parafac4microbiome: exploratory analysis of longitudinal microbiome data using parallel factor analysis

Studies investigating microbial temporal dynamics are increasingly common, leveraging longitudinal designs that collect microbial abundance data across multiple time points from the same subjects. Traditional exploratory approaches like principal component analysis fail to fully utilize this structure. By organizing data as a three-way array-subjects as rows, microbial abundances as columns, and time points as the third dimension-multi-way methods such as parallel factor analysis (PARAFAC) can better capture temporal and structural patterns. This study demonstrates PARAFAC as a method to explore longitudinal microbiome data using three exemplary studies. In the first example, a long-time series of in vitro microbiomes, PARAFAC identifies primary time-resolved variations. The second example, a longitudinal infant gut microbiome study, shows that PARAFAC can distinguish subject groups and enhance comparative analysis, even with moderate missing data. In the third example, a gingivitis intervention study of the oral microbiome, PARAFAC enables the identification of microbial subcommunities of interest through post-hoc clustering. These examples highlight PARAFAC's broad applicability for analyzing longitudinal microbiome data across diverse environments. The approach is implemented in the R package parafac4microbiome, available on the Comprehensive R Archive Network (CRAN), providing researchers with accessible tools for similar analyses.IMPORTANCEUnderstanding how microbiomes change over time can give us valuable insights into their role in health and disease. Many traditional methods like principal component analysis miss important patterns in data collected over time, but parallel factor analysis (PARAFAC) helps uncover these trends in a much clearer way. Using this approach, we were able to identify key changes in microbiomes across different settings, like lab experiments, the infant gut, and the mouth. PARAFAC also works well even when some data is missing, which is a common issue. To make this tool accessible, we have included it in a user-friendly R package, enabling other researchers to analyze microbiome dynamics in their own studies and explore how these changes might influence health and treatments.