this isn't necessarily true. if the study had 1000 women and 100 men, it would be a lot more likely that the result in men was wrong. similarly, if the effect was 20x weaker in men than women, but still existed you would be much more likely to see no effect in men even though effects existed for both.

Not necessarily true in a theoretical sense, sure.

But there's absolutely no indication that they enrolled 10x (or even 2x) more women than men. Nor is there any indication of any effect in men, 20x weaker or otherwise. (If we're charitable, it's pretty much a flat zero.)

Total study size was 282,541 people, 128,322 men and 154,218 women.

From supplementary material 1, page 27: https://www.medrxiv.org/content/10.1101/2023.05.23.23290253v...

> These things, from the data, are approximately equally likely.

They aren't. The paper states that 95% confidence interval for men includes a maximum protective effect of up to -1.9 while the 95% confidence for women include a minimum effect of -1.3.

Thus it is far more likely that there is a protective effect for man than no protective effect for women.

Are you ignoring the fact that it might have a negative effect, rather than a protective effect?

The range for men is -1.9 to +2.1 -- which averages out to +0.2 -- which indeed makes it seem as though the vaccine's trend is to make one slightly more susceptible to Alzheimer's, rather than less susceptible, which is itself borne out in the figure's trend line. (Fig 4.)

For women it's -5.3 to -1.3.

Doesn't this mean that the chance of a true but unobserved -1.9 magnitude effect in men is much greater than the chance of a true but unobserved +0.0 magnitude effect in women?

Sure, but, by the same token, it also means that there's a chance of a true but unobserved +2 magnitude effect in men.

That means there's a decent chance that the real effect in men is in the range e.g. [-1.9, -1.0] but this study was unlucky or underpowered in men to see that effect.

>Are you ignoring the fact that it might have a negative effect, rather than a protective effect?

Nope. We can be 95% confident that there is an effect for women but we can't be 95% certain that there is no effect for men.

Given that the error ranges overlap, we don't even have a high level of certainty that the effect for men doesn't equal the effect for women.

> The range for men is -1.9 to +2.1 -- which averages out to +0.2

Technically it averages out as +0.1

> we can't be 95% certain that there is no effect for men.

They're at P=0.93 right now. So they're very close.

Whereas, for women, P=0.0013.

Taking everything into consideration, that's exactly what I'd call "a high level of certainty that the effect for men doesn't equal the effect for women."

> They're at P=0.93 right now. So they're very close.

A big P value is bad.

> that's exactly what I'd call "a high level of certainty that the effect for men doesn't equal the effect for women."

Then you are operating off a non-standard cutoff for certainty because the paper explicitly states that the difference between the effect on male vs female is only statistically significant for the sub category of Alzheimer's.