Errata: My original calculation underestimated the risk by a factor of about 2x. I neglected two key considerations, which fortunately somewhat canceled each other out. My new estimate from the calculation is 3.0 to 11.7 quality-adjusted days lost to long-term sequelae, with my all-things-considered mean at 45.
The two key things I missed:
- I estimated the risk of a non-hospitalized case is about 10x less than a hospitalized case, and so divided the estimates of disease burden by 10x. The first part is correct, but the second part would only make sense if all disease burden was due to hospitalized cases. In fact, there’s a 15:85% split between hospitalized and non-hospitalized patients in the study (13,654:73,435). So if the disease burden for non-hospitalized is x, the total burden is 0.15*10x + 0.85*x = 2.35x. So we should divide by 2.35, not 10.
- However, as Owain pointed out below, the [demographics](https://www.nature.com/articles/s41586-021-03553-9/tables/1) are non-representative and probably skew high-risk given the median age is 60. the demographics are relatively high-risk. Indeed, this is suggested by the 15% hospitalized figure (which also, I suspect, means they just never included asymptomatic and most mildly symptomatic cases). An ONS survey (Figure 4) put symptoms reported after 5 weeks at 25% (20-30%) for 50-69 year olds and 17.5 (12.5 to 22.5%) for 17 to 24 year olds, which is surprisingly little difference, about a 1.5 decrease. I’d conjecture a 2x decrease in risk (noting that assuming no hospitalization is already doing a lot of work here).
Original post:
I did my own back-of-the-envelope calculation and came up with a similar but slightly higher estimated cost of 1.4 to 5.5 quality-adjusted days lost to long-term sequalea conditional on getting symptomatic COVID case. FWIW, I originally thought the OPs numbers seemed way too low, and was going to write a take-down post—but unfortunately the data did not cooperate with this agenda. I certainly don’t fully trust these numbers: it’s based on a single study, and there were a bunch of places I didn’t keep track of uncertainty, so the true credible interval should definitely be a lot wider. Given that and the right-tailed nature of the distribution, my all-things-considered mean is closer to 30 because of this, but figured I’d share the BOTEC anyway in case it’s helpful to anyone.
My model is pretty simple:
1. What % of symptoms are there at some short-term follow up period (e.g. 4 to 12 weeks)? This we actually have data on.
2. How bad are these symptoms? This is fairly subjective.
3. How much do we expect these symptoms to decay long-term? This is going off priors.
For 1. I used Al-Aly et al (2021) as a starting point, which was based on comparing medical records between a COVID-positive and non-COVID demographically matched control group in the US Department of Veterans Affairs database. Anna Ore felt this was one of the more rigorous ones, and I agree. Medical notes seem more reliable than self-report (though far from infallible), they seem to have actually done a Bonferroni correction, and they tested their methodology didn’t pick up any false positives via both a negative-outcome and negative-exposure controls. Caveat: many other studies have scarier headline figures, and it’s certainly possible relying on medical records skews this low (e.g. doctors might be reluctant to give a diagnosis, many patients won’t go to the doctor for mild symptoms, etc).
They report outcomes that occurred between 30 and 180 days after COVID exposure, although infuriatingly don’t seem to break it down any further by date. Figure 2 shows all statistically significant symptoms, in terms of the excess burden (i.e. increase above control) of the reported symptom per 1000 patients. There were 38 in total, ranging from 2.8% (respiratory signs and symptoms) to 0.15% (pleurisy). In total the excess burden was 26%.
I went through and rated each symptom with a very rough and subjective high / medium / low severity. 2% excess burden of high severity symptoms, 19% medium severity, 5% low severity. I then ballparked that high severity (e.g. heart disease, diabates, heart failure) wiped out 30% of your QALYs, medium severity (e.g. respiratory signs, anxiety disorders, asthma) as 5% and low (e.g. skin rash) as 1%. Caveat: there’s a lot of uncertainty in these numbers. Although I suspect I’ve gone for higher costs than most people would, since I tend to think health has a pretty big impact on productivity.
