  Unscheduled treatment interruptions may lead to reduced quality of care in
radiation therapy (RT). Identifying the RT prescription dose effects on the
outcome of treatment interruptions, mediated through doses distributed into
different organs-at-risk (OARs), can inform future treatment planning. The
radiation exposure to OARs can be summarized by a matrix of dose-volume
histograms (DVH) for each patient. Although various methods for
high-dimensional mediation analysis have been proposed recently, few studies
investigated how matrix-valued data can be treated as mediators. In this paper,
we propose a novel Bayesian joint mediation model for high-dimensional
matrix-valued mediators. In this joint model, latent features are extracted
from the matrix-valued data through an adaptation of probabilistic multilinear
principal components analysis (MPCA), retaining the inherent matrix structure.
We derive and implement a Gibbs sampling algorithm to jointly estimate all
model parameters, and introduce a Varimax rotation method to identify active
indicators of mediation among the matrix-valued data. Our simulation study
finds that the proposed joint model has higher efficiency in estimating causal
decomposition effects compared to an alternative two-step method, and
demonstrates that the mediation effects can be identified and visualized in the
matrix form. We apply the method to study the effect of prescription dose on
treatment interruptions in anal canal cancer patients.
