A Bayesian Causal Model for Matrix‐Valued Exposures With Applications to Radiotherapy Planning

In radiotherapy for cancer, organs surrounding the target tumor, known as organs-at-risk (OARs), should be protected from excessive radiation to avoid toxicity. Radiation exposure to multiple OARs can be summarized using matrix-valued dose-volume histograms (DVH), and understanding the causal relationship between DVHs and toxicity outcomes can improve treatment planning. Conventional causal models are not tailored to high-dimensional, highly correlated matrix-valued data. In this paper, we propose a Bayesian three-component joint model for a matrix-valued DVH exposure with a causal interpretation. Dimension reduction is achieved via multilinear principal component analysis (MPCA), which extracts information from matrices more efficiently than conventional PCA. A Hamiltonian Monte Carlo algorithm is adapted for estimation. We demonstrate the model's performance in estimating average causal effects through simulations. For interpretation, we map dose effects back to the original DVH matrix, illustrating that our model can correctly identify relevant effects in both simulation and application studies.