Using my weightings, we get a 1.6% reduction in QALYs conditional on symptomatic COVID case. I think this is misleading for three reasons:
1. Figure 3 shows that excess burden is much higher for people who were hospitalized, and if anything the gap seems bigger for more severe symptoms (e.g. about 10x less heart failure in people positive but not hospitalized, whereas rates of skin rash were only 2x less). This is good news as vaccines seem significantly more effective at preventing hospitalizations, and if you are fortunate enough to be a young healthy person your chance of being hospitalized was pretty low to begin with. I’m applying a 10x reduction for this.
2. This excess burden is per diagnosis, not per patient. Sick people tend to receive multiple diagnoses. I’m not sure how to handle this. In some cases, badness-of-symptoms does seem roughly additive: if I had a headache, I’d probably pay a similar amount not to also develop a skin rash then if my head didn’t hurt. But it seems odd to say that someone who drops dead from cardiac arrest was more fortunate than another patient with the same cause of death, who also had the misfortune of being diagnosed with heart failure a week earlier. So there’s definitely some double-counting with the diagnosis, which I think justifies a 2-5x decrease.
3. This study was presumably predominantly the original COVID strain (based on a cohort between March 2020 and 30 November 2020). Delta seems, per the OP, about 2-3x worse: so let’s increase it by that factor.
Overall we decrease 1.6% by a factor of 6.5 (10*2/3) to 25 (10*5/2), to get a short-term QALY reduction of 0.064% to 0.24%.
However, El-Aly et al include any symptom reported between 30 to 180 days. What we really care about is chance of lifelong symptoms if someone is experiencing a symptom after 6 months there seems like a considerable chance it’ll be lifelong, but if only 30 days has elapsed the chance of recovery seems much higher. A meta-review by Thompson et al (2021) seems to show a drop of around 2x between symptoms in a 4-12 week period vs 12+ weeks (Table 2), although with some fairly wild variation between studies so I do not trust this that much. In an extremely dubious extrapolation from this, we could say that perhaps symptoms half again from 12 weeks to 6 months, again from 6 months to a year, and after that persist as a permanent injury. In this case, we’d divide the “symptom after 30 days figure” from Al-Aly et al by a factor of 8 to get the permanent injury figure, which seems plausible to me (but again, you could totally argue for a much lower number).
With this final fudge, we get a lifelong QALY reduction of 0.008% to 0.03%. Assuming a 50-year life expectancy, this amounts to 1.4 to 5.5 days of cost from long-term sequelae. Of course, there are also short-term costs (and risk of morbidity!) that is omitted from this analysis, so the total costs will be higher than this.
(I’d personally appreciate you saying how many microcovids you think is equivalent to an hour’s time; that’s the main number I’ve been using to figure out whether various costs are worth it.)
So Adam is saying microcovids are cheaper than the OP does? Connor writes
1 hour of your life lost every 1k-5k uCOVIDs
(Pardon me commenting while not getting into the details on this important topic, I am busy but am trying to track at least whether there’s disagreement and in what direction.)
So, to be clear, his all-things-considered view is about 1.5k uCOVIDs cost an hour, which is toward the edge of my range that corresponds to high risk, while his numerical estimate is at 7.5k uCOVIDs costing an hour, which is just outside of my range that corresponds to low risk (but matches almost exactly with my estimates of Long COVID risk outside of follow-ons from cognitive impairment!). So it sounds like initially he disagreed toward higher risk, then found very similar numbers as I did, now only leans toward the high end of my risk estimate due to priors and right-tail uncertainty. (Apologies if my paraphrase does not do your view justice, Adam.)
This is an accurate summary, thanks! I’ll add my calculation was only for long-term sequelae. Including ~10 days cost from acute effects, my all-things-considered view would be mean of ~40 days, corresponding to 1041 uCOVIDs per hour.
