Having a relatively rare belief that vaccinated people seem much more likely to get asymptomatically infected and to have lower mortality BUT also noting that vaccines do NOT prevent infectiousness and probably cannot push R0 below 1.0.
Much more likely than what? It would seem the relative comparison you want to make would be vs. the unvaccinated, but that’s obviously false (and that’s the important part). It’s true they are more likely to be asymptomatically vs. symptomatically infected (yay mild COVID), but so what? Most of the work is done on any infection at all, e.g. (making up numbers but illustrating the point): P(infected | unvaccinated) = .50, P(asymptomatic | infected for unvaccinated) = .50, and then assume that symptomatic people are less likely to transmit the disease than asymptomatic people because they know to quarantine thanks to the symptoms. So that’s a 25% chance of getting asymptomatically infected feeding into a decision generating a negative externality. P(infected | vaccinated) = .05, P(asymptomatic | infected for vaccinated) = 1.0, let’s assume there are no symptomatic cases of infections among the vaccinated (hahaha), that’s a 5% chance of getting asymptomatically infected feeding in. Again, most of the work is done on any infection at all, so having a higher chance of symptomatic (vs. asymptomatic) infection doesn’t really matter (at the level of vaccine effectiveness and rate of asymptomatic infection we’ve seen).
Do vaccines prevent infectiousness? I remember seeing CDC data over the summer about how symptomatic vaccinateds are as infectious (in viral load) as symptomatic unvaccinateds, so that’s conditional on showing symptoms. But let’s assume asymptomatics in each group are also equally infectious—then we can still favor vaccines because, see above, most of the work is done on any infection at all.
To conclude, I think it’s extremely clear that your (2) is wrong. There is public good value to vaccination.
Thank you for this high quality response! The numbers were helpful and I had to stop and grind out some of the math and parse your sentences carefully.
assume that symptomatic people are less likely to transmit the disease than asymptomatic people because they know to quarantine thanks to the symptoms.
Making this part of the model more quantitative might reveal a crux?
I think we agree here directionally (symptomatic people change behavior in a way that has pro-social results, exposing fewer people “out in the world”) but if the effect was very large (like if the average asymptomatic person infected a mean of 30 people and the average symptomatic person only infected 1.1 people) then I think it might overwhelm other parts of a full model, even with the numbers you specified (which I will get to below).
(Empirical Digression:
This meta-analysis suggests that on the order of a half to a third of all infections occur not “out in the world” but specifically in a medical context… where “worse symptoms” might tend to evolve in order to cause infected people to go to clinics where they could infect a large portion of the people who ever get infected with covid.
This other study suggested that “Brigham and Women’s Hospital” in Boston had a much much lower rate of nosocomial covid, so covid’s evolutionary incentives under endemic conditions might be regionally heterogeneous?
Under an institutional heterogeneity model… it might be pro-socially wise to isolate any region with normally bad hospitals until these breeding grounds of infectious mortality are closed or repaired to adequacy. Obviously we are not wise, however, so this is unlikely to happen even if it was a net good for sure. Also, the model might be false, and it is certainly controversial, so I do not advocate this directly right now, based on current credence levels.)
In terms of your proposed model I think you didn’t specify how many more people the average asymptomatic covid carrier might infect but you did give these:
A common problem in bayesian modeling is to figure out what your “event space” actually contains. In a nutshell: what are you counting? “Mere counting” can sometimes turn out to be hard...
I’m not sure if “infected” for you means “infected in a specific single exposure event during a controlled challenge trial that is a decent proxy for a normal exposure event” or if it means some sort of lifetime all-in summary statistic closer to incidence or prevalence or a time and/or space bounded attack rate.
I mostly focus on these macroscale summary statistics, and so my model is that the attack rate for the period from 2018 to 2025, assuming endemic covid and no eradication and so on, might be close to 100% and it might even be higher than 100% if the numerator is “periods of infectiousness by a single person with covid in a region” (so asymptomatic re-infections cause +1 to the numerator) and the denominator is “total people in that region”.
