It seems to me that methods such as CCA and PCA belong more in the category of exploratory methods akin to data visualization, and that they cannot be viewed as methods “to find out or learn with certainty” [1]. Given this, questions of power might create distractions from the scientific opportunities.
If this is a study in your field of post-ICU cognitive decline, then are there any psychometric theories you can avail yourself of, to posit some latent factors and their nomological connections?