You have to be careful how you read that. The researchers did not find that the shingles vaccine does not protect men (from dementia caused by Alzheimer's). They failed to find statistically significant evidence, in their studied population, that the vaccine protects men.
As the preceding sentence says, this can be plausibly explained by the fact that shingles is more common in women, so whatever protective effect the vaccine has is larger and more measurable.
It could also be that there is a potential effect that this study would have been underpowered to detect, and by chance no trend was visible in this population. That's not inconsistent, or even particularly unlikely, if I'm understanding it right.
(A) To suggest that the lack of effect in men is a statistical anomaly, and that there IS an effect we're not seeing.
(B) To suggest that the effect in women is a statistical anomaly, and that there's nothing there but a fluke.
These things, from the data, are approximately equally likely. Because there was zero effect in men -- in fact, men who took the vaccine were apparently more likely to be diagnosed with Alzheimer's, though this trend was extremely slight.
> 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.)
> 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.
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?
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.
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.)
As the preceding sentence says, this can be plausibly explained by the fact that shingles is more common in women, so whatever protective effect the vaccine has is larger and more measurable.