Abstract
Longitudinal intervention studies with repeated measurements over time are an important type of experimental design in biomedical research. Due to the advent of “omics”-sciences (genomics, transcriptomics, proteomics, metabolomics), longitudinal studies generate increasingly multivariate outcome data. Analysis of such data must take both the longitudinal intervention structure and multivariate nature of the data into account. The ASCA+-framework combines general linear models with principal component analysis and can be used to separate and visualize the multivariate effect of different experimental factors. However, this methodology has not yet been developed for the more complex designs often found in longitudinal intervention studies, which may be unbalanced, involve randomized interventions, and have substantial missing data. Here we describe a new methodology, repeated measures ASCA+ (RM-ASCA+), and show how it can be used to model metabolic changes over time, and compare metabolic changes between groups, in both randomized and non-randomized intervention studies. Tools for both visualization and model validation are discussed. This approach can facilitate easier interpretation of data from longitudinal clinical trials with multivariate outcomes.
Highlights
In recent decades, scientific and technological developments have increased our ability to both collect and manage large amounts of data
A subset of the methods developed to analyze such data are based on the idea of combining two different kinds of statistical methods: 1) analysis of variance (ANOVA), and 2) dimensionality reduction methods such as principal component analysis (PCA) [1]. Combining these methods in various ways allows the researcher to separate and visualize effects from different sources of variation in the data, while accounting for the correlations between the outcome variables. One such method is ANOVA simultaneous component analysis (ASCA), where the response matrix is first decomposed into effect matrices according to the experimental design, and the impact of each experimental factor is visualized by applying PCA to the effect matrices [2]
This methodology has since been extended to unbalanced designs by the adoption of the general linear model (GLM)-framework in estimating the effects, in a method called ASCA+ [3]
Summary
Scientific and technological developments have increased our ability to both collect and manage large amounts of data. A subset of the methods developed to analyze such data are based on the idea of combining two different kinds of statistical methods: 1) analysis of variance (ANOVA), and 2) dimensionality reduction methods such as principal component analysis (PCA) [1] Combining these methods in various ways allows the researcher to separate and visualize effects from different sources of variation in the data, while accounting for the correlations between the outcome variables. One such method is ANOVA simultaneous component analysis (ASCA), where the response matrix is first decomposed into effect matrices according to the experimental design, and the impact of each experimental factor is visualized by applying PCA to the effect matrices [2]. A related approach was recently developed, termed linear mixed modelPCA (LiMM-PCA), in which the ASCA+ methodology is adapted to include random effects [4]
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