IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v76y2020i3p753-766.html
   My bibliography  Save this article

A bivariate joint frailty model with mixture framework for survival analysis of recurrent events with dependent censoring and cure fraction

Author

Listed:
  • Richard Tawiah
  • Geoffrey J. McLachlan
  • Shu Kay Ng

Abstract

In the study of multiple failure time data with recurrent clinical endpoints, the classical independent censoring assumption in survival analysis can be violated when the evolution of the recurrent events is correlated with a censoring mechanism such as death. Moreover, in some situations, a cure fraction appears in the data because a tangible proportion of the study population benefits from treatment and becomes recurrence free and insusceptible to death related to the disease. A bivariate joint frailty mixture cure model is proposed to allow for dependent censoring and cure fraction in recurrent event data. The latency part of the model consists of two intensity functions for the hazard rates of recurrent events and death, wherein a bivariate frailty is introduced by means of the generalized linear mixed model methodology to adjust for dependent censoring. The model allows covariates and frailties in both the incidence and the latency parts, and it further accounts for the possibility of cure after each recurrence. It includes the joint frailty model and other related models as special cases. An expectation‐maximization (EM)‐type algorithm is developed to provide residual maximum likelihood estimation of model parameters. Through simulation studies, the performance of the model is investigated under different magnitudes of dependent censoring and cure rate. The model is applied to data sets from two colorectal cancer studies to illustrate its practical value.

Suggested Citation

  • Richard Tawiah & Geoffrey J. McLachlan & Shu Kay Ng, 2020. "A bivariate joint frailty model with mixture framework for survival analysis of recurrent events with dependent censoring and cure fraction," Biometrics, The International Biometric Society, vol. 76(3), pages 753-766, September.
    • Handle: RePEc:bla:biomet:v:76:y:2020:i:3:p:753-766
    DOI: 10.1111/biom.13202
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13202
    Download Restriction: no
    File URL: https://libkey.io/10.1111/biom.13202?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
    ---><---

    References listed on IDEAS

    as
    1. Judy P. Sy & Jeremy M. G. Taylor, 2000. "Estimation in a Cox Proportional Hazards Cure Model," Biometrics, The International Biometric Society, vol. 56(1), pages 227-236, March.
    2. Peng, Yingwei, 2003. "Estimating baseline distribution in proportional hazards cure models," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 187-201, February.
    3. Xuelin Huang & Robert A. Wolfe, 2002. "A Frailty Model for Informative Censoring," Biometrics, The International Biometric Society, vol. 58(3), pages 510-520, September.
    4. Lei Liu & Robert A. Wolfe & Xuelin Huang, 2004. "Shared Frailty Models for Recurrent Events and a Terminal Event," Biometrics, The International Biometric Society, vol. 60(3), pages 747-756, September.
    5. Debashis Ghosh & D. Y. Lin, 2003. "Semiparametric Analysis of Recurrent Events Data in the Presence of Dependent Censoring," Biometrics, The International Biometric Society, vol. 59(4), pages 877-885, December.
    6. Nader Ebrahimi, 2003. "Identifiability and censored data," Biometrika, Biometrika Trust, vol. 90(3), pages 724-727, September.
    7. 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.
    8. Samuli Ripatti & Juni Palmgren, 2000. "Estimation of Multivariate Frailty Models Using Penalized Partial Likelihood," Biometrics, The International Biometric Society, vol. 56(4), pages 1016-1022, December.
    9. Andreas Wienke & Paul Lichtenstein & Anatoli I. Yashin, 2003. "A Bivariate Frailty Model with a Cure Fraction for Modeling Familial Correlations in Diseases," Biometrics, The International Biometric Society, vol. 59(4), pages 1178-1183, December.
    10. López-Cheda, Ana & Cao, Ricardo & Jácome, M. Amalia & Van Keilegom, Ingrid, 2017. "Nonparametric incidence estimation and bootstrap bandwidth selection in mixture cure models," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 144-165.
    11. Lopez-Cheda, Ana & Cao, Ricardo & Jacome, Amalia & Van Keilegom, Ingrid, 2017. "Nonparametric incidence estimation and bootstrap bandwidth selection in mixture cure models," LIDAM Reprints ISBA 2017001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Lei Liu & Xuelin Huang & Alex Yaroshinsky & Janice N. Cormier, 2016. "Joint frailty models for zero-inflated recurrent events in the presence of a terminal event," Biometrics, The International Biometric Society, vol. 72(1), pages 204-214, March.
    13. Kelvin K. W. Yau, 2001. "Multilevel Models for Survival Analysis with Random Effects," Biometrics, The International Biometric Society, vol. 57(1), pages 96-102, March.
    14. 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.
    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. Shuangshuang Xu & Marco A. R. Ferreira & Erica M. Porter & Christopher T. Franck, 2023. "Bayesian model selection for generalized linear mixed models," Biometrics, The International Biometric Society, vol. 79(4), pages 3266-3278, December.

