A Bayesian approach to joint modeling of matrix‐valued imaging data and treatment outcome with applications to depression studies

In this paper, we propose a unified Bayesian joint modeling framework for studying association between a binary treatment outcome and a baseline matrix‐valued predictor. Specifically, a joint modeling approach relating an outcome to a matrix‐valued predictor through a probabilistic formulation of multilinear principal component analysis is developed. This framework establishes a theoretical relationship between the outcome and the matrix‐valued predictor, although the predictor is not explicitly expressed in the model. Simulation studies are provided showing that the proposed method is superior or competitive to other methods, such as a two‐stage approach and a classical principal component regression in terms of both prediction accuracy and estimation of association; its advantage is most notable when the sample size is small and the dimensionality in the imaging covariate is large. Finally, our proposed joint modeling approach is shown to be a very promising tool in an application exploring the association between baseline electroencephalography data and a favorable response to treatment in a depression treatment study by achieving a substantial improvement in prediction accuracy in comparison to competing methods.