At this point, people I know are not that worried about dying from covid. We’re all vaccinated, we’re mostly young and healthy(ish), and it turns out the odds were always low for us. We’re also not that worried about hospitalization: it’s much more likely than death, but maintaining covid precautions indefinitely is very costly so by and large we’re willing to risk it.

The big unknown here has been long covid. Losing a few weeks to being extremely sick might be worth the risk, but a lifetime of fatigue and reduced cognition is a very big deal. With that in mind, I set out to do some math on what risks we were running. Unfortunately baseline covid has barely been around long enough to have data on long covid, most of it is still terrible, and the vaccine and Delta variant have not been widespread long enough to have much data at all. 

In the end, the conclusion I came to was that for vaccinated people under 40 with <=1 comorbidiy, the cognitive risks of long covid are lost in the noise of other risks they commonly take. Coming to this conclusion involved reading a number of papers, but also a lot of emotional processing around risk and health. I’ve included that processing under a “personal stuff” section, which you can skip if you just want the info but I encourage you to read if you feel yourself starting to yell that I’m not taking small risks of great suffering seriously. I do encourage you to read the caveats section before deciding how much weight to put on my conclusions.

Personal Stuff

This post took a long time to write, much longer than I wanted, because this is not an abstract topic to me. I have chronic pain from nerve damage in my jaw caused by medical incompetence, and my attempts to seek treatment for this continually run into the brick wall of a medical system that doesn’t consider my pain important (tangent: if you have a pain specialist you trust, anywhere in the US, please e-mail me (elizabeth@acesounderglass.com)). I empathize very much with the long covid sufferers who are being told their suffering doesn’t exist because it’s too hard to measure and we can’t prove what caused it.

Additionally, I’m still suffering from side effects from my covid vaccine in April. It’s very minor, chest congestion that doesn’t seem to affect my lung capacity (but I don’t have a clear before picture, so hard to say for sure). But it’s getting worse and while my medical practitioners are taking it seriously, this + the experience with dental pain make me very sensitive to the possibility they might stop if it becomes too much work for them. As I type this, I am taking a supplement stack from a high end internet crackpot because first line treatment failed and there aren’t a lot of other options. And that’s just from the vaccine; I imagine if I actually had covid I would not be one of the people who shakes it off the way I describe later in this post. 

All this is to say that when I describe the long term cognitive impact of covid as being too small to measure with our current tools against our current noise levels, that is very much not the same as saying it’s zero. It’s much worse than that. What I’m saying is that you are taking risks of similar levels of suffering and impairment constantly, which our health system is very bad at measuring, and against that background long covid does not make much of a difference for people within certain age and health parameters. 

A common complaint when people say “X isn’t dangerous to the young and healthy” is that it implies the death and suffering of those who aren’t young and healthy don’t matter. I’m not saying that. It matters a lot, and it’s impossible for me to forget that because I’m very unlikely to be one of the people who gets to totally walk covid off if I catch it. But from looking at the data, there don’t seem to be very many of us in my age group.

Caveats

Medical research in general is really bad, research of a live issue in a pandemic is worse, you should assume these are low quality studies unless I indicate otherwise.

This research was compiled for LessWrong and Redwood Research, with the goal of assessing safety for their office spaces populated by mostly-but-not-entirely-healthy people 25-40, who were much more interested in the cognitive and fatigue sequelae than the physical. Much of this research is applicable outside that group or the sources can be used in that way, but you should know that’s what I focused on.

There isn’t any data on long covid in vaccinated people with breakthrough delta-variant infections. Neither vaccines nor delta have been around long enough for that to exist. Baseline covid has barely been around long enough to have long-term data. What I have here is:

• Data showing that strength of acute infection correlates with long term impact, although not perfectly
• Data on the long term impact of baseline covid, given the strength of an initial infection
• Data on how the vaccine impacts the strength of acute infections
• Data on how delta impacts the strength of acute infections

Data

Long term outcomes correlate with short term outcomes

By far the best study (best does not mean good) comes out of the UK, where the BBC coincidentally started an online intelligence test in January 2020 (giving them a pre-covid baseline) and in May began asking participants if they’d had covid and if so how bad a case. When I said “assume the studies are terrible unless I note otherwise”, this is the study I wanted to highlight as reasonably good. Because they can compare test-takers in a given time period with and without covid they can control for some of the effects of changing a study population over time, which would be the biggest concern. Additionally, my statistical consultant described the paper as “not having any errors that affect the conclusion”, which is extremely good for a medical paper. This study was not ideal for determining sequelae persistence, but they did check if size of effect was correlated with time since symptom onset, and it wasn’t (but their average was only 2 months).

This study showed a very direct correlation between the severity of the acute infection and cognitive decline. I don’t trust its absolute numbers, but the pattern that more severe disease -> more severe persistent effects is very clear

A second study in Wuhan, China (hat tip Connor Flexman) examined long term outcomes of hospitalized patients, based on the intensity of their care (hospitalization, supplemental oxygen, ventilation) found an increase in acute severity was correlated with an increase in sequelae, although it didn’t hold for every symptom (there are a lot of symptoms and the highest-intervention group is small), and they barely looked at cognitive symptoms.

