I have a waveform, for which most people will measure either a peak amplitude or a slope. I have included the area under the curve and several other measures involving the same original waveform. I now have 10 measures on such waveforms (and I have measured these waveforms in 500 patients). Is it legitimate to put all these measures side by side in one big principal component analysis (PCA) to distil a smaller set of principal components. My worry is about the fact that some of the measures are inherently interdependent (for example, peak amplitude will be inherently correlated with area under the curve), so I was afraid it might fail to meet some of the assumptions behind PCA, such as independence of measures. Is there another analysis method I should use instead of PCA? Independent Component Analysis? Another multi-dimensional scaling method? Cluster analysis? Thanks very much!
A bit more detail: In my case, I have made 9 raw measures, x1 .. x9, in each patient. I already know that x2 and x4 are highly correlated, but their difference has important prognostic implications. On one hand, I am afraid PCA would fail to note this difference (because x2 and x4 are so correlated), so I would like to include x2-x4 as a 10th measure. However, I am bothered by the fact that I am thus introducing trivial correlation, which will inflate the importance of x2 and x4 and any noise in them. Thanks again.