IDEAS home Printed from https://ideas.repec.org/a/spr/stabio/v15y2023i1d10.1007_s12561-022-09357-3.html
   My bibliography  Save this article

Semiparametric Density Ratio Model for Survival Data with a Cure Fraction

Author

Listed:
  • Weibin Zhong

    (Bristol Myers Squibb)

  • Guoqing Diao

    (The George Washington University)

Abstract

The paper proposes a class of semiparametric transformation models for survival data with a cure fraction. Particularly, we assume a semiparametric density ratio model for the unknown proper conditional distribution function. The density ratio model is closely related to the generalized linear models and is desirable for modeling skewed survival data. We develop nonparametric likelihood-based estimation and inference procedures. Compared to some existing cure rate models, the estimation of the unknown proper baseline cumulative distribution function is more natural without imposing additional constraints. We establish the consistency and asymptotic normality of the proposed nonparametric maximum likelihood estimators. Extensive simulation studies demonstrate that the proposed methods perform well under practical settings. The proposed methods are also shown to be robust under certain model mis-specifications. We illustrate the proposed methods using two real applications.

Suggested Citation

  • Weibin Zhong & Guoqing Diao, 2023. "Semiparametric Density Ratio Model for Survival Data with a Cure Fraction," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 217-241, April.
    • Handle: RePEc:spr:stabio:v:15:y:2023:i:1:d:10.1007_s12561-022-09357-3
    DOI: 10.1007/s12561-022-09357-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12561-022-09357-3
    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/s12561-022-09357-3?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. Alan Huang & Paul J. Rathouz, 2012. "Proportional likelihood ratio models for mean regression," Biometrika, Biometrika Trust, vol. 99(1), pages 223-229.
    2. Zeng, Donglin & Lin, D.Y., 2007. "Efficient Estimation for the Accelerated Failure Time Model," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1387-1396, December.
    3. Wenbin Lu, 2004. "On semiparametric transformation cure models," Biometrika, Biometrika Trust, vol. 91(2), pages 331-343, June.
    4. Alan Huang, 2014. "Joint Estimation of the Mean and Error Distribution in Generalized Linear Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 186-196, March.
    5. Zhezhen Jin, 2003. "Rank-based inference for the accelerated failure time model," Biometrika, Biometrika Trust, vol. 90(2), pages 341-353, June.
    6. Yingwei Peng & Keith B. G. Dear, 2000. "A Nonparametric Mixture Model for Cure Rate Estimation," Biometrics, The International Biometric Society, vol. 56(1), pages 237-243, March.
    7. Li, Chin-Shang & Taylor, Jeremy M. G. & Sy, Judy P., 2001. "Identifiability of cure models," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 389-395, October.
    8. Li, Yi & Lin, Xihong, 2006. "Semiparametric Normal Transformation Models for Spatially Correlated Survival Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 591-603, June.
    9. Tsodikov A.D. & Ibrahim J.G. & Yakovlev A.Y., 2003. "Estimating Cure Rates From Survival Data: An Alternative to Two-Component Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1063-1078, January.
    10. Diao Guoqing & Ning Jing & qin jing, 2012. "Maximum Likelihood Estimation for Semiparametric Density Ratio Model," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-29, June.
    11. Zeng, Donglin & Yin, Guosheng & Ibrahim, Joseph G., 2006. "Semiparametric Transformation Models for Survival Data With a Cure Fraction," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 670-684, June.
    12. Guoqing Diao & Guosheng Yin, 2012. "A general transformation class of semiparametric cure rate frailty models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 959-989, October.
    13. D. Y. Lin & L. J. Wei & Z. Ying, 2002. "Model-Checking Techniques Based on Cumulative Residuals," Biometrics, The International Biometric Society, vol. 58(1), pages 1-12, March.
    14. Xiaodong Luo & Wei Yann Tsai, 2012. "A proportional likelihood ratio model," Biometrika, Biometrika Trust, vol. 99(1), pages 211-222.
    15. Marchese, Scott & Diao, Guoqing, 2017. "Density ratio model for multivariate outcomes," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 249-261.