Taquet et al used electronic health records to get a relatively unbiased six figure sample size, that also showed a strong correlation between acute and long term outcomes, which we’ll talk about more below.

From this I conclude that your overall risk of long covid is strongly correlated with the strength of the initial infection.

Odds of acute outcomes

Sah et al estimate that 35% of covid cases (implied to be baseline and pre-vaccination) are asymptomatic, with large variation by age. Children (<18) are 46% likely to be asymptomatic, adults 18-59 are 32% likely, adults >=60 are 20% likely. I’m going to round the non-elderly adult number to ⅓ to make the math easier.

The Economist has a great calculator showing your pre-vaccine, pre-Delta risk of hospitalization and death, given your age, sex, and comorbidities. Note that this calculator only includes diagnosed cases, so it excludes both asymptomatic cases and those that did have symptoms but didn’t drive people to seek medical care. Here’s a few sample people:

• A healthy 30 year old man has a 2.7% chance of hospitalization, and <0.1% risk of death
• A healthy 30 year old woman has a 1.7% chance of hospitalization, and <0.1% risk of death
• A 25 year old man with asthma has a 4.2% risk of hospitalization, and <0.1% risk of death
• A 40 year old woman with obesity has a 6.5% risk of hospitalization, and 0.1% risk of death.
• Risk of hospitalization rises steadily with age but the risk of death doesn’t really take off until 50, at which point our healthy man has a death risk of 0.4% and our health woman has a risk of 0.2%

If you’d like, you can use your own numbers in this guesstimate sheet.

And again, that’s only for officially diagnosed and registered cases. If you assume ⅓ of infections in that age group are asymptomatic, the risk drops by ⅓.

If you are hospitalized, your risk of being ventilated is currently very, very low even if you’re in a high risk category. The overall average percent of hospitalized patients who were ventilated was 2.0% in the last week for which data was available (2021-03-24), after dropping steadily for most of the plague. We can assume that’s disproportionately among the elderly and people with severe comorbidities, so if that’s not you your odds are better still. I’m going to count the risk of intubation for our cohort as 0.5%, although that’s likely still an overestimate.

How do vaccines change these odds? According to CDC data from a time period ending 2021-05-01 (so before delta took off), 27% of breakthrough infections that reached the attention of the CDC were asymptomatic, and only 7% were hospitalized due to covid (another 3% were hospitalized for non-covid reasons). It’s very likely that the CDC is undercounting asymptomatic cases, so we’ll continue using our ⅓ number for now. The minimum age of reported breakthrough infection deaths was 71, so we’ll continue to treat the risk of death as 0% for our sample subjects. Additionally, given the timing most vaccinated participants would be elderly or front line workers, raising their risk considerably. A CDC press release goes much farther, saying vaccinated people > 65 had 7% of the hospitalizations of age-matched controls. 

How does delta change these odds? A Scottish study estimated delta had 2x the risk of hospitalization as alpha, which a Danish study estimated as having 1.42x the risk of hospitalization as baseline covid. So very roughly, we’re looking at 3x the risk of hospitalization from delta, relative to baseline.

So for our sample cases above, we have the following odds (note I updated these on the night it was posted, due to a math error. Thanks to Rob Besinger for catching it):

Risk given vaccine, delta	Hospitalized	Intubated
Healthy 30yo man	0.38% = 2.7*.07*3*2/3	.002% = 0.38*.005
Healthy 30yo woman	0.24% = 1.7*.07*3*2/3	.002% = 0.24*.005
Asthmatic 25yo man	0.58% = 4.2*.07*3*2/3	.003% = 0.58*.005
Obese 40yo woman	0.92% = 6.5*.07*3*2/3	.005% = 0.92*.005

That’s not so far from the rate of hospitalization in that age range for the flu (0.6%), with some caveats (the CDC sample includes unvaccinated people and the bucket is 18-49 years old, with the higher end presumably carrying more of the disease burden).

There is concern that vaccine effectiveness wanes over time, which I haven’t incorporated here.

Odds of long term outcomes

In general I ignored studies that merely tracked number of persistent sequelae but not their severity or type, which made it impossible to distinguish between “sense of smell still iffy” from “permanent intellectual crippling”, and studies that didn’t track how long the sequelae persisted. This was, unfortunately, most of them.

We talked about the Great British Intelligence Test above. I initially found this study quite scary. The study used its own tests rather than IQ, but if you assume a standard deviation in their tests is equivalent to a standard deviation in an IQ test, the worst category (ventilation) is equivalent to a 7 point IQ loss. That’s twice as bad as a stroke in this study (although I suspect sampling bias). I suspect the truth is worse still, because the worse your recently acquired cognitive and health issues are, the less likely you are to take a fun internet test advertised as measuring your intellectual strengths. However as I noted above, you are extremely unlikely to be put on a ventilator. 

