In order to take into account the complex structure of repeated measurements from different assays where different treatments are applied on the same subjects, we developed a multilevel multivariate approach combined with our PLS models to highlight the treatment effects within subject separately from the biological variation between subjects (collaboration with A/Prof. B. Liquet).
Two different frameworks are proposed:
1. A discriminant analysis (method = ‘splsda’) enables the selection of features separating the different treatments
2. An integrative analysis (method = ‘spls’) enables the interaction of two matched data sets and the selection of subsets of correlated variables (positively or negatively) across the samples. The approach is unsupervised: no prior knowledge about the samples groups is included.
The multilevel function first decomposes the variance in the data sets X (and Y for sPLS) and applies either sPLS-DA or sPLS on the within-subject variation matrix (see Westerhuis et al. 2010; Liquet et al, 2012). One- or two-factor analyses are available for sPLS-DA. A two factor analysis include two factors that are repeated for the same samples (see below and our case studies).