Missing data imputation using a truncated Gaussian infinite factor model with application to metabolomics data

Metabolomics is the study of small molecules in biological samples. Metabolomics data are typically high-dimensional and contain highly correlated variables and frequent missing values. Both missing at random (MAR) data, due to acquisition or processing errors, and missing not at random (MNAR) data, caused by values falling below detection thresholds, are common. Thus, imputation is a critical component of downstream analysis. Existing imputation methods generally assume one type of data missingness mechanism, or impute values outside the data's physical constraints. A novel truncated Gaussian infinite factor analysis (TGIFA) model is proposed to perform statistically principled and physically realistic imputation in metabolomics data. By incorporating truncated Gaussian assumptions, TGIFA respects the data's physical constraints, while leveraging an infinite latent factor framework to capture high-dimensional dependencies without pre-specifying the number of latent factors. Our Bayesian inference approach enables uncertainty quantification in both the values of the imputed data, and the missing data mechanism. A computationally efficient exchange algorithm enables scalable posterior inference via Markov Chain Monte Carlo. We validate TGIFA through a comprehensive simulation study and demonstrate its utility in a motivating urinary metabolomics dataset, where it yields useful imputations, with associated uncertainty quantification. Open-source R code, available at https://github.com/kfinucane/TGIFA, accompanies TGIFA.