Department of Statistics, Rice University, Houston, Texas, USA.
Department of Statistics, Florida State University, Tallahassee, Florida, USA.
Biometrics. 2023 Sep;79(3):1814-1825. doi: 10.1111/biom.13743. Epub 2022 Sep 10.
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 prespecified 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 Markov chain Monte Carlo (MCMC) tools that are readily implementable. We illustrate substantial advantages of our proposal over existing methods via simulation studies and application to a real data set derived from a clinical study of PD. The R package BSTN available in GitHub implements our model.
张量回归分析在各种临床环境中（包括神经影像学、基因组学和牙科医学）的应用越来越广泛。本文的动机是对牙周病（PD）进行研究，使用三阶张量响应：每个参与者的每个牙齿内预先指定的牙齿部位测量多个生物标志物。仔细研究后，除了响应缺失之外，还会发现响应存在很大的偏度。为了减轻现有分析工具的缺点，我们提出了一种新的贝叶斯张量响应回归方法，该方法有助于解释偏斜张量响应的边际和联合分布上的协变量效应，并在我们的张量模型的封闭特性下容纳随机缺失的响应。此外，我们在仅稀疏张量分量子集上识别其可能变化的情况下，对整体协变量效应进行谨慎评估。我们的方法承诺提供易于实现的马尔可夫链蒙特卡罗（MCMC）工具。通过模拟研究和对源自 PD 临床研究的真实数据集的应用，说明了我们的方法相对于现有方法的显著优势。GitHub 上的 BSTN R 包实现了我们的模型。
