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Why do metabolomics data sets create a high-dimension, low-sample-size problem?

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Diagram illustrating metabolism with two sections: anabolic reaction on the left shows energy used to build larger molecules from smaller ones, while catabolic reaction on the right shows larger molecules breaking down into smaller molecules with energy released. — Metabolomics In anabolic reactions, a cell uses energy to combine small molecules into larger molecules. In catabolic reactions, molecules are broken down, and energy is released.

In metabolomics, the high-dimension, low-sample-size problem—often denoted as $p > > n$ —arises primarily from the nature of nontargeted analytical approaches.1

When researchers perform nontargeted metabolomics, the goal is to capture a comprehensive portrait of the metabolome rather than focusing on a predefined panel of compounds. These broad analyses detect a vast array of molecular variables, including:1

Classic mammalian metabolites from known biochemical pathways1
Food additives and dietary compounds1
Drugs and their metabolic products1
Fermentation products from gut microbes1
Substances with unknown chemical identities1

Because these methods measure such a large number of molecular variables ( $p$ ) relative to the limited number of biological samples ( $n$ ) available for study, the resulting data sets are extremely high-dimensional. This imbalance creates a significant statistical challenge, as it increases the risk of false discovery, necessitating rigorous data treatment to ensure the validity of the findings.1