Note that the regression they did weighed birthweeks closer to the cutoff point more heavily. That's the grey shading of the dots in the figures above. It looks like past about [edit: two years] on either side, there was very little weight given to the data points. They did this because the further apart people are in time of birth in the two groups, the more confounders you'd expect that could skew the analysis.
The main thing of interest is how suddenly the probability of dementia drops for people born directly after the cutoff. I'd expect it to be more gradual if it was due to something like the Great Depression, which didn't have a hard cutoff.
If there was confounding, which I think is possible, I think it'd be related to education. Starting school a year later is the only relevant event I know of, apart from vaccination, that was a major difference in life events between people born directly on either side of that birthdate cutoff.
Someone's comment on
Pubpeer noted a potential interesting detail about the groups being in different school years:
Another thing that ChatGPT suggested to me when I was trying to get it to suggest confounders is related to school year and World War II.
It said that schooling begins at age 5 in Wales, which
seems right. So children born in the weeks before September 1933 would have been 5 before September 1, 1938 and would have entered school that year. Children born in the weeks after, would have entered school a year later, at the end of 1939. Notably,
World War II started September 1, 1939.
Is there a reason children first starting school immediately at the start of WWII would end up better protected from dementia than children who had already completed a year of school? I'm not sure what the connection would be.