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Generalized linear models with linear constraints for microbiome compositional data

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  • Jiarui Lu
  • Pixu Shi
  • Hongzhe Li

Abstract

Motivated by regression analysis for microbiome compositional data, this article considers generalized linear regression analysis with compositional covariates, where a group of linear constraints on regression coefficients are imposed to account for the compositional nature of the data and to achieve subcompositional coherence. A penalized likelihood estimation procedure using a generalized accelerated proximal gradient method is developed to efficiently estimate the regression coefficients. A de‐biased procedure is developed to obtain asymptotically unbiased and normally distributed estimates, which leads to valid confidence intervals of the regression coefficients. Simulations results show the correctness of the coverage probability of the confidence intervals and smaller variances of the estimates when the appropriate linear constraints are imposed. The methods are illustrated by a microbiome study in order to identify bacterial species that are associated with inflammatory bowel disease (IBD) and to predict IBD using fecal microbiome.

Suggested Citation

  • Jiarui Lu & Pixu Shi & Hongzhe Li, 2019. "Generalized linear models with linear constraints for microbiome compositional data," Biometrics, The International Biometric Society, vol. 75(1), pages 235-244, March.
  • Handle: RePEc:bla:biomet:v:75:y:2019:i:1:p:235-244
    DOI: 10.1111/biom.12956
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    References listed on IDEAS

    as
    1. Wei Lin & Pixu Shi & Rui Feng & Hongzhe Li, 2014. "Variable selection in regression with compositional covariates," Biometrika, Biometrika Trust, vol. 101(4), pages 785-797.
    2. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    3. Yuanpei Cao & Wei Lin & Hongzhe Li, 2018. "Two-sample tests of high-dimensional means for compositional data," Biometrika, Biometrika Trust, vol. 105(1), pages 115-132.
    4. Zachary D Kurtz & Christian L Müller & Emily R Miraldi & Dan R Littman & Martin J Blaser & Richard A Bonneau, 2015. "Sparse and Compositionally Robust Inference of Microbial Ecological Networks," PLOS Computational Biology, Public Library of Science, vol. 11(5), pages 1-25, May.
    5. Cun-Hui Zhang & Stephanie S. Zhang, 2014. "Confidence intervals for low dimensional parameters in high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 217-242, January.
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    Citations

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    Cited by:

    1. G. S. Monti & P. Filzmoser, 2022. "Robust logistic zero-sum regression for microbiome compositional data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 301-324, June.
    2. Sean M Devlin & Axel Martin & Irina Ostrovnaya, 2021. "Identifying prognostic pairwise relationships among bacterial species in microbiome studies," PLOS Computational Biology, Public Library of Science, vol. 17(11), pages 1-12, November.
    3. Lingjing Jiang & Niina Haiminen & Anna‐Paola Carrieri & Shi Huang & Yoshiki Vázquez‐Baeza & Laxmi Parida & Ho‐Cheol Kim & Austin D. Swafford & Rob Knight & Loki Natarajan, 2022. "Utilizing stability criteria in choosing feature selection methods yields reproducible results in microbiome data," Biometrics, The International Biometric Society, vol. 78(3), pages 1155-1167, September.
    4. Xu Lin & Hong-Mei Xiao & Hui-Min Liu & Wan-Qiang Lv & Jonathan Greenbaum & Rui Gong & Qiang Zhang & Yuan-Cheng Chen & Cheng Peng & Xue-Juan Xu & Dao-Yan Pan & Zhi Chen & Zhang-Fang Li & Rou Zhou & Xia, 2023. "Gut microbiota impacts bone via Bacteroides vulgatus-valeric acid-related pathways," Nature Communications, Nature, vol. 14(1), pages 1-17, December.
    5. Jordi Saperas-Riera & Glòria Mateu-Figueras & Josep Antoni Martín-Fernández, 2024. "L p -Norm for Compositional Data: Exploring the CoDa L 1 -Norm in Penalised Regression," Mathematics, MDPI, vol. 12(9), pages 1-16, May.
    6. Arun Srinivasan & Lingzhou Xue & Xiang Zhan, 2021. "Compositional knockoff filter for high‐dimensional regression analysis of microbiome data," Biometrics, The International Biometric Society, vol. 77(3), pages 984-995, September.

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