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I don't think it insinuates a causal relationship.

I interpret "30% more likely" as the same as "associated with a 30% increase," which is what the article claims.

I would say that "People who do X are 30% more likely to get X" is commonly understood to imply causation.

How would you phrase it? Because I did not read that as meaning that less sleep caused dementia.

"is associated with" is a much more neutral phrasing. The phrasing did not denote causality but does imply it to a casual reader.