Bayesian Matrix Completion for Hypothesis Testing

TL;DR

This paper introduces a Bayesian hierarchical model for toxicology data that improves bioactivity inference, handles data sparsity, and supports hypothesis testing, with applications to neurodevelopmental and obesity-related chemicals.

Contribution

It presents a novel Bayesian framework that models heteroscedastic errors and nonparametric means, enhancing activity prediction and hypothesis testing in toxicology.

Findings

Identifies chemicals likely active for neurodevelopmental disorders.

Detects chemicals associated with obesity.

Provides out-of-sample activity predictions with uncertainty quantification.

Abstract

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.