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Bayesian Generalized Low Rank Regression Models for Neuroimaging Phenotypes and Genetic Markers

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  • Hongtu Zhu
  • Zakaria Khondker
  • Zhaohua Lu
  • Joseph G. Ibrahim

Abstract

We propose a Bayesian generalized low-rank regression model (GLRR) for the analysis of both high-dimensional responses and covariates. This development is motivated by performing searches for associations between genetic variants and brain imaging phenotypes. GLRR integrates a low rank matrix to approximate the high-dimensional regression coefficient matrix of GLRR and a dynamic factor model to model the high-dimensional covariance matrix of brain imaging phenotypes. Local hypothesis testing is developed to identify significant covariates on high-dimensional responses. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. A simulation study is performed to evaluate the finite sample performance of GLRR and its comparison with several competing approaches. We apply GLRR to investigate the impact of 1071 SNPs on top 40 genes reported by AlzGene database on the volumes of 93 regions of interest (ROI) obtained from Alzheimer's Disease Neuroimaging Initiative (ADNI). Supplementary materials for this article are available online.

Suggested Citation

  • Hongtu Zhu & Zakaria Khondker & Zhaohua Lu & Joseph G. Ibrahim, 2014. "Bayesian Generalized Low Rank Regression Models for Neuroimaging Phenotypes and Genetic Markers," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 977-990, September.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:507:p:977-990
    DOI: 10.1080/01621459.2014.923775
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    Cited by:

    1. Ma, Haiqiang & Li, Ting & Zhu, Hongtu & Zhu, Zhongyi, 2019. "Quantile regression for functional partially linear model in ultra-high dimensions," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 135-147.
    2. Goh, Gyuhyeong & Dey, Dipak K. & Chen, Kun, 2017. "Bayesian sparse reduced rank multivariate regression," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 14-28.
    3. Cook, R. Dennis & Forzani, Liliana & Su, Zhihua, 2016. "A note on fast envelope estimation," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 42-54.
    4. Kun Chen & Yanyuan Ma, 2017. "Analysis of Double Single Index Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 1-20, March.
    5. Durante, Daniele, 2017. "A note on the multiplicative gamma process," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 198-204.
    6. Yeonhee Park & Zhihua Su & Hongtu Zhu, 2017. "Groupwise envelope models for imaging genetic analysis," Biometrics, The International Biometric Society, vol. 73(4), pages 1243-1253, December.
    7. Nie Yunlong & Wang Jie & Wu Sidi & Wang Liangliang & Cao Jiguo & Opoku Eugene & Yasmin Laila & Song Yin & Nathoo Farouk S. & Scarapicchia Vanessa & Gawryluk Jodie, 2020. "Spectral dynamic causal modelling of resting-state fMRI: an exploratory study relating effective brain connectivity in the default mode network to genetics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 19(3), pages 1-18, June.
    8. Bai, Ray & Ghosh, Malay, 2018. "High-dimensional multivariate posterior consistency under global–local shrinkage priors," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 157-170.
    9. Yin Song & Shufei Ge & Jiguo Cao & Liangliang Wang & Farouk S. Nathoo, 2022. "A Bayesian spatial model for imaging genetics," Biometrics, The International Biometric Society, vol. 78(2), pages 742-753, June.

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