This is per actual hour of (quality-adjusted) life expectancy. But given we spend ~1/3rd of our time sleeping, you probably want to value a waking-hour at 1.5x a life-hour (assuming being asleep has neutral valence). If you work a 40 hour work week and only value your productive time (I do not endorse this, by the way), then you’d want to adjust upwards by a factor of (7*24)/40=4.2.
However, this is purely private cost. You probably want to take into account the cost of infecting other people. I’m not confident in how to reason about the exponential growth side of things. If you’re in a country like the US where vaccination rates have plateaued, I tend to expect Delta to spread amongst unvaccinated people until herd immunity is reached. In this scenario you basically want infection rates to be as high as possible without overwhelming the healthcare system, so we get to herd immunity quicker. (This seems to actually be the strategy the UK government is pursuing—although obviously they’ve not explicitly stated this.) But if you’re in a country that’s still actively vaccinating vulnerable people, or where flattening the curve makes sense to protect healthcare systems, then please avoid contributing to exponential growth.
Neglecting the exponential growth side of things and just considering immediate impact on your contacts, how likely are you to transmit? I’d be surprised if it was above 40% per household contact assuming you quarantine when symptomatic (that’s on the higher end of transmission seen even with unvaccinated primary cases), but I’d also be surprised if it was below 5% (lowest figure I’ve seen); I’d guess it’s around 15% for Delta. This means if you have ~6-7 contacts as close as housemates, then your immediate external cost roughly equals your private cost.
Specifically, two studies I’ve seen on secondary attack rate given vaccination (h/t @Linch) give pretty wildly varying figures, but suggest at least 2x reduction in transmission from vaccination. Layan et al (2021) found 40% of household contacts of Israeli medical staff developed an infection (when Alpha was dominant), with vaccination of the primary case reducing transmission by 80%, so an 8% chance of transmission overall. Harris et al (2021) from Public Health England suggest vaccination cuts transmission risk from 10% to 5%, but these figures are likely skewed low due to not systematically testing contacts.
Just to flag I messed up the original calculation and underestimated everything by a factor of 2x, I’ve added an errata.
I’d also recommend Matt Bell’s recent analysis, who estimates 200 days of life lost. This is much higher than the analysis in my comment and the OP. I found the assumptions and sources somewhat pessimistic but ultimately plausible.
The main things driving the difference from my comment were:
Uses data from the UK’s Office of National Statistics that I’d missed, which has a very high number of 55% of people reporting symptoms after 5 weeks, with fairly slow rates of recovery all the way out to 120 days post-infection. Given this is significantly higher than most other studies I’ve seen, I think Matt is being pessimistic by only down-adjusting to 45%, but I should emphasize these numbers are credible and the ONS study is honestly better than most out there.
Long COVID making your life 20% worse is on the pessimistic end. I put most mild symptoms at 5% worse. Ultimately subjective and highly dependent on what symptoms you get.
I think the difference in hospitalized vs non-hospitalized risk is closer to 10x (based on Al-Aly figure) not Matt’s estimate of 2x, that means we should multiply by a factor of ~60% not ~97%.
I should probably argue with Matt directly, but my brief take is that this is just entirely incompatible with what we see on the ground. The friends of mine who got COVID aren’t reporting 45% chance of their life being 20% worse. That’s… an incredibly massive effect that we would definitely see. Would anyone realistically bet on that?
Bell mentions this paper in Nature Medicine that finds only 2.3% of people having symptoms after 12 weeks. (The UK ONS study that is Bell’s main sources estimates 13%). It seems better to take a mean of these estimates than to just drop one of them, as the studies are fairly similar in approach. (Both rely on self-report. The sample size for the Nature paper is >4000).
Note that the 13% figure in the ONS study drops to 1% if you restrict to subjects who had symptoms every week. (The study allows for people to go a week without any symptoms while still counting as a Long Covid case). I realize people report Long Covid as varying over time, but it’s clearly worse to have a condition that causes some fatigue or tiredness at least once a week rather at least once every two weeks.
