Math help?

[rachelmanija]

Hypothetically speaking, if the chance of a vaccinated person being able to contract a certain disease is 6 out of 100, and the odds of a vaccinated person being able to transmit a certain disease is also 6 out of 100, then what is the chance of one random vaccinated person giving that certain disease to one other random vaccinated person?

This is a math problem I need help with, not a factual statement about a disease. I'm trying to express a concept with actual numbers rather than just "very unlikely."

Comments

[slightweasel]

A 6% chance to catch something from someone who has a 6% chance of transmitting it should be:

.06 x .06 = .0036

So, .36%, or 3.6 out of 1000.

[vass]

Good, that was my guess, but I didn't want to comment first since I'm not good at maths.

Of course, this is assuming that a vaccinated person who contracts a disease is just as infectious as an unvaccinated person who contracts the same disease. They might well be less infectious than that. (Oops, reading comprehension 50%. Rachel allowed for that in the hypothetical.)

[rachelmanija]

Yes, there's a lot of unknowns involved. Pfizer is the vaccine in question, hence my 6% number. It's 3% if you only count symptomatic disease.

https://www.nbcnews.com/health/health-news/pfizer-covid-vaccine-cuts-transmission-coronavirus-new-real-world-study-n1260542

The context, as is probably obvious, was a conversation with someone who thinks two fully vaccinated people having unmasked contact should not happen because there's still a chance of getting covid. Thence lies madness, IMO.

[crystalpyramid]

Yeah -- the one on one conversation is probably fine. But once you start to add more people, the risks start to multiply, so people still need to be really careful about larger gatherings. I just had to fill out a survey about whether I feel safe going to a big physics conference in person (no!)

[brainwane]

I like to show such people this risk budget calculator which explicitly shows you what precautions and factors lower or raise risk. Such as:

* how big a person's pod is
* indoors vs. outdoors
* normal conversation vs. singing/shouting
* whether you are unvaccinated, partially vaccinated, or fully vaccinated

Their risk tracker also lets you make calculations based on whether the OTHER person is unvaccinated, partially vaccinated, or fully vaccinated.

*

[minoanmiss]

*makes a note of the risk budget calculator*

[branna]

There’s probably some modification to that number that is contextual. I.e. what is the probability of the transmitting person being exposed and contracting it in the first place? Is that folded into the 6% transmission probability? If not the .36% number is an upper bound.

[rachelmanija]

Thank you!

[rydra_wong]

And another x 0.06, because otherwise you've not factored in person 2's protection against contracting the disease (which is presumably the same level as person 1's), in addition to person 1's protection against being capable of transmitting it.

So 0.0216%.

Deviating towards realism: it's not clear how much the vaccine cuts the chances of being capable of transmitting the virus if you catch it -- it probably does, because it reduces viral load, but I don't know of any estimates of how much.

You still have the double x 0.06 from each vaccinated person's protection against contracting the virus.

Just this bit:

And the odds of a vaccinated person being able to transmit a certain disease is also 6 out of 100

is probably a different, higher number.

[rachelmanija]

So it's actually .06 x .06 x 06?

Going by the Israeli study I linked above, I'm assuming that if you don't have any detectable infection at all, even an asymptomatic one, then you can't transmit it. If that's correct, then the transmission risk would be 6 out of 100.

Personally, I'm not going to worry about fully vaccinated people having contact with each other.

[rydra_wong]

Realistically, I think it'd be more like 0.06 x [unknown] x 0.06.

Because you have :

Risk of person 1 contracting virus, even asymptomatically

x risk of person 1 transmitting virus particles if they are carrying it, which afaik we don't have much info on but where you probably get some risk reduction too -- reduce viral load and people become less contagious

x risk of person 2 contracting virus if they are exposed to it

Personally, I'm not going to worry about fully vaccinated people having contact with each other.

Nope, me neither, at least when it comes to the mRNA vaccines.

The only instance I might worry at all would be if person 2 has a medical condition which makes covid guaranteed death for them and there are still high levels of covid in the general population. Then I'd see why you might still want to be cautious.

I'd also probably be a bit more cautious when it comes to populations which have largely been vaccinated with AZ or J&J etc. (e.g. in the UK), because the level of protection against infection is lower (though protection against hospitalization and death is still very good), so we're going to be more reliant on herd immunity.

With those vaccines, I'd still be cool with fully-vaccinated people having unmasked indoor contact with other fully vaccinated people, but think at the moment they should probably still be practicing risk reduction to reduce their overall exposure. Wear a mask on the bus and in the supermarket and maybe don't go to an indoor restaurant or disco yet -- but having your vaccinated friends round for unmasked coffee, no problem.