Like in the worst possible world, covid evolves to higher and higher mortality, such that all humans are either dying or else vaccinated against the variant that came out in the last 12 months (and also everyone “healthy” is semi-chronically infected in a way that is non-fatal after vaccination), always, in general, like some kind of Paolo Bacigalupi story?
And I get it. If the world is on fire and vaccination protects you from being hurt by being on fire… I’d get the vaccine too. I did get the vaccine, even knowing it was might only be selfishly beneficial. At this point: any port in a storm, you know?
So for me, thinking of “P(infected)” as a summary statistic for a person in a region with endemic covid… that shit is probably going to be very high even for the vaccinated. I think?
Concretely then, I assert P(infected | vaccinated) >> 5% (for an understanding of the relevant event space where this number applies over a long period of time, like any five year period during which covid is endemic and still evolving).
Maybe you know otherwise, and this is a crux?
But I think I’m right, because I think that is basically what it means for covid to be endemic forever. Like… the only people who won’t get infected under endemic conditions (maybe over and over?) will be lifetime shut-ins?
Measles used to have an insanely high R0 and a 1% mortality and we nearly eradicated it back when our medical system was competent, so the the niche is kind of empty?
Before the competent near eradication of measles everyone got “the 1% fatal, high R0, disease”, and if you lived then you lived, and that’s why our genomes are full of disease-protecting alleles. Now the global bio-techno-governing-medical system is either evil or incompetent or both… so maybe there is an open niche? Maybe the human genome will eventually get new alleles for this?
Epistemically (if you with agree my modeling ideas and event space choice) it would be convenient because it might mean that we can just look up the attack rate overall (and maybe look up the relative R0 contributions) and “simply know” the same thing :-)
Personally, if we’re granting that this thing is politically impossible to eradicate, I think the right thing to focus on might be modulating the evolution of covid to be “slow and towards lower mortality”.
(If we can’t eradicate, I suspect this more subtle form of influence over covid is probably also beyond our politico-economic capacities and we will just experience whatever nature does to us, like savages subject to the whims of the lesser gods.)
I am strongly in favor of adequate and as-liberty-respecting-as-possible eradication of covid.
The event space I care about for an infectious disease is the event space that represents the large scale long term summary statistic that cleanly models “the entire herd and its general health”. It is a weird position, but… well… I’m honestly kind of surprised that even 2% of people agree with me? It isn’t like I don’t notice that I’m weird <3
Good job looking for cruxes! I agree with you that quantifying a differential in exposures would help nail down how much we should favor vaccination (or not), but the idea behind the probabilities I laid out was getting at the risk of inducing asymptomatic-spread. At the most unfavorable to vaccination (like how I also assumed vaccination leads to only asymptomatic disease), asymptomatics generate N infections from N exposures with p=1 and symptomatics generate exposures with p=0 (because they quarantine), so we can just look at the risk of inducing asymptomatic-spread without additional layers of calculation.
Though that does indeed depend on the key probabilities going into calculating the risk. If p>>5%, then additional calculation would be warranted, and calibrating the probabilities better would be more important. For example, it’s clear just looking at the conditional probabilities that the turning point is when the relative risk of infection depending on vaccination equals the reciprocal of the relative risk of being asymptomatic conditional on infection depending on vaccination—that is, if vaccinateds are twice as likely to be asymptomatic conditional on infection than unvaccinateds (wow, the RR is a little under 2, but let’s call it 2, Fig 3), we prefer vaccination as long as vaccination cuts the risk of infection by at least half (vaccine effectiveness >= 50%). Any less than half, and then we can’t just prefer vaccination out of hand and have to go through and calculate. And then figuring out the actual differential in exposures (and viral loads!) would be relevant too.