    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. Dongxiao Han & Xiaogang Su & Liuquan Sun & Zhou Zhang & Lei Liu, 2020. "Variable selection in joint frailty models of recurrent and terminal events," Biometrics, The International Biometric Society, vol. 76(4), pages 1330-1339, December.
    2. Narisetty, Naveen & Koenker, Roger, 2022. "Censored quantile regression survival models with a cure proportion," Journal of Econometrics, Elsevier, vol. 226(1), pages 192-203.
    3. Lei Liu & Xuelin Huang & John O'Quigley, 2008. "Analysis of Longitudinal Data in the Presence of Informative Observational Times and a Dependent Terminal Event, with Application to Medical Cost Data," Biometrics, The International Biometric Society, vol. 64(3), pages 950-958, September.
    4. C.-Y. Huang & J. Qin & M.-C. Wang, 2010. "Semiparametric Analysis for Recurrent Event Data with Time-Dependent Covariates and Informative Censoring," Biometrics, The International Biometric Society, vol. 66(1), pages 39-49, March.
    5. Patilea, Valentin & Van Keilegom, Ingrid, 2017. "A general approach for cure models in survival analysis," LIDAM Discussion Papers ISBA 2017008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Peizhi Li & Yingwei Peng & Ping Jiang & Qingli Dong, 2020. "A support vector machine based semiparametric mixture cure model," Computational Statistics, Springer, vol. 35(3), pages 931-945, September.
    7. Justin Chown & Cédric Heuchenne & Ingrid Van Keilegom, 2020. "The nonparametric location-scale mixture cure model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1008-1028, December.
    8. Ana López-Cheda & M. Amalia Jácome & Ricardo Cao, 2017. "Nonparametric latency estimation for mixture cure models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 353-376, June.
    9. Peláez, Rebeca & Van Keilegom, Ingrid & Cao, Ricardo & Vilar, Juan M., 2024. "Probability of default estimation in credit risk using mixture cure models," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    10. Philippe Lambert & Vincent Bremhorst, 2020. "Inclusion of time‐varying covariates in cure survival models with an application in fertility studies," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 333-354, January.
    11. Suvra Pal & Yingwei Peng & Wisdom Aselisewine, 2024. "A new approach to modeling the cure rate in the presence of interval censored data," Computational Statistics, Springer, vol. 39(5), pages 2743-2769, July.
    12. Motahareh Parsa & Ingrid Van Keilegom, 2023. "Accelerated failure time vs Cox proportional hazards mixture cure models: David vs Goliath?," Statistical Papers, Springer, vol. 64(3), pages 835-855, June.
    13. Yimei Li & Liang Zhu & Lei Liu & Leslie L. Robison, 2021. "Regression Analysis of Mixed Panel-Count Data with Application to Cancer Studies," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(1), pages 178-195, April.
    14. Wende Clarence Safari & Ignacio López-de-Ullibarri & María Amalia Jácome, 2023. "Latency function estimation under the mixture cure model when the cure status is available," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 608-627, July.
    15. Yassin Mazroui & Audrey Mauguen & Simone Mathoulin-Pélissier & Gaetan MacGrogan & Véronique Brouste & Virginie Rondeau, 2016. "Time-varying coefficients in a multivariate frailty model: Application to breast cancer recurrences of several types and death," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(2), pages 191-215, April.
    16. 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.
    17. Giuliana Cortese & Thomas H. Scheike, 2022. "Efficient estimation of the marginal mean of recurrent events," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1787-1821, November.
    18. George, Morris & Kumar, V. & Grewal, Dhruv, 2013. "Maximizing Profits for a Multi-Category Catalog Retailer," Journal of Retailing, Elsevier, vol. 89(4), pages 374-396.
    19. Guillaume Horny & Dragana Djurdjevic & Bernhard Boockmann & François Laisney, 2008. "Bayesian Estimation of Cox Models with Non-nested Random Effects: an Application to the Ratification Of ILO Conventions by Developing Countries," Annals of Economics and Statistics, GENES, issue 89, pages 193-214.
    20. 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).

    More about this item

    Statistics

    Access and download statistics

    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:bla:biomet:v:76:y:2020:i:3:p:753-766. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    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.