Menopausal hormone therapy and dementia: nationwide, nested case-control study

The paper notes that further research is needed on whether there is any causative link, or merely correlation:

"Further studies are warranted to determine whether these findings represent an actual effect of menopausal hormone therapy on dementia risk, or whether they reflect an underlying predisposition in women in need of these treatments."

It's not unreasonable to suppose that women who go to the trouble of getting hormone therapy have other conditions, or are experiencing unusually acute effects of aging.

An interesting followup would include a pharmacology component.

Estrogen has numerous routes of administration: intramuscular, oral, topical, sublingual, and even subcutaneous. Each of these will have various pharmacokinetics, some of which include supernatural serum levels.

This is why serum testing is done midway through routes of application that are cyclical. ie to test at the midpoint.

It would be entirely unsurprising if brief though still supernatural levels had an etiological contribution.