I agree with you that the probabilities I’m focusing on are in a much narrower time frame and that widening it out, p will lift off from the rate estimated in the clinical trials (about a 2 month window). As the vaccine effectiveness rate approaches 0%, then indeed we can’t prefer vaccination out of hand. How would that happen? As you suggest, with a long enough time window, the attack rates could equalize at 100%. I don’t actually see that happening (I expect the vaccines don’t only provide probabilistic protection of around 85% but, at least for some, effective immunity). But vaccine effectiveness could reach the reciprocal of the relative risk of being asymptomatic conditional on infection depending on vaccination well before getting to 0%. If you think vaccine effectiveness for the long term will fall below 50%, then we have some more calculating to do. Seeing as effectiveness has stayed about as high as models would tell you, falling below 50% only seems like a real possibility with Omicron, and my guess is we’ll either get a new shot to avoid lower effectiveness [1] [2] or learn that 3 doses work against it.
My prior on vaccine effectiveness staying over 50% even in the long term is strong enough, and the extra research and calculation that would otherwise be required to address this further is daunting enough, that I’ll leave it at that. I don’t want to say the burden of proof is on either of us here, since ultimately it depends on which prior is “deemed” the prior.
I want to reiterate that your general point that a vaccine might not have the public good value we assume it has is legit. We are used to diseases that generate symptomatic infections with high p, so any reduction in symptomatic infection is noticeable and contributes to stopping the spread. If a vaccine pushes infections to “hide” in asymptomatic ones instead (because the disease generates symptomatic infections with low-moderate p), and asymptomatic infections are still highly transmissible, the public good value is not quite so certain, generally speaking.
They’d be vaccinated-lite. The neutralization titers in vaccinated plasma are better than in convalescent plasma. Lots of room to complicate things and get it closer to reality, but that doesn’t touch the public good value thing so much.
You can do better than vaccinated lite. Since we know that neutralization titers in vaccinated decline as a function of time from vaccination, we can say that the unvaccinated recovered are like vaccinated ~4 months from vaccination, or 5 months and then we can treat everyone as vaccinated with x time passed from last vaccination.
4 months since having the third booster provides more protection then 4 months since second shot.
A lot of vaccines out in the world are already 0, 1 months 6 months to give people good lifetime protection because two shoots are not enough to give lifetime protection.
Your POV really turns on (emphasis added):
Much more likely than what? It would seem the relative comparison you want to make would be vs. the unvaccinated, but that’s obviously false (and that’s the important part). It’s true they are more likely to be asymptomatically vs. symptomatically infected (yay mild COVID), but so what? Most of the work is done on any infection at all, e.g. (making up numbers but illustrating the point):
P(infected | unvaccinated) = .50, P(asymptomatic | infected for unvaccinated) = .50, and then assume that symptomatic people are less likely to transmit the disease than asymptomatic people because they know to quarantine thanks to the symptoms. So that’s a 25% chance of getting asymptomatically infected feeding into a decision generating a negative externality.
P(infected | vaccinated) = .05, P(asymptomatic | infected for vaccinated) = 1.0, let’s assume there are no symptomatic cases of infections among the vaccinated (hahaha), that’s a 5% chance of getting asymptomatically infected feeding in. Again, most of the work is done on any infection at all, so having a higher chance of symptomatic (vs. asymptomatic) infection doesn’t really matter (at the level of vaccine effectiveness and rate of asymptomatic infection we’ve seen).
Do vaccines prevent infectiousness? I remember seeing CDC data over the summer about how symptomatic vaccinateds are as infectious (in viral load) as symptomatic unvaccinateds, so that’s conditional on showing symptoms. But let’s assume asymptomatics in each group are also equally infectious—then we can still favor vaccines because, see above, most of the work is done on any infection at all.
To conclude, I think it’s extremely clear that your (2) is wrong. There is public good value to vaccination.
Thank you for this high quality response! The numbers were helpful and I had to stop and grind out some of the math and parse your sentences carefully.
Making this part of the model more quantitative might reveal a crux?
I think we agree here directionally (symptomatic people change behavior in a way that has pro-social results, exposing fewer people “out in the world”) but if the effect was very large (like if the average asymptomatic person infected a mean of 30 people and the average symptomatic person only infected 1.1 people) then I think it might overwhelm other parts of a full model, even with the numbers you specified (which I will get to below).
