High-dimensional Statistics Applications to Batch Effects in Metabolomics

Batch effects are inevitable in large-scale metabolomics. Prior to formal data analysis, batch effect correction (BEC) is applied to prevent from obscuring biological variations, and batch effect evaluation (BEE) is used for correction assessment. However, existing BEE algorithms neglect covariances between the variables, and existing BEC algorithms might fail to adequately correct the covariances. Therefore, we resort to recent advancements in high-dimensional statistics, and respectively propose "quality control-based simultaneous tests (QC-ST)" and "covariance correction (CoCo)". Validated by the simulation data, QC-ST can simultaneously detect the statistical significance of QC samples' mean vectors and covariance matrices across different batches, and has a satisfactory statistical performance in empirical sizes, empirical powers, and computational speed. Then, we apply four QC-based BEC algorithms to two large cohort datasets, and find that extreme gradient boost (XGBoost) performs best in relative standard deviation (RSD) and dispersion-ratio (D-ratio). After prepositive BEC, if QC-ST still suggests that batch effects between some two batches are significant, CoCo should be implemented. And after CoCo (if necessary), the four metrics (i.e., RSD, D-ratio, classification performance, and QC-ST) might be further improved. In summary, under the guidance of QC-ST, we can develop a matching strategy to integrate multiple BEC algorithms more rationally and flexibly, and minimize batch effects for reliable biological conclusions.