A Bayesian Joint Model Framework for Repeated Matrix-Variate Regression with Measurement Error Correction

Abstract

In this thesis, with the purpose of correcting for potential measurement errors in repeatedly-observed matrix-valued surrogates, and examining the underlying association between latent matrix covariates and a binary response, we propose a Bayesian joint model framework. This joint model method imposes a low-rank structure on the covariance matrix of additive measurement errors, and relates the binary response with low-dimensional features extracted from latent matrix covariates. Although in our framework, the latent matrix covariates are not directly observed and used as predictors in the proposed model, a unique formulation of associations between latent covariates and response is derived. Simulation studies demonstrate that our proposed method outperforms other naive methods (i.e., a naive joint model and a naive two-stage model) with respect to the estimates of underlying association. The advantage of the proposed method is more notable in the circumstances where a small sample size but high dimensional matrix covariates are presented. Finally, we apply this proposed framework to a case study that explores the association between a favorable response to antidepressant treatment and resting stage electroencephalography (EEG) data measured under different conditions. Results suggested that our method should be able to handle the attenuation bias induced from measurement errors and to reveal the most underlying association, compared to other competing methods.