Relational Dose-Response Modeling for Cancer Drug Studies

Wesley Tansey, Christopher Tosh, David M. Blei

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. The level of natural variation and technical noise in these experiments is high, even when multiple replicates are run. Further, running all possible combinations of cell lines and drugs may be prohibitively expensive, leading to missing data. Thus, estimating the dose-response curve is a denoising and imputation task. We cast this task as a functional matrix factorization problem: finding low-dimensional structure in a matrix where every entry is a noisy function evaluated at a set of discrete points. We propose Bayesian Tensor Filtering (BTF), a hierarchical Bayesian model of matrices of functions. BTF captures the smoothness in each individual function while also being locally adaptive to sharp discontinuities. The BTF model can incorporate many types of likelihoods, making it flexible enough to handle a wide variety of data. We derive efficient Gibbs samplers for three classes of likelihoods: (i) Gaussian, for which updates are fully conjugate; (ii) binomial and related likelihoods, for which updates are conditionally conjugate through Polya-Gamma augmentation; and (iii) non-conjugate likelihoods, for which we develop an analytic truncated elliptical slice sampling routine. We compare BTF against a state-of-the-art method for dynamic Poisson matrix factorization, showing BTF better reconstructs held out data in synthetic experiments. Finally, we build a dose-response model around BTF and apply it to real data from two multi-sample, multi-drug cancer studies. We show that the BTF-based dose-response model outperforms the current standard approach in biology. Code is available at

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