(Do you mean the Lancet / British intelligence test paper when you say ONS? I embarrassingly don’t see a paper I cited with those letters in it.)
The current way I imagine citing this is to use as a corroboration of my rough estimate of <2% 30yos having Long COVID. I don’t see an easy way to integrate it with IQ loss estimates—since I wouldn’t expect tiny levels of IQ loss to show up on a survey about actual Long COVID symptoms, it seems relatively consistent for 2% symptoms after 12 weeks to still correspond to an average IQ loss of .15 points after 12 weeks (~10% lose 1 IQ point, 1% lose several IQ points). I do think it points downwards somewhat, though, maybe a factor of 2?
I added a link above. The ONS is the UK’s national statistics agency. This is not a peer-reviewed paper but a report they published. (I find these reports to be mixed in quality).
In the Nature paper, they get 2.3% with symptoms overall. But they estimate that 30 yos are less likely than older cohorts to have symptoms at 56 days and so you could adjust down a bit. (Women are also at higher risk according to this study).
I quickly skimmed the El-Aly et al paper. It does look much better than some of the other studies. One concern is the demographics of the patients. Only 25% of people with Covid are younger than 48. Only 12% are female. I’d guess the veterans under 35 are significantly less affluent than LW readers. (Would more affluent veterans use private health care?). At a glance, I can’t see results of any regressions on age but it might be worth contacting the authors about this.
How to adjust for this? One thing is just look at hospitalization risk (see AdamGleave’s adjustment point (1)). However, it seems plausible that younger and healthier people would also recover better from less acute cases (and be less likely to have lingering symptoms). OTOH, there’s anecdata and data (of less high quality IMO) suggesting that Long Covid doesn’t fit the general patter of exponential increases in badness of Covid (and other similar diseases) with age. Overall, I’d still be inclined to make an adjustment of risk down if you are under 35 and healthy.
This is a good point, the demographics here are very skewed. I’m not too worried about it overstating risk, simply because the risk ended up looking not that high (at least after adjusting for hospitalization). I think at this point most of us have incurred more than 5 days of costs from COVID restrictions, so if that was really all the cost from COVID, I’d be pretty relaxed.
I did actually mean 45, in “all-things-considered” I was including uncertainty in whether my toy model was accurate. Since it’s a right-tailed distribution, my model can underestimate the true amount a lot more than it can overestimate it.
For what it’s worth, my all-things-considered view for Delta is now more like 30, as I’ve not really seen anything all that compelling for long COVID being much worse than in the model. I’m not sure about Omicron; it seems to be less virulent, but also more vaccine escape. Somewhere in the 15-90 day range sounds right to me, I’ve not thought enough to pin it down precisely.
These numbers are low, but not low enough to ignore. Earlier we decided that the quality of life hit from long COVID after a non-hospitalized acute case was 18%. If you’re a 35 year old woman, and your risk of ending up with lifelong long COVID from catching COVID is 2.8%, then catching COVID would be the same, statistically speaking, as losing (50 years * 0.18 * 0.028 * 365 days/year) = ~90 days of your life. Ouch.
We can also look at just the “worst case scenario” – catching long COVID that doesn’t go away for years AND limits daily activities a lot. This number feels a bit more like a “mortality” rate – except in this case you don’t actually die, but your life is forever altered, and you can’t hold down a job anymore or do most of the things you used to love to do.
A 35 year old woman runs about an 0.5% chance of the “worst case scenario” outcome if she gets Delta. For comparison, 0.5% is about 42x your chance of dying in a car crash in the next year.
