IDEAS home Printed from https://ideas.repec.org/a/spr/stabio/v14y2022i3d10.1007_s12561-021-09328-0.html
   My bibliography  Save this article

High-Dimensional Mediation Analysis with Applications to Causal Gene Identification

Author

Listed:
  • Qi Zhang

    (University of New Hampshire)

Abstract

Mediation analysis has been a popular framework for elucidating the mediating mechanism of the exposure effect on the outcome in many disciplines including genetic studies. Previous literature in causal mediation primarily focused on the classical settings with univariate exposure and univariate mediator, with recent growing interests in high-dimensional mediator. In this paper, we study the mediation model with high-dimensional exposure, high-dimensional continuous mediator, and a continuous outcome. We introduce two procedures for mediator selection, MedFix and MedMix, and develop the corresponding causal effect tests. Our study is motivated by the causal gene identification problem in biomedical studies, where causal genes are defined as the genes that mediate the genetic effect. For this problem, the genetic variants are the high-dimensional exposure, the gene expressions the high-dimensional mediator, and the phenotype of interest the outcome. We evaluate the proposed methods using a mouse f2 dataset for diabetes study, and extensive real data-driven simulations. We show that the mixed model-based approach (MedMix) leads to higher accuracy in mediator selection with reasonable reproducibility across independent measurements of the response and is more robust against model misspecification. The R code and additional materials are available on Github ( https://github.com/QiZhangStat/highMed ).

