IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i3p559-573.html
   My bibliography  Save this article

Nonparametric regression models for right-censored data using Bernstein polynomials

Author

Listed:
  • Osman, Muhtarjan
  • Ghosh, Sujit K.

Abstract

In some applications of survival analysis with covariates, the commonly used semiparametric assumptions (e.g., proportional hazards) may turn out to be stringent and unrealistic, particularly when there is scientific background to believe that survival curves under different covariate combinations will cross during the study period. We present a new nonparametric regression model for the conditional hazard rate using a suitable sieve of Bernstein polynomials. The proposed nonparametric methodology has three key features: (i) the smooth estimator of the conditional hazard rate is shown to be a unique solution of a strictly convex optimization problem for a wide range of applications; making it computationally attractive, (ii) the model is shown to encompass a proportional hazards structure, and (iii) large sample properties including consistency and convergence rates are established under a set of mild regularity conditions. Empirical results based on several simulated data scenarios indicate that the proposed model has reasonably robust performance compared to other semiparametric models particularly when such semiparametric modeling assumptions are violated. The proposed method is further illustrated on the gastric cancer data and the Veterans Administration lung cancer data.

Suggested Citation

  • Osman, Muhtarjan & Ghosh, Sujit K., 2012. "Nonparametric regression models for right-censored data using Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 559-573.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:559-573
    DOI: 10.1016/j.csda.2011.08.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311003185
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2011.08.019?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. Axel Tenbusch, 1994. "Two-dimensional Bernstein polynomial density estimators," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 41(1), pages 233-253, December.
    2. Torben Martinussen, 2002. "A flexible additive multiplicative hazard model," Biometrika, Biometrika Trust, vol. 89(2), pages 283-298, June.
    3. Lu Tian & David Zucker & L.J. Wei, 2005. "On the Cox Model With Time-Varying Regression Coefficients," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 172-183, March.
    4. I‐Shou Chang & Chao A. Hsiung & Yuh‐Jenn Wu & Che‐Chi Yang, 2005. "Bayesian Survival Analysis Using Bernstein Polynomials," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 447-466, September.
    5. Zongwu Cai & Yanqing Sun, 2003. "Local Linear Estimation for Time‐Dependent Coefficients in Cox's Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 93-111, March.
    6. Dolton, Peter & O'Neill, Donal, 1996. "Unemployment Duration and the Restart Effect: Some Experimental Evidence," Economic Journal, Royal Economic Society, vol. 106(435), pages 387-400, March.
    7. Axel Tenbusch, 1997. "Nonparametric curve estimation with bernstein estimates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 1-30, January.
    8. Spierdijk, Laura, 2008. "Nonparametric conditional hazard rate estimation: A local linear approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2419-2434, January.
    9. Nidhan Choudhuri & Subhashis Ghosal & Anindya Roy, 2004. "Bayesian Estimation of the Spectral Density of a Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1050-1059, December.
    10. Murphy, S. A. & Sen, P. K., 1991. "Time-dependent coefficients in a Cox-type regression model," Stochastic Processes and their Applications, Elsevier, vol. 39(1), pages 153-180, October.
    11. Limin Peng & Yijian Huang, 2007. "Survival analysis with temporal covariate effects," Biometrika, Biometrika Trust, vol. 94(3), pages 719-733.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Roldán López de Hierro, Antonio Francisco & Martínez-Moreno, Juan & Aguilar Peña, Concepción & Roldán López de Hierro, Concepción, 2016. "A fuzzy regression approach using Bernstein polynomials for the spreads: Computational aspects and applications to economic models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 128(C), pages 13-25.
    2. Mirza Nazmul Hasan & Roel Braekers, 2022. "Modelling the association in bivariate survival data by using a Bernstein copula," Computational Statistics, Springer, vol. 37(2), pages 781-815, April.
    3. Ouimet, Frédéric, 2021. "Asymptotic properties of Bernstein estimators on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    4. Xiaoguang Wang & Ziwen Wang, 2021. "EM algorithm for the additive risk mixture cure model with interval-censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 91-130, January.
    5. Da Xu & Hui Zhao & Jianguo Sun, 2018. "Joint analysis of interval-censored failure time data and panel count data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 94-109, January.

