A Bayesian joint model for mediation analysis with matrix-valued mediators.

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.