Exploring Omics data from designed experiments using analysis of variance multiblock Orthogonal Partial Least Squares.

Many experimental factors may have an impact on chemical or biological systems. A thorough investigation of the potential effects and interactions between the factors is made possible by rationally planning the trials using systematic procedures, i.e. design of experiments. However, assessing factors' influences remains often a challenging task when dealing with hundreds to thousands of correlated variables, whereas only a limited number of samples is available. In that context, most of the existing strategies involve the ANOVA-based partitioning of sources of variation and the separate analysis of ANOVA submatrices using multivariate methods, to account for both the intrinsic characteristics of the data and the study design. However, these approaches lack the ability to summarise the data using a single model and remain somewhat limited for detecting and interpreting subtle perturbations hidden in complex Omics datasets. In the present work, a supervised multiblock algorithm based on the Orthogonal Partial Least Squares (OPLS) framework, is proposed for the joint analysis of ANOVA submatrices. This strategy has several advantages: (i) the evaluation of a unique multiblock model accounting for all sources of variation; (ii) the computation of a robust estimator (goodness of fit) for assessing the ANOVA decomposition reliability; (iii) the investigation of an effect-to-residuals ratio to quickly evaluate the relative importance of each effect and (iv) an easy interpretation of the model with appropriate outputs. Case studies from metabolomics and transcriptomics, highlighting the ability of the method to handle Omics data obtained from fixed-effects full factorial designs, are proposed for illustration purposes. Signal variations are easily related to main effects or interaction terms, while relevant biochemical information can be derived from the models.