[rachelmanija]

Yes, I'll still be wearing a mask in public and not eating in restaurants indoors.

[rydra_wong]

All about the harm reduction.

(For multiple reasons, I am having a lot of flashbacks to the early 90s lately.)

[ckd]

As I said sometime in the past year, "I was a teenager in the 1980s. I've already lived through 'deadly disease that limits my social options and is badly handled by a Republican administration', and it didn't need a remake."

[graydon]

It's actually misleading.

The 6% is questionable in any specific case. It's been arrived at appropriately, but it's been arrived at with error bars and it's been arrived at observationally in a disease and behaviour environment that isn't current (and which can't be current because it's inherently backward-looking about what is observed to have happened, and in this specific case applies to a behavioural environment you're not in); put another way, it may not be accurate for currently circulating variations, and it's an average that doesn't describe the risks associated with specific current behaviour, this one time with these people, it describes the risk for a population including a population's behaviour over the studied range of time.

COVID-19 has always been observed to be dose-dependent for both chance of infection and severity so the risk is never a flat number; it's got to have "how long" and "how much virus shedding" and probably unknowns, and it's going to apply every time, not "for all times over an indefinite time frame". So your postulated chance of not getting it, 0.94, gets multiplied for every possible point of transmission (= walking into the same room as an infected person); do that seven times and your chance of not getting it is down around 65%. (0.94 ^ 7)

Vaccination reduces the risk by an order of magnitude is being offered as the useful thumb rule by some knowledgeable folks, though it remains to be seen how well that holds up.

So you have a 1% chance of Long Covid instead of 10%; a 0.1% chance of death (if you're healthy and under 50) but we don't really know about chance of transmission because the disease landscape is changing in multiple ways. (There was that "doors open at the same time for 30 seconds" quarrantinge hotel transmission in New Zealand, for example. Turns out pressure gradients matter! There's solid results that wearing glasses matters, which means it's "any mucous membrane" which means which direction you happen to be facing relative to the infectious person matters.)

In general, the criteria for safety is not vaccination but the extent to which the disease is circulating and how contact is managed because while vaccinated person in contact with a vaccinated person is a much reduced risk, the more operative question is how much contact either vaccinated person is having with potentially infected persons in what environments. Airflow matters, and it matters in currently poorly-understood ways.

My take is that the only really effective approach is to assume that absolutely everyone, including you, are infected and shedding. Once the local transmission rate drops to zero (no new cases for a couple weeks) it's time to change that operating assumption. In the meantime, vaccination reduces but does not eliminate your risk of lasting harm.

[redbird]

How much difference do glasses make outdoors, do you know? I've been going without on cloudy days because they fog up when I'm masked.

[graydon]

I don't know.

My recollection of the study I'm aware of says that it found glasses wearers as a category were 30% less likely to get COVID than non-glasses wearers, controlling for other factors. They didn't try to relate this to any specific behaviour, probably because they didn't have the data.

I suspect but absolutely cannot back up that there's an element of dumb luck involved -- what direction you're facing, when you happen to rub your eyes, etc. -- but the implication that eyes are a significant avenue of infection seems inescapable. So I'd be inclined -- have myself in fact so done -- to get a rigid mask with a gasket to avoid glasses-fogging. (https://o2canada.com/ and it's not like they're wrong about the anti-pollution utility.)

[recessional]

Honestly it's quite possible that the difference has as much to do with the fact that those of us with glasses tend to have masks with better seals than anything.

But overall none of it's super definitive and Precise anyway.

[graydon]

But overall none of it's super definitive and Precise anyway.

Oh yeah.

The confidence intervals on some of this stuff -- 95% confidence that the answer, which we have reported as sixty-three, lies between two and a hundred and five -- are unsettling.

[sholio]

So your postulated chance of not getting it, 0.94, gets multiplied for every possible point of transmission (= walking into the same room as an infected person); do that seven times and your chance of not getting it is down around 65%. (0.94 ^ 7)

No, that is not how epidemiology works and not how vaccines work. According to your math, even if someone's had a vaccine, their chances of not getting sick rapidly drop close to zero if they're around infected people, and if vaccines worked like that, they'd be pretty useless. The point of vaccines is that they make you immune. They just don't make everyone immune to the same degree, so exposure does matter, but only up to a point and more so for some people than others.

The 95% figure is based on epidemiological studies of people who've had the vaccine, who were 95% less likely than placebo recipients to get it after 2+ months of data collection, i.e. averaging all collective Covid exposure in the entire group during that time. This doesn't mean everyone in the group got Covid or that all were exposed at the same rate. But this is broad epidemiological data, not a per-exposure percentage risk.

