A proposal was made to outline principles for evaluating vaccine efficacy. Like how to understand 91% efficiency. I explain. Only you won't like it.
The simplest example is the percentage of vaccine efficacy = 100 * (1- "proportion of cases with vaccine" / "proportion of cases without vaccine"). That is, if 0.5% of the sufferers got sick with the vaccine, and 1% got sick without the vaccine, then the effectiveness of the vaccine will be 50%.
Now about the bad. To illustrate the wildness of the calculations, I had to pull out a netbook with a 1998 statistical program from the closet. It is easy to substitute shares in it and get the result.
So that's it. Usually, when testing a vaccine, they take a crowd of people, divide it approximately in half, vaccinate someone, not vaccinate someone and wait to see what will come of it.
Imagine that in one group of people so many percent fell ill, and in another group - so many percent.
Let's say that there were 20 people in the vaccinated group, and 50% of them got sick, and in the other group there were 30 unvaccinated people, but 90% of them got sick.
Is the vaccine working? And the devil only knows ...
On such a number of people it will not be possible to compare. How so? What's the catch? And these are brothers, statistics. You can't just take two percentages and compare them. There is always a chance to make mistakes and find differences where there are none. According to these initial data, there is no difference between the groups at all.
We need to drive out more people in order to exclude all sorts of random mistakes.
So, to calculate the difference, they take larger groups so as not to be mistaken. And they find a statistically significant difference.
Let's say they drove two groups of 200 people each, vaccinated one group, and it turned out that 90% of this vaccinated group got sick. And in the unvaccinated group, 92% of the people fell ill. The difference of 2% is confirmed by iron. Statistics are good. We got a reliable result.
Will we be vaccinated with such a vaccine? Probably not. Not such a big difference to risk anything. Because of the 2%, no one will start a vaccination campaign. This is another catch.
Typically, the vaccine should reduce the likelihood of getting sick by 50%. That is, roughly speaking, in the group where the people were not vaccinated, 40 people fell ill, and in the group where they were vaccinated - 20. The vaccine was found to be 50% effective. Normul. It suits us. And there were some big groups. Things are good.
But another confidence interval is added.
This is such a dirty trick that evaluates the reliability of the assessment. That is, in statistics, when there are two groups of different people who also die there periodically, you need to assess the reliability of this comparison.
In fact, we cannot say that the vaccine is 50% effective. We estimate efficiency in a certain range.
Even if we calculated everything correctly, we can only be sure that with a probability of 95% our calculation result lies somewhere within the confidence interval.
That is, the effectiveness of the vaccine is not 50%, somewhere hidden in the range from 40% to 60%.
If you look at the results of scientific studies, then there really will be 91% efficiency, but there will still be a confidence interval in parentheses. It means that in the most unfavorable scenario (if people turn out to be clumsy and like all chronicles for selection), then the effectiveness of the vaccine will approach the lower limit of the confidence interval.
People are all different. Statistics (fate) can turn so that in a certain area at a certain time they will gather like on an airplane in that joke, the most notorious pessimists and losers who have nothing acts.
So for such losers, the lower limit of the confidence interval should be at least 30%. That is, if the dudes are not lucky, then a new experimental vaccine must be at least 30% effective. Otherwise, it was not worth breeding this whole badag with a new vaccine.
This is not some fantastic situation. When the South African mutant viruses appeared, the effectiveness of the available vaccines fell to those barely acceptable limits. But for now, the vaccines are holding on.
Available?
Taking this opportunity, I congratulate the defenders on behalf of the lieutenant of the reserve medical service!
