%. 0.5% seems closer to a lower bound to me than anything else. (Of course, those are point estimates. I don’t have strong views on whether 0.125% is outside some appropriate confidence interval, but my impression was that 0.125% was Ioannidis’s point estimate, and interpreted as such, it seems clearly much too low!)
UPDATE: Oh I see. I found an age table that I had overlooked initially. It turns out cruises are really popular for people at age 70-79 (there are about 20% more people of that age than 60-69, whereas it’s the other way around for US demographics). This distribution makes Ioannidis’s figures look more plausible, though the difference doesn’t seem large enough to fully bridge the gap between 0.3% and 0.125%, especially because the 80-89 bracket seems to be represented proportionally again. Still, I don’t anymore think that 0.125% is horribly off.
You found an age distribution for the infected population on the Diamond Princess, but you’re using it as if it’s the age distribution for everyone on the ship. Older people are more likely to get infected, so the infected population in the US will lean older as well—closer to the distribution on the ship. To do a good age adjustment we need to know the ages of the people on the ship who were not infected.
Interesting! Do you think this is established? I haven’t looked into this, but my guess would have been that the risk is similar because young people are less scared of the virus. But yeah, good point about further adjustments being needed to get the best estimate.
Hmm, maybe you’re right. The South Korean distribution of cases by age here suggests that it’s actually most common by far among people in their twenties, and the larger number of confirmed cases among older people is a statistical artifact resulting from test criteria. The data do look a bit suspicious though.
Right, I got that it was them doing the math correction not you. Still, they did the math and give an age breakdown of the passengers and a crude sanity check gives a number within about 30% of what they report.