IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v78y2022i3p867-879.html
   My bibliography  Save this article

A consistent version of distance covariance for right‐censored survival data and its application in hypothesis testing

Author

Listed:
  • Dominic Edelmann
  • Thomas Welchowski
  • Axel Benner

Abstract

Distance covariance is a powerful new dependence measure that was recently introduced by Székely et al. and Székely and Rizzo. In this work, the concept of distance covariance is extended to measuring dependence between a covariate vector and a right‐censored survival endpoint by establishing an estimator based on an inverse‐probability‐of‐censoring weighted U‐statistic. The consistency of the novel estimator is derived. In a large simulation study, it is shown that induced distance covariance permutation tests show a good performance in detecting various complex associations. Applying the distance covariance permutation tests on a gene expression dataset from breast cancer patients outlines its potential for biostatistical practice.

Suggested Citation

  • Dominic Edelmann & Thomas Welchowski & Axel Benner, 2022. "A consistent version of distance covariance for right‐censored survival data and its application in hypothesis testing," Biometrics, The International Biometric Society, vol. 78(3), pages 867-879, September.
    • Handle: RePEc:bla:biomet:v:78:y:2022:i:3:p:867-879
    DOI: 10.1111/biom.13470
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13470
    Download Restriction: no
    File URL: https://libkey.io/10.1111/biom.13470?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
    ---><---

