IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v65y2013i1p149-166.html
   My bibliography  Save this article

On Mann–Whitney tests for comparing sojourn time distributions when the transition times are right censored

Author

Listed:
  • Jie Fan
  • Somnath Datta

Abstract

We consider the problem of comparing sojourn time distributions of a transient state in a general multistate system in two samples (groups) when the transition times are right censored. Using the reweighting principle, a two-sample Mann–Whitney type of $$U$$ -statistic is constructed that compares only the uncensored sojourn times from the two distributions. A second Mann–Whitney type of statistic is also constructed using a different reweighting that allows for comparisons when one of the two sojourn times is either uncensored or singly censored. Both these statistics are asymptotically unbiased, asymptotically normally distributed and reduce to the standard Mann–Whitney statistic when there is no censoring. A test of equality of sojourn time distributions in two independent samples is constructed by symmetrizing the second statistic. The testing methodology is illustrated using a data set on kidney disease patients. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • Jie Fan & Somnath Datta, 2013. "On Mann–Whitney tests for comparing sojourn time distributions when the transition times are right censored," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 149-166, February.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:1:p:149-166
    DOI: 10.1007/s10463-012-0378-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-012-0378-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-012-0378-5?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. Robert L. Strawderman, 2005. "The accelerated gap times model," Biometrika, Biometrika Trust, vol. 92(3), pages 647-666, September.
    2. 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.
    3. Yijian Huang, 2002. "Censored regression with the multistate accelerated sojourn times model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 17-29, January.
    4. Fan, Jie & Datta, Somnath, 2011. "Fitting marginal accelerated failure time models to clustered survival data with potentially informative cluster size," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3295-3303, December.
    5. Douglas E. Schaubel, 2004. "Regression methods for gap time hazard functions of sequentially ordered multivariate failure time data," Biometrika, Biometrika Trust, vol. 91(2), pages 291-303, June.
    6. D. Y. Lin & Zhiliang Ying, 2001. "Nonparametric Tests for the Gap Time Distributions of Serial Events Based on Censored Data," Biometrics, The International Biometric Society, vol. 57(2), pages 369-375, June.
    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. Sankaran, P.G. & Anisha, P., 2012. "Additive hazards models for gap time data with multiple causes," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1454-1462.
    2. Hong Zhu, 2014. "Non-parametric Analysis of Gap Times for Multiple Event Data: An Overview," International Statistical Review, International Statistical Institute, vol. 82(1), pages 106-122, April.
    3. Jean‐Yves Dauxois & Sophie Sencey, 2009. "Non‐parametric Tests for Recurrent Events under Competing Risks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 649-670, December.
    4. Chia-Hui Huang, 2019. "Mixture regression models for the gap time distributions and illness–death processes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 168-188, January.
    5. Pang Du & Yihua Jiang & Yuedong Wang, 2011. "Smoothing Spline ANOVA Frailty Model for Recurrent Event Data," Biometrics, The International Biometric Society, vol. 67(4), pages 1330-1339, December.
    6. Kang, Fangyuan & Sun, Liuquan & Zhao, Xingqiu, 2015. "A class of transformed hazards models for recurrent gap times," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 151-167.
    7. Jieli Ding & Liuquan Sun, 2017. "Additive mixed effect model for recurrent gap time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 223-253, April.
    8. Jin-Jian Hsieh & A. Adam Ding & Weijing Wang, 2011. "Regression Analysis for Recurrent Events Data under Dependent Censoring," Biometrics, The International Biometric Society, vol. 67(3), pages 719-729, September.
    9. Kattumannil, Sudheesh K. & E.P., Sreedevi, 2022. "Non-parametric estimation of cumulative (residual) extropy," Statistics & Probability Letters, Elsevier, vol. 185(C).
    10. Sudheesh K. Kattumannil & P. Anisha, 2019. "A simple non-parametric test for decreasing mean time to failure," Statistical Papers, Springer, vol. 60(1), pages 73-87, February.
    11. Salim Bouzebda & Amel Nezzal & Tarek Zari, 2022. "Uniform Consistency for Functional Conditional U -Statistics Using Delta-Sequences," Mathematics, MDPI, vol. 11(1), pages 1-39, December.
    12. Ao Yuan & Mihai Giurcanu & George Luta & Ming T. Tan, 2017. "U-statistics with conditional kernels for incomplete data models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 271-302, April.
    13. Austin, Matthew D. & Betensky, Rebecca A., 2014. "Eliminating bias due to censoring in Kendall’s tau estimators for quasi-independence of truncation and failure," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 16-26.
    14. Xiaoyan Sun & Limin Peng & Yijian Huang & HuiChuan J. Lai, 2016. "Generalizing Quantile Regression for Counting Processes With Applications to Recurrent Events," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 145-156, March.
    15. Xuelin Huang & Lei Liu, 2007. "A Joint Frailty Model for Survival and Gap Times Between Recurrent Events," Biometrics, The International Biometric Society, vol. 63(2), pages 389-397, June.
    16. Ritesh Ramchandani & Dianne M. Finkelstein & David A. Schoenfeld, 2020. "Estimation for an accelerated failure time model with intermediate states as auxiliary information," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 1-20, January.
    17. Salim Bouzebda & Thouria El-hadjali & Anouar Abdeldjaoued Ferfache, 2023. "Uniform in Bandwidth Consistency of Conditional U-statistics Adaptive to Intrinsic Dimension in Presence of Censored Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1548-1606, August.
    18. Marija Cuparić & Bojana Milošević, 2022. "New characterization-based exponentiality tests for randomly censored data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 461-487, June.
    19. V. N. Sreeja & P. G. Sankaran, 2007. "Proportional mean residual life model for gap time distributions of recurrent events," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 319-336.
    20. Chia-Hui Huang & Yi-Hau Chen, 2017. "Regression analysis for bivariate gap time with missing first gap time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 83-101, 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:aistmt:v:65:y:2013:i:1:p:149-166. 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.