COVID Probability

#1
Thanks for taking a minute to check this out. It's been a long time since my college Stats class and I don't have the chops to do this anymore. I need help settling a debate with a friend regarding COVID and the probability of contracting COVID after being fully vaccinate. Not trying to be political. Just looking for the numbers.

Here are the basic assumptions based on the CDC's numbers for California:
CA population: 39,510,000
Total current contagious cases: 34,000 (this is based on an average of 2417 new cases/day and a contagion time frame of 14 days. We are also assuming these people are out and about in the population, not staying at home.)
Assuming I have daily contact with 10 random people.
Assuming I have a vaccine efficacy rate of 90%.
What are my daily odds of actually contracting COVID?

I know there are a lot more actual variables, but I didn't want to get bogged down in that. Just wanted a rough idea.

I appreciate any time and input.
Best Regards,
John
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
There are an insane amount of assumptions to be made here...


(34,000/39,510,000) + (33,999/39,509,999) +,..., (33,990/39,509,990), for probability of an interaction w/ an infected person.

probability of transmission based on data from trial 90% = 1 - 0.1 = (5/1000) / (50/1000), it is a relative measure, and the number of at risk people they would have been exposed to could have been higher than your environment. So you don't even need the CA numbers unless you know the denominator in the VE studies and you are going to reweight the VE estimate based on that.

Given the VE point estimate you are looking at risk of : 0.5% for vaccinated person
5% for unvaccinated person

given CA is similar to the study. Look to literature to see what the risks actually were since 0.1% and 1% would also get you a 90% VE. Relative measures are trick to apply unless you know the prevalences per treatment arm.
 
#3
Thanks for the input! And I understand the assumptions are large and basic, and there's a high probability that I have no idea what I'm talking about and will get the terms wrong. My thinking was to first determine the likelihood of running into an infected person, as you did. If I'm understanding the formula correctly, we'd be looking (given 10 people) at a 0.86% chance of running into an infected person on any given day. What I don't know, given a 90% efficacy rate, how do I convert/combine that into a total odds of contracting the virus on any given day. Assuming that's even possible.
 
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#4
I would think the chances of catching covid are tied to how many have it and can still spread it. Not how many got it in a specific time frame, unless you are assuming those are the only ones to spread it. The probability of catching it is not likely to be known. You would have to know how many actually had it, not how many were detected. And how likely you were to come in contact with them in cases where you could catch it.

Given what we know the rates for most, if unknowable, are probably not high.
 

hlsmith

Less is more. Stay pure. Stay poor.
#5
The VE part would be too difficult to incorporate, since variants are now prevalent, we don't know the actions of people in the studies (beyond assumed being typical), and the community exposures would have been different for them. What would need to be known is some type of almost lab data saying what the probability of infection in an average vaccinated person is when directly exposed to an average SARS-CoV-2 infected person. If you had that, then you could add it to the contact data.

I don't think most people get that the VE values are a relative estimate between the groups and actually reflects moderation to severe symptoms and likely misses asymptomatic infections as well.
 

fed2

Active Member
#6
Yes I think noetsi and hlsmith are right the the VE is a relative risk: it doesn't say what the actual risk is, just relative to placebo. Also I don't know that it really says anything about per contact transmission probabilities, that requires certain data that I think is not collected in most of the trials, in my 30 second appraisal of them. You probably need to look up the 'transmission probability'. Actually those experiments can lead to some interesting stats in their own right.
 
#7
Reality can be interesting. The New England Journal of Medicine did at article stating that the Moderna vaccine lasted six months. I heard news cast the other day built on that which stated the protection only lasted six months and then went away. Which is not what the article says I think, although I don't get the journal.
 
#8
The question came from a debate with a colleague, and from listening to some politicians and "scientists" talking about continuing to require mask wearing even after being fully vaccinated. The governor of CA is saying after June 15th (our current "back to business" date) we will still have mandatory mask requirements, even for the fully vaccinated. Again, not being political. Trying to be rational and scientific. When I play with the numbers in my head, I really can't see the rationalization for that.

By June 15th, pretty much anyone who wants to be vaccinated, will be. I've heard different number, but herd immunity is hit somewhere between 60-70% of the population. If you look at the case numbers now, 2 months out, they are dropping exponentially. So between all the people who'll have been vaccinated and the people who've had it and recovered, by June 15th what are the odds of even running into a person with COVID, let alone catching it after you've been fully vaccinated? It has to be extraordinarily infinitesimal. I was trying to see if I could come up with some actual number, but I lack the skill.
 
