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Two major challenges in statistical methods for biomedical imaging data are dimension reduction and the mitigation of nuisance variable associations. For instance, in neuroimaging research, a primary goal is to identify patterns in the brain attributable to a disease but not to motion in the scanner.
Recent methods have proposed simple modifications to principal component analysis (PCA) to simultaneously address dimension reduction and nuisance variable adjustment. While such methods may perform well in-sample, their generalizability is limited when applying the rotations obtained from PCA in one sample to a new sample where the distribution of the nuisance variables and other features may have changed.
We propose a generalizable two-stage PCA method involving stratification by nuisance variables. We demonstrate in imaging data that nuisance variable associations with the first few principal components may be substantially reduced when using our method, compared to conventional PCA and other previously proposed methods.
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