Utilities for quantifying separation in PCA/PLS-DA scores plots

Abstract

Metabolic fingerprinting studies rely on interpretations drawn from low-dimensional representations of spectral data generated by methods of multivariate analysis such as principal components analysis and projection to latent structures discriminant analysis. The growth of metabolic fingerprinting and chemometric analyses involving these low-dimensional scores plots necessitates the use of quantitative statistical measures to describe significant differences between experimental groups. Our updated version of the PCAtoTree software provides methods to reliably visualize and quantify separations in scores plots through dendrograms employing both nonparametric and parametric hypothesis testing to assess node significance, as well as scores plots identifying 95% confidence ellipsoids for all experimental groups.

Figure 1

(a) 2D OPLS-DA scores plot illustrating 95% confidence ellipses for data having one predictive and one orthogonal PLS component. The symbol shape and color of each point correspond to the groups in Figure 2. Discrimination in the first component is between wild-type and antibiotic-treated Mycobacterium smegmatis, and separations along the second component indicate metabolic differences between various antibiotic treatments. The antibiotics cluster together based on a shared biological target (cell wall synthesis, mycolic acid biosynthesis, or transcription, translation and DNA supercoiling). Three compounds of unknown in vivo activity were shown to cluster together with inhibitors of cell wall synthesis inferring a potential biological target. Interestingly, the M. smegmatis strain is resistant to ampicillin resulting in the ampicillin-treated cells clustering closer to untreated cells. (b) 3D PCA scores plot with superimposed 95% confidence ellipsoids drawn as meshes containing group points. The ellipses and ellipsoids define the statistical significance of class separation and provide an illustration where two groups actually belong to the same biological classification. Group ‘SN’ refers to mock-transfected pancreatic cancer cells grown as a control group, while ‘SM’ refers to MUC1-overexpressing pancreatic cancer cells. Separations in scores space relate to metabolic differences in pancreatic cancer due to MUC1 overexpression.

Figure 2

(a) Dendrogram generated using Euclidean distances between group means from the OPLS-DA scores in Figure 1(a). Bootstrap statistics reported at each branch are for 5,000 bootstrap iterations. (b) Dendrogram generated from identical scores using Mahalanobis distances, with p -values for the null hypothesis reported at each branch.