I think the main differences are using studies with higher excess burdens and using a lower reduction factor to translate to lifelong risk. On the latter:
In the end we need to make an educated guess, even if it’s a low-confidence one, as to how often long COVID that lasts 4.5 months ends up being lifelong. Based on the SARS data, we could guess that 80% of hospitalized acute COVID patients that that have long COVID at 4.5 months end up having it for the rest of their life. Patients with milder COVID cases tend to get less physiological damage during acute infection, so it’s possible they’ll have higher recovery rates. Again taking an educated guess and going on even less data, we might expect that 50% of long COVID cases for mild acute patients at 4.5 months end up being lifelong.
Errata: My original calculation underestimated the risk by a factor of about 2x. I neglected two key considerations, which fortunately somewhat canceled each other out. My new estimate from the calculation is 3.0 to 11.7 quality-adjusted days lost to long-term sequelae, with my all-things-considered mean at 45.
The two key things I missed:
- I estimated the risk of a non-hospitalized case is about 10x less than a hospitalized case, and so divided the estimates of disease burden by 10x. The first part is correct, but the second part would only make sense if all disease burden was due to hospitalized cases. In fact, there’s a 15:85% split between hospitalized and non-hospitalized patients in the study (13,654:73,435). So if the disease burden for non-hospitalized is x, the total burden is 0.15*10x + 0.85*x = 2.35x. So we should divide by 2.35, not 10.
- However, as Owain pointed out below, the [demographics](https://www.nature.com/articles/s41586-021-03553-9/tables/1) are non-representative and probably skew high-risk given the median age is 60. the demographics are relatively high-risk. Indeed, this is suggested by the 15% hospitalized figure (which also, I suspect, means they just never included asymptomatic and most mildly symptomatic cases). An ONS survey (Figure 4) put symptoms reported after 5 weeks at 25% (20-30%) for 50-69 year olds and 17.5 (12.5 to 22.5%) for 17 to 24 year olds, which is surprisingly little difference, about a 1.5 decrease. I’d conjecture a 2x decrease in risk (noting that assuming no hospitalization is already doing a lot of work here).
Original post:
I did my own back-of-the-envelope calculation and came up with a similar but slightly higher estimated cost of 1.4 to 5.5 quality-adjusted days lost to long-term sequalea conditional on getting symptomatic COVID case. FWIW, I originally thought the OPs numbers seemed way too low, and was going to write a take-down post—but unfortunately the data did not cooperate with this agenda. I certainly don’t fully trust these numbers: it’s based on a single study, and there were a bunch of places I didn’t keep track of uncertainty, so the true credible interval should definitely be a lot wider. Given that and the right-tailed nature of the distribution, my all-things-considered mean is closer to 30 because of this, but figured I’d share the BOTEC anyway in case it’s helpful to anyone.
My model is pretty simple:
1. What % of symptoms are there at some short-term follow up period (e.g. 4 to 12 weeks)? This we actually have data on.
2. How bad are these symptoms? This is fairly subjective.
3. How much do we expect these symptoms to decay long-term? This is going off priors.
For 1. I used Al-Aly et al (2021) as a starting point, which was based on comparing medical records between a COVID-positive and non-COVID demographically matched control group in the US Department of Veterans Affairs database. Anna Ore felt this was one of the more rigorous ones, and I agree. Medical notes seem more reliable than self-report (though far from infallible), they seem to have actually done a Bonferroni correction, and they tested their methodology didn’t pick up any false positives via both a negative-outcome and negative-exposure controls. Caveat: many other studies have scarier headline figures, and it’s certainly possible relying on medical records skews this low (e.g. doctors might be reluctant to give a diagnosis, many patients won’t go to the doctor for mild symptoms, etc).
They report outcomes that occurred between 30 and 180 days after COVID exposure, although infuriatingly don’t seem to break it down any further by date. Figure 2 shows all statistically significant symptoms, in terms of the excess burden (i.e. increase above control) of the reported symptom per 1000 patients. There were 38 in total, ranging from 2.8% (respiratory signs and symptoms) to 0.15% (pleurisy). In total the excess burden was 26%.
