That’s what this article by Wang et al suggests. Quantitatively, they found that:

- In CSF tau-positive individuals (i.e. those with >= 500 pg/mL; ~ 1/4 of the total cohort), CSF tau correlates positively with AD-like cortical thinning, explaining 15% of the variance after covariate correction, under their model, whereas amyloid beta has no significant association.
- In CSF amyloid-positive individuals (i.e. those with >= 500 pg/mL; ~ 1/2 of the total cohort), CSF amyloid levels correlates positively with hippocampal volume [1], explaining 7% of the total variance after covariate correction, under their model, whereas now tau has no significant association.

[1]: This direction makes sense: *low *amyloid CSF levels correlate with higher brain amyloid lesions.