IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v40y2025i2d10.1007_s00180-024-01520-2.html
   My bibliography  Save this article

Hypothesis testing in Cox models when continuous covariates are dichotomized: bias analysis and bootstrap-based test

Author

Listed:
  • Hyunman Sim

    (Seoul National University)

  • Sungjeong Lee

    (Celltrion, Inc.)

  • Bo-Hyung Kim

    (Kyung Hee University Hospital
    Kyung Hee University)

  • Eun Shin

    (Hallym University Dongtan Sacred Heart Hospital)

  • Woojoo Lee

    (Seoul National University)

Abstract

Hypothesis testing for the regression coefficient associated with a dichotomized continuous covariate in a Cox proportional hazards model has been considered in clinical research. Although most existing testing methods do not allow covariates, except for a dichotomized continuous covariate, they have generally been applied. Through an analytic bias analysis and a numerical study, we show that the current practice is not free from an inflated type I error and a loss of power. To overcome this limitation, we develop a bootstrap-based test that allows additional covariates and dichotomizes two-dimensional covariates into a binary variable. In addition, we develop an efficient algorithm to speed up the calculation of the proposed test statistic. Our numerical study demonstrates that the proposed bootstrap-based test maintains the type I error well at the nominal level and exhibits higher power than other methods, as well as that the proposed efficient algorithm reduces computational costs.

Suggested Citation

  • Hyunman Sim & Sungjeong Lee & Bo-Hyung Kim & Eun Shin & Woojoo Lee, 2025. "Hypothesis testing in Cox models when continuous covariates are dichotomized: bias analysis and bootstrap-based test," Computational Statistics, Springer, vol. 40(2), pages 907-927, February.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:2:d:10.1007_s00180-024-01520-2
    DOI: 10.1007/s00180-024-01520-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-024-01520-2
    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/s00180-024-01520-2?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. Lausen, Berthold & Schumacher, Martin, 1996. "Evaluating the effect of optimized cutoff values in the assessment of prognostic factors," Computational Statistics & Data Analysis, Elsevier, vol. 21(3), pages 307-326, March.
    2. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
    3. Contal, Cecile & O'Quigley, John, 1999. "An application of changepoint methods in studying the effect of age on survival in breast cancer," Computational Statistics & Data Analysis, Elsevier, vol. 30(3), pages 253-270, May.
    4. Regina Nuzzo, 2014. "Scientific method: Statistical errors," Nature, Nature, vol. 506(7487), pages 150-152, February.
    5. Joel L. Horowitz, 2019. "Bootstrap Methods in Econometrics," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 193-224, August.
    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. Heinzl, Harald & Tempfer, Clemens, 2001. "A cautionary note on segmenting a cyclical covariate by minimum P-value search," Computational Statistics & Data Analysis, Elsevier, vol. 35(4), pages 451-461, February.
    2. Tunes-da-Silva, Gisela & Klein, John P., 2011. "Cutpoint selection for discretizing a continuous covariate for generalized estimating equations," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 226-235, January.
    3. Hollander, Norbert & Schumacher, Martin, 2006. "Estimating the functional form of a continuous covariate's effect on survival time," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 1131-1151, February.
    4. Yu-Min Huang, 2019. "Binary surrogates with stratified samples when weights are unknown," Computational Statistics, Springer, vol. 34(2), pages 653-682, June.
    5. Hothorn, Torsten & Lausen, Berthold, 2003. "On the exact distribution of maximally selected rank statistics," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 121-137, June.
    6. Ruijun Bu & Fredj Jawadi & Yuyi Li, 2020. "A multifactor transformed diffusion model with applications to VIX and VIX futures," Econometric Reviews, Taylor & Francis Journals, vol. 39(1), pages 27-53, January.
    7. Couaillier, Cyril & Scalone, Valerio, 2024. "Risk-to buffer: setting cyclical and structural banks capital requirements through stress test," Working Paper Series 2966, European Central Bank.
    8. Nyakabawo, Wendy & Miller, Stephen M. & Balcilar, Mehmet & Das, Sonali & Gupta, Rangan, 2015. "Temporal causality between house prices and output in the US: A bootstrap rolling-window approach," The North American Journal of Economics and Finance, Elsevier, vol. 33(C), pages 55-73.
    9. Stomberg, Christopher & White, Halbert, 2000. "Bootstrapping the Information Matrix Test," University of California at San Diego, Economics Working Paper Series qt158451cr, Department of Economics, UC San Diego.
    10. Jyotirmoy Sarkar, 2018. "Will P†Value Triumph over Abuses and Attacks?," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 7(4), pages 66-71, July.
    11. Stuart Peacock & Jeffrey Richardson, 2007. "Supplier-induced demand: re-examining identification and misspecification in cross-sectional analysis," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 8(3), pages 267-277, September.
    12. Queirós, Francisco, 2024. "Asset bubbles and product market competition," Theoretical Economics, Econometric Society, vol. 19(1), January.
    13. Zhang, Shulin & Song, Peter X.-K. & Shi, Daimin & Zhou, Qian M., 2012. "Information ratio test for model misspecification on parametric structures in stochastic diffusion models," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3975-3987.
    14. repec:ebl:ecbull:v:3:y:2008:i:5:p:1-7 is not listed on IDEAS
    15. James E. Prieger, "undated". "Conditional Moment Tests for Parametric Duration Models," Department of Economics 00-10, California Davis - Department of Economics.
    16. Felix Holzmeister & Magnus Johannesson & Robert Böhm & Anna Dreber & Jürgen Huber & Michael Kirchler, 2023. "Heterogeneity in effect size estimates: Empirical evidence and practical implications," Working Papers 2023-17, Faculty of Economics and Statistics, Universität Innsbruck.
    17. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(3), pages 361-376, June.
    18. Qiu, Zhiping & Peng, Limin & Manatunga, Amita & Guo, Ying, 2019. "A smooth nonparametric approach to determining cut-points of a continuous scale," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 186-210.
    19. Ozkan, F. Gulcin, 2003. "Explaining ERM realignments: Insights from optimising models of currency crises," Journal of Macroeconomics, Elsevier, vol. 25(4), pages 491-507, December.
    20. Zhenlin Yang, 2013. "LM Tests of Spatial Dependence Based on Bootstrap Critical Values," Working Papers 03-2013, Singapore Management University, School of Economics.
    21. Godfrey, L. G. & Veall, M. R., 1998. "Bootstrap-based critical values for tests of common factor restrictions," Economics Letters, Elsevier, vol. 59(1), pages 1-5, April.

    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:compst:v:40:y:2025:i:2:d:10.1007_s00180-024-01520-2. 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.