# Matrix Linear Models for Connecting Metabolite Composition to Individual Characteristics

## TL;DR

This paper introduces a new statistical method to analyze how metabolite levels relate to individual traits, using a flexible framework that integrates biological knowledge.

## Contribution

The novelty is a unified bilinear matrix linear model (MLM) that combines association and enrichment analysis in metabolomics.

## Key findings

- The MLM approach effectively integrates metabolite characteristics with individual traits in a single step.
- The method successfully disentangles overlapping triglyceride features like double bonds and carbon atoms.
- The approach is demonstrated on three metabolomic studies, showing flexibility and interoperability.

## Abstract

Background/Objectives: High-throughput metabolomics data provide a detailed molecular window into biological processes. We consider the problem of assessing how association of metabolite levels with individual (sample) characteristics, such as sex or treatment, depend on metabolite characteristics such as pathways. Typically, this is done using a two-step process. In the first step, we assess the association of each metabolite with individual characteristics. In the second step, an enrichment analysis is performed by metabolite characteristics. Methods: We combine the two steps using a bilinear model based on the matrix linear model (MLM) framework previously developed for high-throughput genetic screens. Our method can estimate relationships in metabolites sharing known characteristics, whether categorical (such as type of lipid or pathway) or numerical (such as number of double bonds in triglycerides). Results: We demonstrate the flexibility and interoperability of MLMs by applying them to three metabolomic studies. We show that our approach can separate the contribution of the overlapping triglyceride characteristics, such as the number of double bonds and the number of carbon atoms. Conclusion: The matrix linear model offers a flexible, efficient, and interpretable framework for integrating external information and examining complex relationships in metabolomics data. Our method has been implemented in the open-source Julia package, MatrixLM. Data analysis scripts with example data analyses are also available.