Bayesian Matrix Completion for Hypothesis Testing

High-throughput screening (HTS) is a well-established technology that rapidly and efficiently screens thousands of chemicals for potential toxicity. Massive testing using HTS primarily aims to differentiate active vs inactive chemicals for different types of biological endpoints. However, even using high-throughput technology, it is not feasible to test all possible combinations of chemicals and assay endpoints, resulting in a majority of missing combinations. Our goal is to derive posterior probabilities of activity for each chemical by assay endpoint combination, addressing the sparsity of HTS data. We propose a Bayesian hierarchical framework, which borrows information across different chemicals and assay endpoints in a low-dimensional latent space. This framework facilitates out-of-sample prediction of bioactivity potential for new chemicals not yet tested. Furthermore, this paper makes a novel attempt in toxicology to simultaneously model heteroscedastic errors as well as a nonparametric mean function. It leads to a broader definition of activity whose need has been suggested by toxicologists. Simulation studies demonstrate that our approach shows superior performance with more realistic inferences on activity than current standard methods. Application to an HTS data set identifies chemicals that are most likely active for two disease outcomes: neurodevelopmental disorders and obesity. Code is available on Github.