MultANOVA Followed by Post Hoc Analyses for Designed High-Dimensional Data: A Comprehensive Framework That Outperforms ASCA, rMANOVA, and VASCA

Abstract

Analytical platforms generate high-dimensional data, where the number of variables usually exceeds the number of observations. Such data are frequently derived from an experimental design, where samples have been collected to identify potential variation in the factors or interactions of interest. To circumvent issues related to large data sizes when evaluating factor and interaction effects, ANOVA simultaneous component analysis (ASCA), regularized multivariate analysis of variance (rMANOVA), and variable selection ASCA (VASCA) have been proposed previously. However, they require computationally intensive methods to test the effects of factors and interactions. In the present paper, multiple ANOVAs (MultANOVA) is proposed as a simple yet effective alternative to the above methods. MultANOVA has the advantage of being direct and fast, as it does not rely on intensive calculation methods, while incorporating a variable selection strategy. This method entails the execution of multiple ANOVAs, one per variable, with multiple test corrections. Subsequent post hoc analyses are also introduced. These encompass multiple least-squares difference tests (MultLSD) for the pairwise comparison of multivariate least-squares means and diagonal canonical discriminant analysis (DCDA) with approximate confidence ellipses to visualize significant effects. MultANOVA is compared to the aforementioned methods based on simulations, which demonstrate that it holds the nominal alpha risk as opposed to rMANOVA and VASCA, while being more powerful than ASCA and VASCA. Even though MultANOVA is proven less powerful than VASCA for variable selection, it has been demonstrated to hold the nominal risk, whereas VASCA does not. Finally, the MultANOVA framework is illustrated based on metagenomics, metabolomics, and spectroscopic data.