(Empirical Digression:
This meta-analysis suggests that on the order of a half to a third of all infections occur not “out in the world” but specifically in a medical context… where “worse symptoms” might tend to evolve in order to cause infected people to go to clinics where they could infect a large portion of the people who ever get infected with covid.
This other study suggested that “Brigham and Women’s Hospital” in Boston had a much much lower rate of nosocomial covid, so covid’s evolutionary incentives under endemic conditions might be regionally heterogeneous?
Under an institutional heterogeneity model… it might be pro-socially wise to isolate any region with normally bad hospitals until these breeding grounds of infectious mortality are closed or repaired to adequacy. Obviously we are not wise, however, so this is unlikely to happen even if it was a net good for sure. Also, the model might be false, and it is certainly controversial, so I do not advocate this directly right now, based on current credence levels.)
In terms of your proposed model I think you didn’t specify how many more people the average asymptomatic covid carrier might infect but you did give these:
A common problem in bayesian modeling is to figure out what your “event space” actually contains. In a nutshell: what are you counting? “Mere counting” can sometimes turn out to be hard...
I’m not sure if “infected” for you means “infected in a specific single exposure event during a controlled challenge trial that is a decent proxy for a normal exposure event” or if it means some sort of lifetime all-in summary statistic closer to incidence or prevalence or a time and/or space bounded attack rate.
I mostly focus on these macroscale summary statistics, and so my model is that the attack rate for the period from 2018 to 2025, assuming endemic covid and no eradication and so on, might be close to 100% and it might even be higher than 100% if the numerator is “periods of infectiousness by a single person with covid in a region” (so asymptomatic re-infections cause +1 to the numerator) and the denominator is “total people in that region”.
Like in the worst possible world, covid evolves to higher and higher mortality, such that all humans are either dying or else vaccinated against the variant that came out in the last 12 months (and also everyone “healthy” is semi-chronically infected in a way that is non-fatal after vaccination), always, in general, like some kind of Paolo Bacigalupi story?
And I get it. If the world is on fire and vaccination protects you from being hurt by being on fire… I’d get the vaccine too. I did get the vaccine, even knowing it was might only be selfishly beneficial. At this point: any port in a storm, you know?
So for me, thinking of “P(infected)” as a summary statistic for a person in a region with endemic covid… that shit is probably going to be very high even for the vaccinated. I think?
Concretely then, I assert P(infected | vaccinated) >> 5% (for an understanding of the relevant event space where this number applies over a long period of time, like any five year period during which covid is endemic and still evolving).
Maybe you know otherwise, and this is a crux?
But I think I’m right, because I think that is basically what it means for covid to be endemic forever. Like… the only people who won’t get infected under endemic conditions (maybe over and over?) will be lifetime shut-ins?
Measles used to have an insanely high R0 and a 1% mortality and we nearly eradicated it back when our medical system was competent, so the the niche is kind of empty?
Before the competent near eradication of measles everyone got “the 1% fatal, high R0, disease”, and if you lived then you lived, and that’s why our genomes are full of disease-protecting alleles. Now the global bio-techno-governing-medical system is either evil or incompetent or both… so maybe there is an open niche? Maybe the human genome will eventually get new alleles for this?
Epistemically (if you with agree my modeling ideas and event space choice) it would be convenient because it might mean that we can just look up the attack rate overall (and maybe look up the relative R0 contributions) and “simply know” the same thing :-)
Personally, if we’re granting that this thing is politically impossible to eradicate, I think the right thing to focus on might be modulating the evolution of covid to be “slow and towards lower mortality”.
(If we can’t eradicate, I suspect this more subtle form of influence over covid is probably also beyond our politico-economic capacities and we will just experience whatever nature does to us, like savages subject to the whims of the lesser gods.)
I am strongly in favor of adequate and as-liberty-respecting-as-possible eradication of covid.
