Covid vaccines: how effective? Variants, duration of immunity, efficacy on contamination and on severe cases?

[Janic]

brilliant demonstration useless for a guy who is not screwed to analyze real stats already carried out for a century and more on the corresponding diseases and vaccinations. There, hop, the boast is gone!

[ABC2019]

brilliant demonstration useless for a guy who is not screwed to analyze real stats already carried out for a century and more on the corresponding diseases and vaccinations. There, hop, the boast is gone!

always in shape in the morning, big fool

[Janic]

always in shape in the morning, big fool

always so bad in science, the pseudo scientist of operetta!

[ABC2019]

always in shape in the morning, big fool

always so bad in science, the pseudo scientist of operetta!

owiii ... again ... sir the great scientist ...

[Christophe]

Go some math for those who like ...

Let there be two possible characteristics A and B in a population N.

The probability of having both A and B can be calculated in two equivalent ways
* either we say that we must have A (probability p (A)), but also B knowing that we have A (probability noted p (B | A), probability of B knowing that A, therefore calculated in the subpopulation restricted to those who are A)

total probability p (A) p (B | A)

* or the reverse, we say that we must have B, but also A knowing that B is symmetrical

probability p (B) p (A | B)

the two are equal, it is p (A and B) = N (A and B) / N, and so we have

p (A) p (B | A) = p (B) p (A | B)

and we obtain the fundamental formula called "Bayes formula"
p (B | A) = p (B) p (A | B) / p (A)

which is widely used in a whole sector of probabilities, Bayesian probabilities, which aim to answer questions like: knowing that A has a probability p1 of occurring in hypothesis B, and p2 in hypothesis not B, what is the probability that B is true if I observe A (an absolutely central question, most discussions on this forum can fit into this framework).


Let's apply here to A = to be vaccinated and B = to be infected

The probability of being infected when vaccinated , is equal to the probability of being vaccinated when you are infected , multiplied by the ratio of the odds of being infected over the odds of being vaccinated.

It is this factor that is forgotten when we confuse the two: the proportion of vaccinated among the infected, and the proportion of infected among the vaccinated.

We can write the same relation for the unvaccinated (non A)

p (B | not A) = p (B) p (not A | B) / p (not A)

by dividing one by the other, we can assess the ratio between the probability of being infected when we are vaccinated, to the probability of being infected when we are not vaccinated, which is the thing that really interests us (l vaccine efficacy)

p (B | A) / p (B | not A) = p (A | B) / p (not A | B) * p (not A) / p (A)

Who says that the ratio of the probabilities of being infected when one is vaccinated, compared to unvaccinated, is equal to the ratio of the number of vaccinated to the unvaccinated in infected , multiplied by the ratio of the proportion of unvaccinated to the proportion of vaccinated in the population.

Once again it is this ratio of the number of vaccinated to the number of unvaccinated in the population which is forgotten and which must be taken into account when looking at the number of vaccinated among the infected.

this ratio varies quite rapidly with the proportion of vaccinated. With 50% vaccinated, it is 1, so it does not change the result. With 60% of vaccinated, it is 60/40 = 1,5, and with 90% of vaccinated, it takes 90/10 = 9

the re-evaluation is all the more spectacular as one approaches 100%, it becomes "infinite" at 100% since of course there are zero unvaccinated infected. All the "spectacular" examples take well on high rates of vaccination (but if it is only 50% the factor does not play any more, and below 50%, it acts in the opposite direction)

Strangely, the consequence is that the best case for evaluating vaccine effectiveness is to look at the proportion of vaccinated among the contaminated, not when everyone is vaccinated, but when only 50% are vaccinated (because there the two populations are equal) !!!

Well it is of course the same result as Christophe but put in a simple form: to have the vaccine effectiveness, it is necessary to make the relation between the proportion of vaccinated by the unvaccinated in the sick, but correct by the ratio of the non vaccinated over those vaccinated in the total population.

NB: I calculate the ratio r of the probabilities of being infected depending on whether we are vaccinated or not, but this ratio is equal to 1 when the probabilities are equal, therefore when the vaccine efficacy is "zero". The vaccine efficacy is rather 1 - r: if r = 1, the efficacy is zero, if r = 1/10, it is 90%. If r> 1, the efficacy is negative, i.e. the probability of being infected is greater if you are vaccinated than if you are not vaccinated.)

What blah blah for the wind ... you too are afraid to show with your finger the real effectiveness of the vaccine in the field on my curves yesterday?

[Janic]

christophe

What blah blah for the wind ... you too are afraid to show with your finger the real effectiveness of the vaccine in the field on my curves yesterday?

absolutely! His little passing game works with black pebbles and white ones! But it no longer works in the living where, as he says elsewhere, it is much more complex than this little stupid game there!

[Janic]

always so bad in science, the pseudo scientist of operetta!

: Arrowd:
owiii ... again ... sir the great scientist

Since you recognize him, I will not upset you. But that's right, better to be a great scientist (thanks for the highly deserved compliment) than a boastful pseudoscientist dwarf who doesn't give a damn about analyzing real stats! and no one in French!

[ABC2019]

What blah blah for the wind ... you too are afraid to show with your finger the real effectiveness of the vaccine in the field on my curves yesterday?

I give the rigorous theory which makes it possible to understand what must be done to deduce the real effectiveness of the vaccine - I have not checked but to the eye your curves are correct and simply reproduce the above formula, quite simple to apply.

now to answer your question, you have to know the real proportion of vaccinated, with the caveats that I mentioned, is that all this supposes that there are only two categories between vaccinated and unvaccinated, then that the effectiveness of the vaccination varies in fact continuously according to the number of injections and the time after the injection, it reaches a maximum and then decreases again. So talking about "the real effectiveness of the vaccine" is not that simple.

[ABC2019]

Since you recognize him, I will not upset you. But that's right, better to be a great scientist ...

oh yes, I thought you didn't believe in science ...

and apart from you then, who is it that you consider to be "great scientists"?

[Janic]

by ABC2019 "01/07/21, 11:24

Janic wrote:
Since you recognize him, I will not upset you. But that's right, better to be a great scientist ...

oh yes, I thought you didn't believe in science ...

you believe that I believe even if I don't believe what you believe; is that what you mean?

and apart from you then, who is it that you consider to be "great scientists"?

if I were a narcissist like you, I would say me, me and me again. It's what you think about yourself! and so:
better be a great scientist (thanks for the highly deserved compliment) that a boastful pseudoscientist dwarf not fucked up analyzing real stats! and archi null in French!