Biometrics. 2022 Aug 18. doi: 10.1111/biom.13743. Online ahead of print.
Tensor regression analysis is finding vast emerging applications in a variety of clinical settings, including neuroimaging, genomics and dental medicine. The motivation for this paper is a study of periodontal disease (PD) with an order 3 tensor response: multiple biomarkers measured at pre-specified tooth sites within each tooth, for each participant. A careful investigation would reveal considerable skewness in the responses, in addition to response missingness. To mitigate the shortcomings of existing analysis tools, we propose a new Bayesian tensor response regression method that facilitates interpretation of covariate effects on both marginal and joint distributions of highly skewed tensor responses, and accommodates missing-at-random responses under a closure property of our tensor model. Furthermore, we present a prudent evaluation of the overall covariate effects while identifying their possible variations on only a sparse subset of the tensor components. Our method promises MCMC tools that are readily implementable. We illustrate substantial advantages of our proposal over existing methods via simulation studies and application to a real dataset derived from a clinical study of PD. The R package BSTN available in GitHub implements our model. This article is protected by copyright. All rights reserved.