I am working on a microarray dataset with n samples x m genes, with metadata including a grouping of interest and other summary statistics, e.g. age, bmi. My objective is to find genes that may be related to my grouping of interest (cancer vs. control).
My question is: would it be valid to conduct PCA on the dataset and then correlating/testing each PC with my grouping of interest and other metadata to determine whether any of them are related to a PC?
Then, if I do find a PC that is significantly associated with my grouping, would it be valid to take the eigenvectors (the V matrix in SVD) of that PC sorted from greatest to smallest (absolute values) to determine the genes that may be driving that PC and therefore related to my metadata of interest?