I'm newbie to multivariate analysis and working on a project where I'm interested in the strength of association between two pathways (proteomic data). Abstractly speaking, each pathway is represented by a collection of k variables (protein expression levels). For example: pathway A comprises 3 proteins (measured for 100 subjects), and the pathway B comprises 5 proteins (measured for the same subjects). So, I need to compute 'correlation' between two matrices 100x3 and 100x5.

QUESTION How to compute correlation in this case? The naive way is to compute pair-wise correlation and then pool them somehow or via canonical correlation analysis.

Any other ideas?

  • $\begingroup$ Usually you have random variables, from which you calculate the correlation. Maybe I know too little about pathway analysis. To me it seems that you have 100 2D random variables. If you want to determine the correlation between the individual components (A and B), then you'd take these. In a scatter plot, plotting A vs B you'd directly see the covariance. Am I missing something? $\endgroup$ – cherub May 31 '18 at 14:37
  • $\begingroup$ Thanks for suggestion, I’ll do the scatter plot. The main question how would you summarise the pair wise correlation in a single metric (number)? $\endgroup$ – Arnold Klein May 31 '18 at 17:05

The only way to compute the correlation between two matrices is to use canonical correlation analysis. However you could compare the RV coefficient (I made a post about how to calculate it), which is a measure of the correlation in a matrix.

However you could use the GSVA method to transform your data to have a score for each pathway and then calculate the correlation with these transformed values.

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