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Compositional knockoff filter for high‐dimensional regression analysis of microbiome data

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  • Arun Srinivasan
  • Lingzhou Xue
  • Xiang Zhan

Abstract

A critical task in microbiome data analysis is to explore the association between a scalar response of interest and a large number of microbial taxa that are summarized as compositional data at different taxonomic levels. Motivated by fine‐mapping of the microbiome, we propose a two‐step compositional knockoff filter to provide the effective finite‐sample false discovery rate (FDR) control in high‐dimensional linear log‐contrast regression analysis of microbiome compositional data. In the first step, we propose a new compositional screening procedure to remove insignificant microbial taxa while retaining the essential sum‐to‐zero constraint. In the second step, we extend the knockoff filter to identify the significant microbial taxa in the sparse regression model for compositional data. Thereby, a subset of the microbes is selected from the high‐dimensional microbial taxa as related to the response under a prespecified FDR threshold. We study the theoretical properties of the proposed two‐step procedure, including both sure screening and effective false discovery control. We demonstrate these properties in numerical simulation studies to compare our methods to some existing ones and show power gain of the new method while controlling the nominal FDR. The potential usefulness of the proposed method is also illustrated with application to an inflammatory bowel disease data set to identify microbial taxa that influence host gene expressions.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:biomet:v:77:y:2021:i:3:p:984-995
    DOI: 10.1111/biom.13336
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    References listed on IDEAS

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    1. Xiang Zhan & Anna Plantinga & Ni Zhao & Michael C. Wu, 2017. "A fast small‐sample kernel independence test for microbiome community‐level association analysis," Biometrics, The International Biometric Society, vol. 73(4), pages 1453-1463, December.
    2. 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.
    3. Lingzhou Xue & Hui Zou, 2011. "Sure independence screening and compressed random sensing," Biometrika, Biometrika Trust, vol. 98(2), pages 371-380.
    4. Chen Xu & Jiahua Chen, 2014. "The Sparse MLE for Ultrahigh-Dimensional Feature Screening," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1257-1269, September.
    5. 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.
    6. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    7. Runze Li & Wei Zhong & Liping Zhu, 2012. "Feature Screening via Distance Correlation Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1129-1139, September.
    8. Emmanuel Candès & Yingying Fan & Lucas Janson & Jinchi Lv, 2018. "Panning for gold: ‘model‐X’ knockoffs for high dimensional controlled variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(3), pages 551-577, June.
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    1. Srinivasan, Arun & Xue, Lingzhou & Zhan, Xiang, 2023. "Identification of microbial features in multivariate regression under false discovery rate control," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).

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