IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v117y2018icp194-206.html
   My bibliography  Save this article

Regression analysis for the proportional hazards model with parameter constraints under case-cohort design

Author

Listed:
  • Deng, Lifeng
  • Ding, Jieli
  • Liu, Yanyan
  • Wei, Chengdong

Abstract

To reduce the cost and improve the efficiency of cohort studies, case-cohort design is a widely used biased-sampling scheme for time-to-event data. In modeling process, case-cohort studies can benefit further from taking parameters’ prior information, such as the histological type and disease stage of the cancer in medical, the liquidity and market demand of the enterprise in finance. Regression analysis of the proportional hazards model with parameter constraints under case-cohort design is studied. Asymptotic properties are derived by applying the Lagrangian method based on Karush–Kuhn–Tucker conditions. The consistency and asymptotic normality of the constrained estimator are established. A modified minorization–maximization algorithm is developed for the calculation of the constrained estimator. Simulation studies are conducted to assess the finite-sample performance of the proposed method. An application to a Wilms tumor study demonstrates the utility of the proposed method in practice.

Suggested Citation

  • Deng, Lifeng & Ding, Jieli & Liu, Yanyan & Wei, Chengdong, 2018. "Regression analysis for the proportional hazards model with parameter constraints under case-cohort design," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 194-206.
    • Handle: RePEc:eee:csdana:v:117:y:2018:i:c:p:194-206
    DOI: 10.1016/j.csda.2017.08.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947317301937
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2017.08.013?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. Hunter D.R. & Lange K., 2004. "A Tutorial on MM Algorithms," The American Statistician, American Statistical Association, vol. 58, pages 30-37, February.
    2. Jinde Wang, 2000. "Approximate Representation of Estimators in Constrained Regression Problems," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 21-33, March.
    3. Donglin Zeng & D. Y. Lin, 2006. "Efficient estimation of semiparametric transformation models for counting processes," Biometrika, Biometrika Trust, vol. 93(3), pages 627-640, September.
    4. Shou-En Lu & Joanna H. Shih, 2006. "Case-Cohort Designs and Analysis for Clustered Failure Time Data," Biometrics, The International Biometric Society, vol. 62(4), pages 1138-1148, December.
    5. Donglin Zeng & D. Y. Lin, 2014. "Efficient Estimation of Semiparametric Transformation Models for Two-Phase Cohort Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 371-383, March.
    6. Wei Yann Tsai, 2009. "Pseudo-partial likelihood for proportional hazards models with biased-sampling data," Biometrika, Biometrika Trust, vol. 96(3), pages 601-615.
    7. Ding, Jieli & Tian, Guo-Liang & Yuen, Kam Chuen, 2015. "A new MM algorithm for constrained estimation in the proportional hazards model," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 135-151.
    8. N. E. Breslow & N. Chatterjee, 1999. "Design and analysis of two‐phase studies with binary outcome applied to Wilms tumour prognosis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(4), pages 457-468.
    9. Jianwen Cai & Donglin Zeng, 2007. "Power Calculation for Case–Cohort Studies with Nonrare Events," Biometrics, The International Biometric Society, vol. 63(4), pages 1288-1295, December.
    10. Qi, Lihong & Wang, C.Y. & Prentice, Ross L., 2005. "Weighted Estimators for Proportional Hazards Regression With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1250-1263, December.
    11. S. Kang & J. Cai, 2009. "Marginal hazards model for case-cohort studies with multiple disease outcomes," Biometrika, Biometrika Trust, vol. 96(4), pages 887-901.
    12. Tian, Guo-Liang & Ng, Kai Wang & Tan, Ming, 2008. "EM-type algorithms for computing restricted MLEs in multivariate normal distributions and multivariate t-distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4768-4778, 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. Jieli Ding & Tsui-Shan Lu & Jianwen Cai & Haibo Zhou, 2017. "Recent progresses in outcome-dependent sampling with failure time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 57-82, January.
    2. Qingning Zhou & Jianwen Cai & Haibo Zhou, 2018. "Outcome†dependent sampling with interval†censored failure time data," Biometrics, The International Biometric Society, vol. 74(1), pages 58-67, March.
    3. Jon Arni Steingrimsson & Robert L. Strawderman, 2017. "Estimation in the Semiparametric Accelerated Failure Time Model With Missing Covariates: Improving Efficiency Through Augmentation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1221-1235, July.
    4. Yayun Xu & Soyoung Kim & Mei-Jie Zhang & David Couper & Kwang Woo Ahn, 2022. "Competing risks regression models with covariates-adjusted censoring weight under the generalized case-cohort design," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(2), pages 241-262, April.
    5. Ding, Jieli & Tian, Guo-Liang & Yuen, Kam Chuen, 2015. "A new MM algorithm for constrained estimation in the proportional hazards model," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 135-151.
    6. Mingzhe Wu & Ming Zheng & Wen Yu & Ruofan Wu, 2018. "Estimation and variable selection for semiparametric transformation models under a more efficient cohort sampling design," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 570-596, September.
    7. Chyong-Mei Chen & Pao-sheng Shen & Yi Liu, 2021. "On semiparametric transformation model with LTRC data: pseudo likelihood approach," Statistical Papers, Springer, vol. 62(1), pages 3-30, February.
    8. Soyoung Kim & Donglin Zeng & Jianwen Cai, 2018. "Analysis of multiple survival events in generalized case‐cohort designs," Biometrics, The International Biometric Society, vol. 74(4), pages 1250-1260, December.
    9. Erik T. Parner & Per K. Andersen & Morten Overgaard, 2020. "Cumulative risk regression in case–cohort studies using pseudo-observations," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 639-658, October.
    10. Yichen Lou & Peijie Wang & Jianguo Sun, 2023. "A semi-parametric weighted likelihood approach for regression analysis of bivariate interval-censored outcomes from case-cohort studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 628-653, July.
    11. 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.
    12. 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.
    13. Yu-Jen Cheng & Chiung-Yu Huang, 2014. "Combined estimating equation approaches for semiparametric transformation models with length-biased survival data," Biometrics, The International Biometric Society, vol. 70(3), pages 608-618, September.
    14. Ying Yan & Haibo Zhou & Jianwen Cai, 2017. "Improving efficiency of parameter estimation in case-cohort studies with multivariate failure time data," Biometrics, The International Biometric Society, vol. 73(3), pages 1042-1052, September.
    15. Qingning Zhou & Jianwen Cai & Haibo Zhou, 2020. "Semiparametric inference for a two-stage outcome-dependent sampling design with interval-censored failure time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 85-108, January.
    16. Jichang Yu & Haibo Zhou & Jianwen Cai, 2021. "Accelerated failure time model for data from outcome-dependent sampling," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 15-37, January.
    17. Na Hu & Xuerong Chen & Jianguo Sun, 2015. "Regression Analysis of Length-biased and Right-censored Failure Time Data with Missing Covariates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 438-452, June.
    18. Poulami Maitra & Leila D. A. F. Amorim & Jianwen Cai, 2020. "Multiplicative rates model for recurrent events in case-cohort studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 134-157, January.
    19. Qui Tran & Kelley M. Kidwell & Alex Tsodikov, 2018. "A joint model of cancer incidence, metastasis, and mortality," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(3), pages 385-406, July.
    20. Torben Martinussen & Klaus K. Holst & Thomas H. Scheike, 2016. "Cox regression with missing covariate data using a modified partial likelihood method," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 570-588, October.

    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:117:y:2018:i:c:p:194-206. 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.