    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. Alexandre Leblanc, 2010. "A bias-reduced approach to density estimation using Bernstein polynomials," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 459-475.
    2. Alexandre Leblanc, 2012. "On estimating distribution functions using Bernstein polynomials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 919-943, October.
    3. Guoqing Diao & Donglin Zeng & Song Yang, 2013. "Efficient Semiparametric Estimation of Short-Term and Long-Term Hazard Ratios with Right-Censored Data," Biometrics, The International Biometric Society, vol. 69(4), pages 840-849, December.
    4. Guoqing Diao & Anand N. Vidyashankar & Sarah Zohar & Sandrine Katsahian, 2021. "Competing Risks Model with Short-Term and Long-Term Covariate Effects for Cancer Studies," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(1), pages 142-159, April.
    5. Torben Martinussen & Odd O. Aalen & Thomas H. Scheike, 2008. "The Mizon–Richard Encompassing Test for the Cox and Aalen Additive Hazards Models," Biometrics, The International Biometric Society, vol. 64(1), pages 164-171, March.
    6. Jun Yan & Jian Huang, 2012. "Model Selection for Cox Models with Time-Varying Coefficients," Biometrics, The International Biometric Society, vol. 68(2), pages 419-428, June.
    7. Yanqing Sun & Rajeshwari Sundaram & Yichuan Zhao, 2009. "Empirical Likelihood Inference for the Cox Model with Time‐dependent Coefficients via Local Partial Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 444-462, September.
    8. Chin-Tsang Chiang & Mei-Cheng Wang, 2009. "Varying-coefficient model for the occurrence rate function of recurrent events," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 197-213, March.
    9. Chin-Tsang Chiang, 2011. "A more flexible joint latent model for longitudinal and survival time data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(2), pages 151-170, March.
    10. Xiao Song & C. Y. Wang, 2008. "Semiparametric Approaches for Joint Modeling of Longitudinal and Survival Data with Time-Varying Coefficients," Biometrics, The International Biometric Society, vol. 64(2), pages 557-566, June.
    11. Fei Heng & Yanqing Sun & Seunggeun Hyun & Peter B. Gilbert, 2020. "Analysis of the time-varying Cox model for the cause-specific hazard functions with missing causes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 731-760, October.
    12. Alexandre Leblanc, 2009. "Chung–Smirnov property for Bernstein estimators of distribution functions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(2), pages 133-142.
    13. Huazhen Lin & Zhe Fei & Yi Li, 2016. "A Semiparametrically Efficient Estimator of the Time-Varying Effects for Survival Data with Time-Dependent Treatment," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 649-663, September.
    14. Anderl, Eva & Schumann, Jan Hendrik & Kunz, Werner, 2016. "Helping Firms Reduce Complexity in Multichannel Online Data: A New Taxonomy-Based Approach for Customer Journeys," Journal of Retailing, Elsevier, vol. 92(2), pages 185-203.
    15. Yanqing Sun & Seunggeun Hyun & Peter Gilbert, 2008. "Testing and Estimation of Time-Varying Cause-Specific Hazard Ratios with Covariate Adjustment," Biometrics, The International Biometric Society, vol. 64(4), pages 1070-1079, December.
    16. Huazhen Lin & Hyokyoung G. Hong & Baoying Yang & Wei Liu & Yong Zhang & Gang-Zhi Fan & Yi Li, 2019. "Nonparametric Time-Varying Coefficient Models for Panel Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(3), pages 548-566, December.
    17. Hongyuan Cao & Mathew M. Churpek & Donglin Zeng & Jason P. Fine, 2015. "Analysis of the Proportional Hazards Model With Sparse Longitudinal Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1187-1196, September.
    18. Bouezmarni, Taoufik & Rombouts, Jeroen V.K. & Taamouti, Abderrahim, 2010. "Asymptotic properties of the Bernstein density copula estimator for [alpha]-mixing data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 1-10, January.
    19. Qu, Lianqiang & Song, Xinyuan & Sun, Liuquan, 2018. "Identification of local sparsity and variable selection for varying coefficient additive hazards models," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 119-135.
    20. Frédéric Ouimet, 2021. "General Formulas for the Central and Non-Central Moments of the Multinomial Distribution," Stats, MDPI, vol. 4(1), pages 1-10, 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:eee:csdana:v:56:y:2012:i:3:p:559-573. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.