# A Bayesian Model of Dose-Response for Cancer Drug Studies

## TL;DR

This paper introduces Bayesian Tensor Filtering (BTF), a hierarchical Bayesian model that improves dose-response analysis in cancer drug studies by sharing information across similar drugs and cell lines, and effectively handling complex data structures.

## Contribution

The paper presents BTF, a novel Bayesian model with structured priors and a new sampling algorithm, specifically designed for multi-sample, multi-treatment cancer drug dose-response data.

## Key findings

- BTF outperforms existing methods in benchmark tests.
- BTF reveals new potential biomarkers of drug sensitivity.
- The model effectively captures dose-response curves with sharp jumps.

## Abstract

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.