The event space I care about for an infectious disease is the event space that represents the large scale long term summary statistic that cleanly models “the entire herd and its general health”. It is a weird position, but… well… I’m honestly kind of surprised that even 2% of people agree with me? It isn’t like I don’t notice that I’m weird <3
Good job looking for cruxes! I agree with you that quantifying a differential in exposures would help nail down how much we should favor vaccination (or not), but the idea behind the probabilities I laid out was getting at the risk of inducing asymptomatic-spread. At the most unfavorable to vaccination (like how I also assumed vaccination leads to only asymptomatic disease), asymptomatics generate N infections from N exposures with p=1 and symptomatics generate exposures with p=0 (because they quarantine), so we can just look at the risk of inducing asymptomatic-spread without additional layers of calculation.
Though that does indeed depend on the key probabilities going into calculating the risk. If p>>5%, then additional calculation would be warranted, and calibrating the probabilities better would be more important. For example, it’s clear just looking at the conditional probabilities that the turning point is when the relative risk of infection depending on vaccination equals the reciprocal of the relative risk of being asymptomatic conditional on infection depending on vaccination—that is, if vaccinateds are twice as likely to be asymptomatic conditional on infection than unvaccinateds (wow, the RR is a little under 2, but let’s call it 2, Fig 3), we prefer vaccination as long as vaccination cuts the risk of infection by at least half (vaccine effectiveness >= 50%). Any less than half, and then we can’t just prefer vaccination out of hand and have to go through and calculate. And then figuring out the actual differential in exposures (and viral loads!) would be relevant too.
I agree with you that the probabilities I’m focusing on are in a much narrower time frame and that widening it out, p will lift off from the rate estimated in the clinical trials (about a 2 month window). As the vaccine effectiveness rate approaches 0%, then indeed we can’t prefer vaccination out of hand. How would that happen? As you suggest, with a long enough time window, the attack rates could equalize at 100%. I don’t actually see that happening (I expect the vaccines don’t only provide probabilistic protection of around 85% but, at least for some, effective immunity). But vaccine effectiveness could reach the reciprocal of the relative risk of being asymptomatic conditional on infection depending on vaccination well before getting to 0%. If you think vaccine effectiveness for the long term will fall below 50%, then we have some more calculating to do. Seeing as effectiveness has stayed about as high as models would tell you, falling below 50% only seems like a real possibility with Omicron, and my guess is we’ll either get a new shot to avoid lower effectiveness [1] [2] or learn that 3 doses work against it.
My prior on vaccine effectiveness staying over 50% even in the long term is strong enough, and the extra research and calculation that would otherwise be required to address this further is daunting enough, that I’ll leave it at that. I don’t want to say the burden of proof is on either of us here, since ultimately it depends on which prior is “deemed” the prior.
I want to reiterate that your general point that a vaccine might not have the public good value we assume it has is legit. We are used to diseases that generate symptomatic infections with high p, so any reduction in symptomatic infection is noticeable and contributes to stopping the spread. If a vaccine pushes infections to “hide” in asymptomatic ones instead (because the disease generates symptomatic infections with low-moderate p), and asymptomatic infections are still highly transmissible, the public good value is not quite so certain, generally speaking.
How do you incorporate unvaccinated who recovered from covid in your model? Are they equivalent to vaccinated?
They’d be vaccinated-lite. The neutralization titers in vaccinated plasma are better than in convalescent plasma. Lots of room to complicate things and get it closer to reality, but that doesn’t touch the public good value thing so much.
You can do better than vaccinated lite. Since we know that neutralization titers in vaccinated decline as a function of time from vaccination, we can say that the unvaccinated recovered are like vaccinated ~4 months from vaccination, or 5 months and then we can treat everyone as vaccinated with x time passed from last vaccination.
4 months since having the third booster provides more protection then 4 months since second shot.
A lot of vaccines out in the world are already 0, 1 months 6 months to give people good lifetime protection because two shoots are not enough to give lifetime protection.
Do we have a lot of data on people who had the third booster four months ago?