  Exploratory cancer drug studies test multiple tumor cell lines against
multiple candidate drugs. The goal in each paired (cell line, drug) experiment
is to map out the dose-response curve of the cell line as the dose level of the
drug increases. We propose Bayesian Tensor Filtering (BTF), a hierarchical
Bayesian model for dose-response modeling in multi-sample, multi-treatment
cancer drug studies. BTF uses low-dimensional embeddings to share statistical
strength between similar drugs and similar cell lines. Structured shrinkage
priors in BTF encourage smoothness in the dose-response curves while remaining
adaptive to sharp jumps when the data call for it. We focus on a pair of cancer
drug studies exhibiting a particular pathology in their experimental design,
leading us to a non-conjugate monotone mixture-of-Gammas likelihood. To perform
posterior inference, we develop a variant of the elliptical slice sampling
algorithm for sampling from linearly-constrained multivariate normal priors
with non-conjugate likelihoods. In benchmarks, BTF outperforms state-of-the-art
methods for covariance regression and dynamic Poisson matrix factorization. On
the two cancer drug studies, BTF outperforms the current standard approach in
biology and reveals potential new biomarkers of drug sensitivity in cancer.
Code is available at https://github.com/tansey/functionalmf.
