ESTIMATION AND INFERENCE IN METABOLOMICS WITH NON-RANDOM MISSING DATA AND LATENT FACTORS.

High throughput metabolomics data are fraught with both non-ignorable missing observations and unobserved factors that influence a metabolite's measured concentration, and it is well known that ignoring either of these complications can compromise estimators. However, current methods to analyze these data can only account for the missing data or unobserved factors, but not both. We therefore developed MetabMiss, a statistically rigorous method to account for both non-random missing data and latent factors in high throughput metabolomics data. Our methodology does not require the practitioner specify a likelihood for the missing data, and makes investigating the relationship between the metabolome and tens, or even hundreds, of phenotypes computationally tractable. We demonstrate the fidelity of Metab-Miss's estimates using both simulated and real metabolomics data, and prove their asymptotic correctness when the sample size and number of metabolites grows to infinity.