For people with “symptoms, but not respiratory symptoms”, the cognitive damage is ~equivalent to 0.6 IQ points. For “medical assistance at home”, it’s 1.8 points. These are both likely to be overestimates given that the study only included known (although not necessarily formally diagnosed) cases. Additionally, while the paper claims to control for education, income, etc, bad things are more likely to happen to people in worse environments, and it’s impossible to entirely back that out.

Taquet et al used electronic health records to get a relatively unbiased six figure sample size, and found unhospitalized diagnosed covid patients (pre-Delta, pre-vaccine) had a 11% likelihood of a new neuro or psych diagnosis after their covid diagnosis, hospitalized patients had a 15% likelihood, and ICU patients had 26% likelihood. The majority of these were mood disorders (3.86%/4.49%/5.82% for home/hospitalized/ICU) and anxiety (6.81%/6.91%/9.79%). This seems quite bad, until you compare it to the overall numbers for depression in the time period, a naive reading of which suggests that covid had a protective effect

These numbers aren’t directly comparable. The second study is much lower quality and includes rediagnoses (although the total depression diagnosis numbers for the covid patients are 13.10%/14.69%/15.43%- still under the total increase in depression in the general population study). 

Overall this seems well within what you’d expect from getting a scary disease at a scary time, and not evidence of widespread neuro or psych impact of covid. Even if you take the numbers at face value, they exclude most people who were asymptomatic or treated at home without a formal diagnosis.

A UK metareview found the prevalence at 12 weeks of symptoms affecting daily life ranged from 1.2% (average age: 20, minimum 18) to 4.8% (average age: 63). The cohort with average age 31 had a mean prevalence of 2.8%. This is based on self-reports on survey data, which will again exclude asymptomatic cases- if you use the ⅓ figure and assume no long covid among the asymptomatic, that becomes 1.8% of 25-45 year olds with covid developing long covid that affects their daily life, which is well within the Lizardman Constant.

On the other hand, medicine is notoriously bad at measuring persistent, low-level, amorphous-yet-real effects. The Lizardman Constant doesn’t mean prevalences below 4% don’t exist, it means they’re impossible to measure using naive tools.

Comparison to other diseases

The Taquet study did compare covid patients to those with other respiratory diseases (including the flu, not controlling for disease severity or patient age), and found covid to be modestly worse except for myoneural junction and other muscular diseases, where covid 5xed the risk (although it’s still quite low in absolute terms). Dementia risk is also doubled, presumably mostly among the elderly.

Additionally, cognitive impairment following critical illness, and especially following intubation, is a well known phenomenon. This puts the Great British Intelligence Test numbers in perspective- being/needed to be ventilated is quite bad, but it’s always been that bad, there doesn’t appear to be any unique-to-covid badness.

Conclusion

My tentative conclusion is that the risks to me of cognitive, mood, or fatigue side effects lasting >12 weeks from long covid are small relative to risks I was already taking, including the risk of similar long term issues from other common infectious diseases. Being hospitalized would create a risk of noticeable side effects, but is very unlikely post-vaccine (although immunity persistence is a major unresolved concern).

I want to emphasize again that “small relative to risks you were already taking” doesn’t necessarily mean “too small to worry about”. For comparison, Josh Jacobson did a quick survey of the risks of driving and came to roughly the same conclusion: the risks are very small compared to the overall riskiness of life for people in their 30s. Josh isn’t stupid, so he obviously doesn’t mean “car accidents don’t happen” or “car accidents aren’t dangerous when they happen”. What he means is that if you’re 35 with 15 years driving experience and not currently impaired, the marginal returns to improvements are minor. 

And yet. I have a close friend who somehow got in three or four moderate car accidents in < 7 years, giving her maybe-permanent soft tissue damage (to answer the obvious question: no, the accidents weren’t her fault. Sometimes she wasn’t even driving). Statistically, that friend doesn’t exist. No one gets in that many car accidents that quickly without it being their fault. And yet the law of large numbers has to catch up with someone. Too small to measure can be very large.

What this means is not that covid is safe, but that you should think about covid in the context of your overall risk portfolio. Depending on who you are that could include other contagious diseases, driving, drugs-n-alcohol, skydiving, camping, poor diet, insufficient exercise, too much exercise, and breathing outside. If you decide your current risk level is too high, or are suddenly realizing you were too risk-tolerant in the past, reducing covid risk in particular might not be the best bang for your buck. Paying for a personal trainer, higher quality food, or a HEPA filter should be on your radar as much as reducing social contact, although for all I know that will end up being the best choice for you personally. 

Change my mind

My own behavior and plans have changed a lot based on this research, so I’m extremely interested in counterarguments. To make that easy, here’s a non-exhaustive list of things that would change my mind:

1. Evidence that long covid gets worse over time, rather than slowly improving (note that I did look at data from SARS 1 and failed to find this).
2. New variants increase the risk to what it was or was feared to be in April 2020
3. Evidence of more severe vaccine attenuation than we’re currently seeing.
4. Credible paths through which the risk could drop shortly in the next six months.

Thanks to LessWrong and Redwood Research for funding this research, and to Connor Flexman and Ray Arnold for comments on drafts.