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Like many other clinical and economic studies, each subject of our motivating transplant study is at risk of recurrent events of non-fatal tissue rejections as well as the terminating event of death due to total graft rejection. For such studies, our model and associated Bayesian analysis aim for some practical advantages over competing methods. Our semiparametric latent-class-based joint model has coherent interpretation of the covariate (including race and gender) effects on all functions and model quantities that are relevant for understanding the effects of covariates on future event trajectories. Our fully Bayesian method for estimation and prediction uses a complete specification of the prior process of the baseline functions. We also derive a practical and theoretically justifiable partial likelihood-based semiparametric Bayesian approach to deal with the analysis when there is a lack of prior information about baseline functions. Our model and method can accommodate fixed as well as time-varying covariates. Our Markov Chain Monte Carlo tools for both Bayesian methods are implementable via publicly available software. Our Bayesian analysis of transplant study and simulation study demonstrate practical advantages and improved performance of our approach.
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Bayesian Regression Analysis of Skewed Tensor Responses
Abstract 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.
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- Award ID(s):
- 1908969
- PAR ID:
- 10486004
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 79
- Issue:
- 3
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 1814-1825
- Size(s):
- p. 1814-1825
- Sponsoring Org:
- National Science Foundation
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