I went through and rated each symptom with a very rough and subjective high / medium / low severity. 2% excess burden of high severity symptoms, 19% medium severity, 5% low severity. I then ballparked that high severity (e.g. heart disease, diabates, heart failure) wiped out 30% of your QALYs, medium severity (e.g. respiratory signs, anxiety disorders, asthma) as 5% and low (e.g. skin rash) as 1%. Caveat: there’s a lot of uncertainty in these numbers. Although I suspect I’ve gone for higher costs than most people would, since I tend to think health has a pretty big impact on productivity.
Using my weightings, we get a 1.6% reduction in QALYs conditional on symptomatic COVID case. I think this is misleading for three reasons:
1. Figure 3 shows that excess burden is much higher for people who were hospitalized, and if anything the gap seems bigger for more severe symptoms (e.g. about 10x less heart failure in people positive but not hospitalized, whereas rates of skin rash were only 2x less). This is good news as vaccines seem significantly more effective at preventing hospitalizations, and if you are fortunate enough to be a young healthy person your chance of being hospitalized was pretty low to begin with. I’m applying a 10x reduction for this.
2. This excess burden is per diagnosis, not per patient. Sick people tend to receive multiple diagnoses. I’m not sure how to handle this. In some cases, badness-of-symptoms does seem roughly additive: if I had a headache, I’d probably pay a similar amount not to also develop a skin rash then if my head didn’t hurt. But it seems odd to say that someone who drops dead from cardiac arrest was more fortunate than another patient with the same cause of death, who also had the misfortune of being diagnosed with heart failure a week earlier. So there’s definitely some double-counting with the diagnosis, which I think justifies a 2-5x decrease.
3. This study was presumably predominantly the original COVID strain (based on a cohort between March 2020 and 30 November 2020). Delta seems, per the OP, about 2-3x worse: so let’s increase it by that factor.
Overall we decrease 1.6% by a factor of 6.5 (10*2/3) to 25 (10*5/2), to get a short-term QALY reduction of 0.064% to 0.24%.
However, El-Aly et al include any symptom reported between 30 to 180 days. What we really care about is chance of lifelong symptoms if someone is experiencing a symptom after 6 months there seems like a considerable chance it’ll be lifelong, but if only 30 days has elapsed the chance of recovery seems much higher. A meta-review by Thompson et al (2021) seems to show a drop of around 2x between symptoms in a 4-12 week period vs 12+ weeks (Table 2), although with some fairly wild variation between studies so I do not trust this that much. In an extremely dubious extrapolation from this, we could say that perhaps symptoms half again from 12 weeks to 6 months, again from 6 months to a year, and after that persist as a permanent injury. In this case, we’d divide the “symptom after 30 days figure” from Al-Aly et al by a factor of 8 to get the permanent injury figure, which seems plausible to me (but again, you could totally argue for a much lower number).
With this final fudge, we get a lifelong QALY reduction of 0.008% to 0.03%. Assuming a 50-year life expectancy, this amounts to 1.4 to 5.5 days of cost from long-term sequelae. Of course, there are also short-term costs (and risk of morbidity!) that is omitted from this analysis, so the total costs will be higher than this.
(I’d personally appreciate you saying how many microcovids you think is equivalent to an hour’s time; that’s the main number I’ve been using to figure out whether various costs are worth it.)
The calculation would be pretty straightforward:
3.5 days mean, let’s assume another 2 days or so in terms of sickness, so 5.5 days lost in total for 1M microcovids.
5.5 days = 130 hours
Which implies that ~7600 (1MM / 130) microcovids is ~1 hour of life lost.
So Adam is saying microcovids are cheaper than the OP does? Connor writes
(Pardon me commenting while not getting into the details on this important topic, I am busy but am trying to track at least whether there’s disagreement and in what direction.)
According to this specific calculation. He does say his all things considered view is like 5x the cost.