Suggested Citation

  • Qi Zhang, 2022. "High-Dimensional Mediation Analysis with Applications to Causal Gene Identification," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(3), pages 432-451, December.
  • Handle: RePEc:spr:stabio:v:14:y:2022:i:3:d:10.1007_s12561-021-09328-0
    DOI: 10.1007/s12561-021-09328-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12561-021-09328-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s12561-021-09328-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Zhong, Ping-Shou & Chen, Song Xi, 2011. "Tests for High-Dimensional Regression Coefficients With Factorial Designs," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 260-274.
    3. R. M. Daniel & B. L. De Stavola & S. N. Cousens & S. Vansteelandt, 2015. "Causal mediation analysis with multiple mediators," Biometrics, The International Biometric Society, vol. 71(1), pages 1-14, March.
    4. Juming Pan & Junfeng Shang, 2018. "Adaptive LASSO for linear mixed model selection via profile log-likelihood," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(8), pages 1882-1900, April.
    5. Tingni Sun & Cun-Hui Zhang, 2012. "Scaled sparse linear regression," Biometrika, Biometrika Trust, vol. 99(4), pages 879-898.
    6. Tingni Sun & Cun-Hui Zhang, 2010. "Comments on: ℓ 1 -penalization for mixture regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 270-275, August.
    7. Abhik Ghosh & Magne Thoresen, 2018. "Non-concave penalization in linear mixed-effect models and regularized selection of fixed effects," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 179-210, April.
    8. Tyler J. Vanderweele, 2011. "Controlled Direct and Mediated Effects: Definition, Identification and Bounds," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(3), pages 551-563, September.
    9. Kim, Yongdai & Choi, Hosik & Oh, Hee-Seok, 2008. "Smoothly Clipped Absolute Deviation on High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1665-1673.
    10. Ruixuan Rachel Zhou & Liewei Wang & Sihai Dave Zhao, 2020. "Estimation and inference for the indirect effect in high-dimensional linear mediation models," Biometrika, Biometrika Trust, vol. 107(3), pages 573-589.
    11. Jürg Schelldorfer & Peter Bühlmann & Sara Van De Geer, 2011. "Estimation for High‐Dimensional Linear Mixed‐Effects Models Using ℓ 1 ‐Penalization," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(2), pages 197-214, June.
    12. Rohart, Florian & San Cristobal, Magali & Laurent, Béatrice, 2014. "Selection of fixed effects in high dimensional linear mixed models using a multicycle ECM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 209-222.
    13. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    14. Yen-Tsung Huang & Wen-Chi Pan, 2016. "Hypothesis test of mediation effect in causal mediation model with high-dimensional continuous mediators," Biometrics, The International Biometric Society, vol. 72(2), pages 402-413, June.
    15. Rajen D. Shah & Peter Bühlmann, 2018. "Goodness‐of‐fit tests for high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(1), pages 113-135, January.
    16. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Simona Buscemi & Antonella Plaia, 2020. "Model selection in linear mixed-effect models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 529-575, December.
    2. Lina Liao & Cheolwoo Park & Hosik Choi, 2019. "Penalized expectile regression: an alternative to penalized quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 409-438, April.
    3. Gueuning, Thomas & Claeskens, Gerda, 2016. "Confidence intervals for high-dimensional partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 13-29.
    4. Lan, Wei & Zhong, Ping-Shou & Li, Runze & Wang, Hansheng & Tsai, Chih-Ling, 2016. "Testing a single regression coefficient in high dimensional linear models," Journal of Econometrics, Elsevier, vol. 195(1), pages 154-168.
    5. Cai, Xizhen & Zhu, Yeying & Huang, Yuan & Ghosh, Debashis, 2022. "High-dimensional causal mediation analysis based on partial linear structural equation models," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    6. Gaorong Li & Liugen Xue & Heng Lian, 2012. "SCAD-penalised generalised additive models with non-polynomial dimensionality," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 681-697.
    7. Xiaotong Shen & Wei Pan & Yunzhang Zhu & Hui Zhou, 2013. "On constrained and regularized high-dimensional regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 807-832, October.
    8. Umberto Amato & Anestis Antoniadis & Italia De Feis & Irene Gijbels, 2021. "Penalised robust estimators for sparse and high-dimensional linear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 1-48, March.
    9. Guo, Xu & Li, Runze & Liu, Jingyuan & Zeng, Mudong, 2023. "Statistical inference for linear mediation models with high-dimensional mediators and application to studying stock reaction to COVID-19 pandemic," Journal of Econometrics, Elsevier, vol. 235(1), pages 166-179.
    10. Shan Luo & Zehua Chen, 2014. "Sequential Lasso Cum EBIC for Feature Selection With Ultra-High Dimensional Feature Space," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1229-1240, September.
    11. Toshio Honda, 2021. "The de-biased group Lasso estimation for varying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 3-29, February.
    12. Peter Bühlmann & Jacopo Mandozzi, 2014. "High-dimensional variable screening and bias in subsequent inference, with an empirical comparison," Computational Statistics, Springer, vol. 29(3), pages 407-430, June.
    13. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    14. Li, Xinjue & Zboňáková, Lenka & Wang, Weining & Härdle, Wolfgang Karl, 2019. "Combining Penalization and Adaption in High Dimension with Application in Bond Risk Premia Forecasting," IRTG 1792 Discussion Papers 2019-030, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    15. Lan Wang & Yichao Wu & Runze Li, 2012. "Quantile Regression for Analyzing Heterogeneity in Ultra-High Dimension," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 214-222, March.
    16. Jingxuan Luo & Lili Yue & Gaorong Li, 2023. "Overview of High-Dimensional Measurement Error Regression Models," Mathematics, MDPI, vol. 11(14), pages 1-22, July.
    17. Canhong Wen & Xueqin Wang & Shaoli Wang, 2015. "Laplace Error Penalty-based Variable Selection in High Dimension," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 685-700, September.
    18. Sokbae Lee & Myung Hwan Seo & Youngki Shin, 2016. "The lasso for high dimensional regression with a possible change point," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 193-210, January.
    19. Lian, Heng & Li, Jianbo & Hu, Yuao, 2013. "Shrinkage variable selection and estimation in proportional hazards models with additive structure and high dimensionality," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 99-112.
    20. Panxu Yuan & Xiao Guo, 2022. "High-dimensional inference for linear model with correlated errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(1), pages 21-52, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stabio:v:14:y:2022:i:3:d:10.1007_s12561-021-09328-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.