OAC-PCA: orthogonal adjustment of confounding effects in principal component analysis for metabolomics data mining

Principal component analysis (PCA) is widely used in mass spectrometry-based metabolomics for exploratory data mining. Statistical testing of loading values can extract metabolite features associated with score patterns, but this approach requires principal components (PCs) to remain orthogonal while loadings are defined as correlation coefficients between PC scores and variables. Adjustment for Confounding PCA (AC-PCA) was previously developed to explore biologically meaningful components from data matrices affected by biological and technical confounders. However, AC-PCA does not simultaneously ensure PC orthogonality and a correlation-coefficient definition of loadings, limiting the statistical interpretation of its loadings. Here, we reformulated AC-PCA as Orthogonal Adjustment for Confounding effects in PCA (OAC-PCA). In OAC-PCA, PCs remain orthogonal, and loadings retain this correlation-coefficient interpretation. These properties enable statistical testing of metabolite associations while accounting for confounding effects.