So, to be clear, his all-things-considered view is about 1.5k uCOVIDs cost an hour, which is toward the edge of my range that corresponds to high risk, while his numerical estimate is at 7.5k uCOVIDs costing an hour, which is just outside of my range that corresponds to low risk (but matches almost exactly with my estimates of Long COVID risk outside of follow-ons from cognitive impairment!). So it sounds like initially he disagreed toward higher risk, then found very similar numbers as I did, now only leans toward the high end of my risk estimate due to priors and right-tail uncertainty. (Apologies if my paraphrase does not do your view justice, Adam.)
This is an accurate summary, thanks! I’ll add my calculation was only for long-term sequelae. Including ~10 days cost from acute effects, my all-things-considered view would be mean of ~40 days, corresponding to 1041 uCOVIDs per hour.
This is per actual hour of (quality-adjusted) life expectancy. But given we spend ~1/3rd of our time sleeping, you probably want to value a waking-hour at 1.5x a life-hour (assuming being asleep has neutral valence). If you work a 40 hour work week and only value your productive time (I do not endorse this, by the way), then you’d want to adjust upwards by a factor of (7*24)/40=4.2.
However, this is purely private cost. You probably want to take into account the cost of infecting other people. I’m not confident in how to reason about the exponential growth side of things. If you’re in a country like the US where vaccination rates have plateaued, I tend to expect Delta to spread amongst unvaccinated people until herd immunity is reached. In this scenario you basically want infection rates to be as high as possible without overwhelming the healthcare system, so we get to herd immunity quicker. (This seems to actually be the strategy the UK government is pursuing—although obviously they’ve not explicitly stated this.) But if you’re in a country that’s still actively vaccinating vulnerable people, or where flattening the curve makes sense to protect healthcare systems, then please avoid contributing to exponential growth.
Neglecting the exponential growth side of things and just considering immediate impact on your contacts, how likely are you to transmit? I’d be surprised if it was above 40% per household contact assuming you quarantine when symptomatic (that’s on the higher end of transmission seen even with unvaccinated primary cases), but I’d also be surprised if it was below 5% (lowest figure I’ve seen); I’d guess it’s around 15% for Delta. This means if you have ~6-7 contacts as close as housemates, then your immediate external cost roughly equals your private cost.
Specifically, two studies I’ve seen on secondary attack rate given vaccination (h/t @Linch) give pretty wildly varying figures, but suggest at least 2x reduction in transmission from vaccination. Layan et al (2021) found 40% of household contacts of Israeli medical staff developed an infection (when Alpha was dominant), with vaccination of the primary case reducing transmission by 80%, so an 8% chance of transmission overall. Harris et al (2021) from Public Health England suggest vaccination cuts transmission risk from 10% to 5%, but these figures are likely skewed low due to not systematically testing contacts.
Just to flag I messed up the original calculation and underestimated everything by a factor of 2x, I’ve added an errata.
I’d also recommend Matt Bell’s recent analysis, who estimates 200 days of life lost. This is much higher than the analysis in my comment and the OP. I found the assumptions and sources somewhat pessimistic but ultimately plausible.
The main things driving the difference from my comment were:
Uses data from the UK’s Office of National Statistics that I’d missed, which has a very high number of 55% of people reporting symptoms after 5 weeks, with fairly slow rates of recovery all the way out to 120 days post-infection. Given this is significantly higher than most other studies I’ve seen, I think Matt is being pessimistic by only down-adjusting to 45%, but I should emphasize these numbers are credible and the ONS study is honestly better than most out there.
Long COVID making your life 20% worse is on the pessimistic end. I put most mild symptoms at 5% worse. Ultimately subjective and highly dependent on what symptoms you get.
I think the difference in hospitalized vs non-hospitalized risk is closer to 10x (based on Al-Aly figure) not Matt’s estimate of 2x, that means we should multiply by a factor of ~60% not ~97%.
I should probably argue with Matt directly, but my brief take is that this is just entirely incompatible with what we see on the ground. The friends of mine who got COVID aren’t reporting 45% chance of their life being 20% worse. That’s… an incredibly massive effect that we would definitely see. Would anyone realistically bet on that?