[graydon]

Sterilizing vaccines don't work like that.

None of the COVID vaccines are sterilizing; there's some confidence they reduce rate of transmission (while how much, and how variably, and with what variants, remains an open question), and functional vaccines are rare in humans (there's a literature about functional vaccines in chickens, but so far as I know the COVID vaccines are the first widespread use of a functional vaccine in humans) but so far as I understand it with functional vaccines you do perform the "risk per exposure" calculation because you're only functionally immune -- you won't get severely ill -- but you're still at risk of both catching the disease per exposure and becoming infectious if you are exposed, same as you were unvaccinated, only some amount less. How much less is not known.

The probability calculation I gave is nonsense; we don't know what counts as exposure and we don't know the risk per exposure and so on. But something like that calculation, if you knew the real numbers, would apply for a functional vaccine. So hopefully useful "feel for risks" math.

The epidemiological study is not in question at all, but it happened in a context of people who didn't know they were vaccinated and behaved as though they were at risk. The numbers nigh-certainly move if people stop behaving like they're at risk in a population that's still got a high rate of transmission due to being incompletely vaccinated. We don't yet know how much they move; everybody hopes it's hardly at all but there's only one way to find out.

[sholio]

functional vaccines are rare in humans (there's a literature about functional vaccines in chickens, but so far as I know the COVID vaccines are the first widespread use of a functional vaccine in humans

I don't know where you got that information, but it's wrong. Sterilizing vaccines are relatively rare and many common vaccines don't provide complete, sterilizing immunity, including the flu, hepatitis, rotavirus, and pertussis vaccines.

However, from the perspective of the vaccinated person, it doesn't actually make that much difference - they are still immune, it's just that the virus may be able to breed in their body without making them sick. Theoretically, they may still be able to pass the disease to an unvaccinated person. However, we're talking about vaccinated people socializing with each other, and one vaccinated person infecting another vaccinated person with a symptomatic case of covid is still going to be a vanishingly rare occurrence - they would have to be actively contagious, and the other person would have to be one of the unlucky ones whose immune response didn't take or is sufficiently depressed that they're able to catch it.

It's true that we don't know how this is going to function in the general population once people start behaving normally again, and the vaccinated and non-vaccinated population mingle. But, again, that's not what was asked about and not what we're talking about - the topic is vaccinated people, who are otherwise being careful, socializing with each other vaccinated people, and all the science points to the odds of the two of them being able to infect each other being really, really tiny.

[graydon]

all the science points to the odds of the two of them being able to infect each other being really, really tiny

No argument!

[grayswandir]

This all sounds very much like what I was assuming was probably the case, though I hadn't looked into it. But ugh, it sure makes it sound like in the "land of the free," where like half the population is likely to refuse vaccination, we're kind of screwed. :/

[graydon]

The historical expectation for a novel plague seems to be somewhere between a fifth and a quarter of the population dying.

Even in the parts of the Anglosphere that are doing really badly with COVID, the expectation is much better than that.

Plus while it's likely going to take more than one round of vaccines it does look like vaccination at worst keeps the vaccinated from severe harm. Which turns the whole thing into a solvable problem, even if it's going to take awhile.

It'd be better to be Taiwan or Vietnam, public-health-response-wise, but this is recoverable.

[grayswandir]

Yeah, fair enough. I didn't actually mean "screwed" in the dramatic sense of widespread death. Just, it seems like it's going to be quite some time before not wearing a mask in enclosed public spaces will seem like a good idea again, even for vaccinated people, as long as a lot of other people still aren't vaccinated.

[graydon]

This year's entire lack of catching colds has made me wonder if not wearing a mask in enclosed public spaces was ever a good idea. (The flu numbers, too. To date this season, there has been no evidence of community circulation of influenza despite continued testing above seasonal levels. It looks a lot like what slows COVID stops influenza. )

I still feel severely dorky out in public in a mask, despite everything, but it does seem like an effective and useful thing to do in general, not just during a pandemic.

[ethelmay]

The 6% isn't your chance of getting it unless your chance was 100% without the jab. The measles jab is 97% effective, and nowhere near 3% of people get measles, because most of us are never exposed.

I figure my current chance of getting COVID (no jab yet, low risk behavior) is under 1%, and with immunization would be 6% of that. Of course my behavior will change some, but gradually, and I don't expect to be in any "100% I would have gotten sick without the jab" situations for a long while (I hope never, but I might hit a pocket of COVID-pos folks somewhere).