    References listed on IDEAS

    as
    1. Wenliang Pan & Xueqin Wang & Weinan Xiao & Hongtu Zhu, 2019. "A Generic Sure Independence Screening Procedure," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 928-937, April.
    2. Jialiang Li & Qi Zheng & Limin Peng & Zhipeng Huang, 2016. "Survival impact index and ultrahigh‐dimensional model‐free screening with survival outcomes," Biometrics, The International Biometric Society, vol. 72(4), pages 1145-1154, December.
    3. Simon N. Wood, 2003. "Thin plate regression splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 95-114, February.
    4. L. Peng & J. P. Fine, 2008. "Nonparametric Tests for Continuous Covariate Effects with Multistate Survival Data," Biometrics, The International Biometric Society, vol. 64(4), pages 1080-1089, December.
    5. Zhao, Sihai Dave & Li, Yi, 2012. "Principled sure independence screening for Cox models with ultra-high-dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 397-411.
    6. Rui Song & Wenbin Lu & Shuangge Ma & X. Jessie Jeng, 2014. "Censored rank independence screening for high-dimensional survival data," Biometrika, Biometrika Trust, vol. 101(4), pages 799-814.
    7. Dominic Edelmann & Konstantinos Fokianos & Maria Pitsillou, 2019. "An Updated Literature Review of Distance Correlation and Its Applications to Time Series," International Statistical Review, International Statistical Institute, vol. 87(2), pages 237-262, August.
    8. Somnath Datta & Dipankar Bandyopadhyay & Glen A. Satten, 2010. "Inverse Probability of Censoring Weighted U‐statistics for Right‐Censored Data with an Application to Testing Hypotheses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 680-700, December.
    9. Xueqin Wang & Wenliang Pan & Wenhao Hu & Yuan Tian & Heping Zhang, 2015. "Conditional Distance Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1726-1734, December.
    10. Zhang, Jing & Liu, Yanyan & Wu, Yuanshan, 2017. "Correlation rank screening for ultrahigh-dimensional survival data," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 121-132.
    11. Anders Gorst-Rasmussen & Thomas Scheike, 2013. "Independent screening for single-index hazard rate models with ultrahigh dimensional features," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 217-246, March.
    12. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
    13. Yongwu Shao & R. Dennis Cook & Sanford Weisberg, 2007. "Marginal tests with sliced average variance estimation," Biometrika, Biometrika Trust, vol. 94(2), pages 285-296.
    14. Chen, Xiaolin & Chen, Xiaojing & Wang, Hong, 2018. "Robust feature screening for ultra-high dimensional right censored data via distance correlation," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 118-138.
    15. Heidi Dvinge & Anna Git & Stefan Gräf & Mali Salmon-Divon & Christina Curtis & Andrea Sottoriva & Yongjun Zhao & Martin Hirst & Javier Armisen & Eric A. Miska & Suet-Feung Chin & Elena Provenzano & Gu, 2013. "The shaping and functional consequences of the microRNA landscape in breast cancer," Nature, Nature, vol. 497(7449), pages 378-382, May.
    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. Jing Zhang & Qihua Wang & Xuan Wang, 2022. "Surrogate-variable-based model-free feature screening for survival data under the general censoring mechanism," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 379-397, April.
    2. Zhong, Wei & Wang, Jiping & Chen, Xiaolin, 2021. "Censored mean variance sure independence screening for ultrahigh dimensional survival data," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    3. Jing Zhang & Yanyan Liu & Hengjian Cui, 2021. "Model-free feature screening via distance correlation for ultrahigh dimensional survival data," Statistical Papers, Springer, vol. 62(6), pages 2711-2738, December.
    4. Jing Zhang & Haibo Zhou & Yanyan Liu & Jianwen Cai, 2021. "Conditional screening for ultrahigh-dimensional survival data in case-cohort studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 632-661, October.
    5. Xiaolin Chen & Catherine Chunling Liu & Sheng Xu, 2021. "An efficient algorithm for joint feature screening in ultrahigh-dimensional Cox’s model," Computational Statistics, Springer, vol. 36(2), pages 885-910, June.
    6. Xiaolin Chen & Yi Liu & Qihua Wang, 2019. "Joint feature screening for ultra-high-dimensional sparse additive hazards model by the sparsity-restricted pseudo-score estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1007-1031, October.
    7. Hyokyoung G. Hong & Xuerong Chen & David C. Christiani & Yi Li, 2018. "Integrated powered density: Screening ultrahigh dimensional covariates with survival outcomes," Biometrics, The International Biometric Society, vol. 74(2), pages 421-429, June.
    8. Chen, Xiaolin & Chen, Xiaojing & Wang, Hong, 2018. "Robust feature screening for ultra-high dimensional right censored data via distance correlation," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 118-138.
    9. Hong, Hyokyoung G. & Zheng, Qi & Li, Yi, 2019. "Forward regression for Cox models with high-dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 268-290.
    10. Yang Qu & Yu Cheng, 2023. "Volume under the ROC surface for high-dimensional independent screening with ordinal competing risk outcomes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(4), pages 735-751, October.
    11. Jing Zhang & Haibo Zhou & Yanyan Liu & Jianwen Cai, 2021. "Feature screening for case‐cohort studies with failure time outcome," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 349-370, March.
    12. Pan, Yingli, 2022. "Feature screening and FDR control with knockoff features for ultrahigh-dimensional right-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    13. Chen, Xiaolin & Zhang, Yahui & Chen, Xiaojing & Liu, Yi, 2019. "A simple model-free survival conditional feature screening," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 156-160.
    14. Qu, Lianqiang & Wang, Xiaoyu & Sun, Liuquan, 2022. "Variable screening for varying coefficient models with ultrahigh-dimensional survival data," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).
    15. Jing Pan & Yuan Yu & Yong Zhou, 2018. "Nonparametric independence feature screening for ultrahigh-dimensional survival data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 821-847, October.
    16. Grace Y. Yi & Wenqing He & Raymond. J. Carroll, 2022. "Feature screening with large‐scale and high‐dimensional survival data," Biometrics, The International Biometric Society, vol. 78(3), pages 894-907, September.
    17. Jialiang Li & Qi Zheng & Limin Peng & Zhipeng Huang, 2016. "Survival impact index and ultrahigh‐dimensional model‐free screening with survival outcomes," Biometrics, The International Biometric Society, vol. 72(4), pages 1145-1154, December.
    18. Jing Zhang & Guosheng Yin & Yanyan Liu & Yuanshan Wu, 2018. "Censored cumulative residual independent screening for ultrahigh-dimensional survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(2), pages 273-292, April.
    19. Jinfeng Xu & Wai Keung Li & Zhiliang Ying, 2020. "Variable screening for survival data in the presence of heterogeneous censoring," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1171-1191, December.
    20. Zhang, Jing & Liu, Yanyan & Wu, Yuanshan, 2017. "Correlation rank screening for ultrahigh-dimensional survival data," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 121-132.

    More about this item

    Statistics

    Access and download statistics

    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:bla:biomet:v:78:y:2022:i:3:p:867-879. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    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.