    16. Rebecca A. Betensky & David A. Schoenfeld, 2001. "Nonparametric Estimation in a Cure Model with Random Cure Times," Biometrics, The International Biometric Society, vol. 57(1), pages 282-286, March.
    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. Guoqing Diao & Ao Yuan, 2019. "A class of semiparametric cure models with current status data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 26-51, January.
    2. Hanin, Leonid & Huang, Li-Shan, 2014. "Identifiability of cure models revisited," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 261-274.
    3. Hu, Tao & Xiang, Liming, 2016. "Partially linear transformation cure models for interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 257-269.
    4. Weibin Zhong & Guoqing Diao, 2023. "Joint semiparametric models for case‐cohort designs," Biometrics, The International Biometric Society, vol. 79(3), pages 1959-1971, September.
    5. Jue Hou & Christina D. Chambers & Ronghui Xu, 2018. "A nonparametric maximum likelihood approach for survival data with observed cured subjects, left truncation and right-censoring," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 612-651, October.
    6. Hu, Tao & Xiang, Liming, 2013. "Efficient estimation for semiparametric cure models with interval-censored data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 139-151.
    7. Lu Wang & Pang Du & Hua Liang, 2012. "Two-Component Mixture Cure Rate Model with Spline Estimated Nonparametric Components," Biometrics, The International Biometric Society, vol. 68(3), pages 726-735, September.
    8. Luis E. Nieto‐Barajas & Guosheng Yin, 2008. "Bayesian Semiparametric Cure Rate Model with an Unknown Threshold," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 540-556, September.
    9. Guoqing Diao & Guosheng Yin, 2012. "A general transformation class of semiparametric cure rate frailty models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 959-989, October.
    10. Yeqian Liu & Tao Hu & Jianguo Sun, 2017. "Regression analysis of current status data in the presence of a cured subgroup and dependent censoring," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(4), pages 626-650, October.
    11. Zhang, Jiajia & Peng, Yingwei & Li, Haifen, 2013. "A new semiparametric estimation method for accelerated hazards mixture cure model," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 95-102.
    12. Marchese, Scott & Diao, Guoqing, 2017. "Density ratio model for multivariate outcomes," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 249-261.
    13. Wenbin Lu, 2008. "Maximum likelihood estimation in the proportional hazards cure model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 545-574, September.
    14. Bremhorst, Vincent & Lambert, Philippe, 2013. "Flexible estimation in cure survival models using Bayesian P-splines," LIDAM Discussion Papers ISBA 2013039, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Xu, Linzhi & Zhang, Jiajia, 2010. "Multiple imputation method for the semiparametric accelerated failure time mixture cure model," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1808-1816, July.
    16. Weiyu Li & Valentin Patilea, 2018. "A dimension reduction approach for conditional Kaplan–Meier estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 295-315, June.
    17. Chen, Chyong-Mei & Lu, Tai-Fang C., 2012. "Marginal analysis of multivariate failure time data with a surviving fraction based on semiparametric transformation cure models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 645-655.
    18. Ana López-Cheda & Yingwei Peng & María Amalia Jácome, 2023. "Nonparametric estimation in mixture cure models with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 467-495, June.
    19. Bremhorst, Vincent & Lambert, Philippe, 2016. "Flexible estimation in cure survival models using Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 270-284.
    20. Yuan Mengdie & Diao Guoqing, 2014. "Semiparametric Odds Rate Model for Modeling Short-Term and Long-Term Effects with Application to a Breast Cancer Genetic Study," The International Journal of Biostatistics, De Gruyter, vol. 10(2), pages 1-19, November.

    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:15:y:2023:i:1:d:10.1007_s12561-022-09357-3. 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.