Bell mentions this paper in Nature Medicine that finds only 2.3% of people having symptoms after 12 weeks. (The UK ONS study that is Bell’s main sources estimates 13%). It seems better to take a mean of these estimates than to just drop one of them, as the studies are fairly similar in approach. (Both rely on self-report. The sample size for the Nature paper is >4000).
Note that the 13% figure in the ONS study drops to 1% if you restrict to subjects who had symptoms every week. (The study allows for people to go a week without any symptoms while still counting as a Long Covid case). I realize people report Long Covid as varying over time, but it’s clearly worse to have a condition that causes some fatigue or tiredness at least once a week rather at least once every two weeks.
Great paper, thank you!
(Do you mean the Lancet / British intelligence test paper when you say ONS? I embarrassingly don’t see a paper I cited with those letters in it.)
The current way I imagine citing this is to use as a corroboration of my rough estimate of <2% 30yos having Long COVID. I don’t see an easy way to integrate it with IQ loss estimates—since I wouldn’t expect tiny levels of IQ loss to show up on a survey about actual Long COVID symptoms, it seems relatively consistent for 2% symptoms after 12 weeks to still correspond to an average IQ loss of .15 points after 12 weeks (~10% lose 1 IQ point, 1% lose several IQ points). I do think it points downwards somewhat, though, maybe a factor of 2?
I added a link above. The ONS is the UK’s national statistics agency. This is not a peer-reviewed paper but a report they published. (I find these reports to be mixed in quality).
In the Nature paper, they get 2.3% with symptoms overall. But they estimate that 30 yos are less likely than older cohorts to have symptoms at 56 days and so you could adjust down a bit. (Women are also at higher risk according to this study).
Oops, thought that was a top-level reply to me when I clicked on it, rather than a reply to Adam. Sorry. Makes more sense in context.
I quickly skimmed the El-Aly et al paper. It does look much better than some of the other studies. One concern is the demographics of the patients. Only 25% of people with Covid are younger than 48. Only 12% are female. I’d guess the veterans under 35 are significantly less affluent than LW readers. (Would more affluent veterans use private health care?). At a glance, I can’t see results of any regressions on age but it might be worth contacting the authors about this.
How to adjust for this? One thing is just look at hospitalization risk (see AdamGleave’s adjustment point (1)). However, it seems plausible that younger and healthier people would also recover better from less acute cases (and be less likely to have lingering symptoms). OTOH, there’s anecdata and data (of less high quality IMO) suggesting that Long Covid doesn’t fit the general patter of exponential increases in badness of Covid (and other similar diseases) with age. Overall, I’d still be inclined to make an adjustment of risk down if you are under 35 and healthy.
This is a good point, the demographics here are very skewed. I’m not too worried about it overstating risk, simply because the risk ended up looking not that high (at least after adjusting for hospitalization). I think at this point most of us have incurred more than 5 days of costs from COVID restrictions, so if that was really all the cost from COVID, I’d be pretty relaxed.
The gender skew could be an issue, e.g. chronic fatigue syndrome seems to occur at twice the rate in women than men.
I’m assuming the all-things-considered mean should be 4.5?
I did actually mean 45, in “all-things-considered” I was including uncertainty in whether my toy model was accurate. Since it’s a right-tailed distribution, my model can underestimate the true amount a lot more than it can overestimate it.
For what it’s worth, my all-things-considered view for Delta is now more like 30, as I’ve not really seen anything all that compelling for long COVID being much worse than in the model. I’m not sure about Omicron; it seems to be less virulent, but also more vaccine escape. Somewhere in the 15-90 day range sounds right to me, I’ve not thought enough to pin it down precisely.
Here’s another BOTEC, by Matt Bell:
I think the main differences are using studies with higher excess burdens and using a lower reduction factor to translate to lifelong risk. On the latter: