We aim to infer bioactivity of each chemical by assay endpoint combination, addressing sparsity of toxicology data. We propose a Bayesian hierarchical framework which borrows information across different chemicals and assay endpoints, facilitates out-of-sample prediction of activity for chemicals not yet assayed, quantifies uncertainty of predicted activity, and adjusts for multiplicity in hypothesis testing. Furthermore, this paper makes a novel attempt in toxicology to simultaneously model heteroscedastic errors and a nonparametric mean function, leading to a broader definition of activity whose need has been suggested by toxicologists. Real application identifies chemicals most likely active for neurodevelopmental disorders and obesity.

The United States Environmental Protection Agency (EPA) screens thousands of chemicals primarily to differentiate those that are active vs inactive for different types of biological endpoints. However, it is not feasible to test all possible combinations of chemicals, assay endpoints, and concentrations, resulting in a majority of missing combinations. Our goal is to derive posterior probabilities of activity for each chemical by assay endpoint combination. Therefore, we are faced with a task of matrix completion in the context of hypothesis testing for sparse functional data. We propose a Bayesian hierarchical framework, which borrows information across different chemicals and assay endpoints. Our model predicts bioactivity profiles of whether the dose-response curve is constant or not, using low-dimensional latent attributes of chemicals and of assay endpoints. This framework facilitates out-of-sample