#9
The numbers I have heard for herd immunity is more in the order of 80-90 % but misses a key point. The vaccine will not stop people from getting covid19 apparently. It will make the cases mild since the body has the antibodies. But the disease can still be passed on which is the reason for the mandate. I think that gets missed in discussions of the vaccine.

People think you can not get COVID with the vaccine, but you can. At some point, in theory but probably not for real, herd immunity will eliminate the disease. The problem with that theory is that it can still survive in those not vaccinated and from outside the US.
 
#10
Well, I think that's the what the efficacy rate is for. That's why it's said to be only 95% effective. In the test group 5% of the vaccinated still got it. At least that's my understanding. So I would assume those 5% can still pass it on. It is 100% effective against death. I don't think the goal is, nor should it be, no one ever gets sick. It doesn't appear eradication is possible, especially with the variants. Just like with the flu. But again, the odds of running into a COVID infected person in public and being that 5% that can get it seems extremely low.
 
#11
The problem with incorrect science (from the NY Times today)

“This should be the end of deep cleaning,” Allen said, noting that the misplaced focus on surfaces has had real costs. “It has led to closed playgrounds, it has led to taking nets off basketball courts, it has led to quarantining books in the library. It has led to entire missed school days for deep cleaning. It has led to not being able to share a pencil. So that’s all that hygiene theater, and it’s a direct result of not properly classifying surface transmission as low risk.”

https://news.yahoo.com/era-overzealous-cleaning-finally-come-120654927.html

A worse problem is people lose faith in scientist. Which many already hold in low regard.
 
#12
Well, I think that's the what the efficacy rate is for. That's why it's said to be only 95% effective. In the test group 5% of the vaccinated still got it. At least that's my understanding. So I would assume those 5% can still pass it on. It is 100% effective against death. I don't think the goal is, nor should it be, no one ever gets sick. It doesn't appear eradication is possible, especially with the variants. Just like with the flu. But again, the odds of running into a COVID infected person in public and being that 5% that can get it seems extremely low.
I think everyone can still pass it on not a small number.
 

hlsmith

Less is more. Stay pure. Stay poor.
#13
Reality can be interesting. The New England Journal of Medicine did at article stating that the Moderna vaccine lasted six months. I heard news cast the other day built on that which stated the protection only lasted six months and then went away. Which is not what the article says I think, although I don't get the journal.
Next Tuesday I will start modeling the antibody data I have. I believe starting around three months after infection people dip below the positive threshold which was established awhile back and never really tested on infected patients months out. So you are still making the antibodies (IgGs), but they wane with time. However the immune system is badass and has other weapons in its arsenal like to cells.
 
#14
So is the vaccine only useful for six months hlsmith? If the immune system dealt with covid we would not need a vaccine would we?

I suspect you mean t cells not to cells
 

hlsmith

Less is more. Stay pure. Stay poor.
#15
The problem with incorrect science (from the NY Times today)

“This should be the end of deep cleaning,” Allen said, noting that the misplaced focus on surfaces has had real costs. “It has led to closed playgrounds, it has led to taking nets off basketball courts, it has led to quarantining books in the library. It has led to entire missed school days for deep cleaning. It has led to not being able to share a pencil. So that’s all that hygiene theater, and it’s a direct result of not properly classifying surface transmission as low risk.”

https://news.yahoo.com/era-overzealous-cleaning-finally-come-120654927.html

A worse problem is people lose faith in scientist. Which many already hold in low regard.

Aerosalized transmission is the treat. Idiots at my gym have never worn masks. I have been fully vaccinated for months and always wear my mask, part of the 3% that do. Though these idiots all of a sudden wipe the machines down, which wouldNt be such an issue if you wore a mask and balked droplets. I typically don't put my hands in my offices at the gym making wiping down machines instead of wearing a mask even stupider preference.
 

hlsmith

Less is more. Stay pure. Stay poor.
#16
T cells, yes. I'll update duration next week, but someone could have 95% lower antibody response hypothetically, though what is the true threshold for not being able to combat exposure. UNKNOWN.