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Matrix Linear Models: an application to a metabolomic study

Gregory Farage1, Timothy J. Garrett2, Michelle A. Puchowicz3, Qingming Dong4, Christopher J. Cieker4, Dale Childress5, Edwards A. Park4, Claire L. Simpson6, Rajendra Raghow4, Marshall B. Elam4, 5, Śaunak Sen1

1Department of Preventive Medicine, College of Medicine, University of Tennessee Health Science Center, Memphis, TN
2Department of Pathology, Immunology and Laboratory Medicine, University of Florida Health, Gainesville, FL
3Department of Pediatrics, College of Medicine, University of Tennessee Health Science Center, Memphis, TN
4Department of Pharmacology, College of Medicine, University of Tennessee Health Science Center, Memphis, TN
5Department of Medicine, College of Medicine, University of Tennessee Health Science Center, Memphis, TN
6Department of Genetics, Genomics & Informatics, College of Medicine, University of Tennessee Health Science Center, Memphis, TN

Abstract

High-throughput omics data provide a detailed molecular window into biological processes, but extracting information remains a significant challenge. Integrating multimodal data sources improves interpretation compared to analyzing just one source. We used metabolite attributes to shed light on how the metabolome differs in patients with and without statin-associated muscle symptoms (SAMS). A confounding factor in these associations was fish oil supplementation which we adjusted for in our analysis. The Matrix Linear Models (MLMs) framework, which belongs to the bilinear models family, was used to study associations in structured high-throughput data. This framework allows estimating relationships in metabolites sharing established characteristics, whether categorical (e.g., type of metabolites or lipids) or numerical (e.g., number of double bonds in triglycerides). Standard analyses using high-throughput data usually ignore externally-available information about measurement attributes. The MLM method lays out a flexible structure to find the connections between sample characteristics and attributes of measures. This framework can be applied to various studies where attributes of measures are known, such as drug screening of cancer cell lines or eQTL experiments.

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References:

  • Liang, J. W., Nichols, R. J., & Sen, Ś. (2019). Matrix linear models for high-throughput chemical genetic screens. Genetics, 212(4), 1063–1073. doi: 10.1534/genetics.119.302299.
  • Liang, J. W. & Sen, Ś. (2021). Sparse matrix linear models for structured high-throughput data. To appear in The Annals of Applied Statistics. arXiv preprint: arXiv:1712.05767 [stat.CO].

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