A Bayesian Model of Dose-Response for Cancer Drug Studies

Bayesian Matrix Completion for Hypothesis Testing

“…In order to account for mechanistic similarities among chemicals and/or assay endpoints as well as to tackle sparsity of the data, we require a more sophisticated hierarchy that borrows information across both rows and columns of the matrix. Tansey et al (2019) propose hierarchical functional matrix factorization methods to infer dose-response curves, approximating the row and the column space using low-dimensional latent attributes. However, their model lacks a formal testing framework and assumes a matrix data structure where all cells have the same number of replicates at the same number of unique doses.…”

“…In the ToxCast/Tox21 data, the number of unique doses differs within a column, and the number of replicates at each dose varies within a cell. Still, we can adapt low rank approximations addressing matrix completion problems (Mnih and Salakhutdinov, 2008;Koren et al, 2009;Purushotham et al, 2012;Tansey et al, 2019) to a multiple hypothesis testing framework. We construct π ij with a latent factor model, assuming that low-dimensional latent attributes account for associations relevant to the mean effect among chemicals or among assay endpoints.…”