WITHDRAWN - A Bayesian Causal Model for Matrix-Valued Exposure with Applications to Radiotherapy Planning

Music City Center 

In cancer radiotherapy, radiation dose to organs-at-risk (OARs) adjacent to the target tumor should be minimized to avoid toxicity. Dose-volume histograms (DVH) used to summarize radiation exposure can be arranged in a matrix form to represent the dose to multiple OARs. Understanding the causal link between this matrix-valued exposure and toxicity could inform treatment planning, but conventional causal models are not tailored to high-dimensional matrix-valued data. We propose a Bayesian joint model for matrix-valued DVH exposure, with regularization. Dimension reduction is achieved via multilinear principal component analysis, which extracts features from both rows and columns of the matrix. A Hamiltonian Monte Carlo algorithm is adapted for estimation. Simulations assess the model's performance, and an application is presented to demonstrate the model's ability to identify relevant effects. For interpretation, the dose effects are mapped back to the original DVH matrix. We also extend the model to account for biologically monotonic dose effects on toxicity outcomes using a projection approach and discuss how this monotonicity constraint impacts causal interpretation of the model.

Bayesian Modeling

Causal Inference

Dose-Volume Histograms

Matrix-Valued Data

Multilinear Principal Component Analysis

Radiotherapy Planning 

Section on Bayesian Statistical Science