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

Area of Science:

• Medical Physics
• Biostatistics
• Radiotherapy Research

Background:

• Protecting organs-at-risk (OARs) from radiation is crucial in cancer radiotherapy to prevent toxicity.
• Dose-volume histograms (DVHs) summarize radiation exposure to OARs, but conventional causal models struggle with their high-dimensional, matrix-valued nature.
• Improved causal inference from DVHs can enhance radiotherapy treatment planning and patient outcomes.

Purpose of the Study:

• To propose a novel Bayesian three-component joint model for matrix-valued DVH exposure with causal interpretation.
• To address the limitations of conventional causal models in handling high-dimensional and correlated DVH data.
• To develop a method for accurately estimating causal effects of radiation dose on OARs and toxicity.

Main Methods:

• Utilized multilinear principal component analysis (MPCA) for efficient dimension reduction of matrix-valued DVHs.
• Developed a Bayesian three-component joint model for causal inference.
• Adapted a Hamiltonian Monte Carlo algorithm for model parameter estimation.
• Validated the model through simulations and application studies.

Main Results:

• The proposed Bayesian model effectively estimates average causal effects from matrix-valued DVH data.
• Multilinear principal component analysis (MPCA) demonstrated superior information extraction compared to conventional PCA.
• The model successfully mapped dose effects back to the original DVH matrix for clear interpretation.
• The model correctly identified relevant causal effects in both simulated and real-world radiotherapy data.

Conclusions:

• The novel Bayesian joint model provides a robust framework for causal inference with matrix-valued DVHs in radiotherapy.
• The approach enhances the understanding of the relationship between radiation dose and OAR toxicity.
• This methodology holds significant potential for improving radiotherapy treatment planning and minimizing treatment-related toxicities.