IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v25y2016i4d10.1007_s11749-015-0468-9.html
   My bibliography  Save this article

Testing for decreasing heterogeneity in a new time-varying frailty model

Author

Listed:
  • Marco Munda

    (Université catholique de Louvain)

  • Catherine Legrand

    (Université catholique de Louvain)

  • Luc Duchateau

    (Faculty of Veterinary Medicine Ghent University)

  • Paul Janssen

    (Hasselt University)

Abstract

Frailty models adjust for between-cluster variability in survival data by including a cluster-specific random factor, the frailty term, in the Cox model. The frailty term is assumed to be constant over time. This assumption is questionable in some particular settings, e.g., in cancer clinical trials on chronic myeloid leukaemia. We therefore relax the time-constant heterogeneity assumption and consider frailty models with a time-varying frailty term. Instead of working with hazard models, we rather model the log cumulative hazard function, making use of the mixed model framework, and introduce a time-varying random effect at that level. Simulations demonstrate that the proposed method has acceptable size and power to detect time-dependent clustering. The method is applied to data from a large-scale multicentre clinical trial in patients with chronic myeloid leukaemia.

Suggested Citation

  • Marco Munda & Catherine Legrand & Luc Duchateau & Paul Janssen, 2016. "Testing for decreasing heterogeneity in a new time-varying frailty model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 591-606, December.
    • Handle: RePEc:spr:testjl:v:25:y:2016:i:4:d:10.1007_s11749-015-0468-9
    DOI: 10.1007/s11749-015-0468-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-015-0468-9
    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/s11749-015-0468-9?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. Teodorescu, B. & Van Keilegom, I., 2010. "A goodness-of-fit test for generalised conditional linear models under left truncation and right censoring," LIDAM Reprints ISBA 2010019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. K. F. Lam & Y. W. Lee & T. L. Leung, 2002. "Modeling Multivariate Survival Data by a Semiparametric Random Effects Proportional Odds Model," Biometrics, The International Biometric Society, vol. 58(2), pages 316-323, June.
    3. Bianca Teodorescu & Ingrid Van Keilegom, 2010. "A goodness-of-fit test for generalised conditional linear models under left truncation and right censoring," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 547-566.
    4. Teodorescu, B. & Van Keilegom, I. & Cao, R., 2010. "Generalized time-dependent conditional linear models under left truncation and right censoring," LIDAM Reprints ISBA 2010014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Goele Massonnet & Paul Janssen & Tomasz Burzykowski, 2008. "Fitting Conditional Survival Models to Meta‐Analytic Data by Using a Transformation Toward Mixed‐Effects Models," Biometrics, The International Biometric Society, vol. 64(3), pages 834-842, September.
    6. Michael L. Pennell & David B. Dunson, 2006. "Bayesian Semiparametric Dynamic Frailty Models for Multiple Event Time Data," Biometrics, The International Biometric Society, vol. 62(4), pages 1044-1052, December.
    7. Bianca Teodorescu & Ingrid Keilegom & Ricardo Cao, 2010. "Generalized time-dependent conditional linear models under left truncation and right censoring," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(3), pages 465-485, June.
    8. Gerda Claeskens & Rosemary Nguti & Paul Janssen, 2008. "One-sided tests in shared frailty models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 69-82, May.
    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. Legrand, Catherine & Munda, Marco & Janssen, P. & Duchateau, L., 2012. "A general class of time-varying coefficients models for right censored data," LIDAM Discussion Papers ISBA 2012041, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    3. Dennis Schmidt & Rainer Schwabe, 2015. "On optimal designs for censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 237-257, April.
    4. Bijwaard, Govert, 2011. "Unobserved Heterogeneity in Multiple-Spell Multiple-States Duration Models," IZA Discussion Papers 5748, Institute of Labor Economics (IZA).
    5. Rondeau, Virginie & Marzroui, Yassin & Gonzalez, Juan R., 2012. "frailtypack: An R Package for the Analysis of Correlated Survival Data with Frailty Models Using Penalized Likelihood Estimation or Parametrical Estimation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 47(i04).
    6. Bedair, Khaled & Hong, Yili & Li, Jie & Al-Khalidi, Hussein R., 2016. "Multivariate frailty models for multi-type recurrent event data and its application to cancer prevention trial," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 161-173.
    7. Igari, Ryosuke & Hoshino, Takahiro, 2018. "A Bayesian data combination approach for repeated durations under unobserved missing indicators: Application to interpurchase-timing in marketing," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 150-166.
    8. Bas Straathof & Sander van Veldhuizen, 2012. "Market size, institutions, and the value of rights provided by patents," CPB Discussion Paper 226, CPB Netherlands Bureau for Economic Policy Analysis.
    9. Li, Xiaohu & Lin, Jianhua, 2011. "Stochastic orders in time transformed exponential models with applications," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 47-52, July.
    10. Ram Thapa & Harold E. Burkhart & Jie Li & Yili Hong, 2016. "Modeling Clustered Survival Times of Loblolly Pine with Time-dependent Covariates and Shared Frailties," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(1), pages 92-110, March.
    11. Munda, Marco & Rotolo, Federico & Legrand, Catherine, 2012. "parfm: Parametric Frailty Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i11).
    12. Paul Embrechts & Marius Hofert, 2011. "Comments on: Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 263-270, August.
    13. Ramesh Gupta, 2016. "Properties of additive frailty model in survival analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 1-17, January.
    14. Balkema, A.A. & Embrechts, P. & Nolde, N., 2010. "Meta densities and the shape of their sample clouds," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1738-1754, August.
    15. Neil Murray & Heike Link, 2020. "A Duration Approach for Estimating the Marginal Renewal Cost at German Motorways," Discussion Papers of DIW Berlin 1898, DIW Berlin, German Institute for Economic Research.
    16. Virginia Zarulli, 2016. "Unobserved Heterogeneity of Frailty in the Analysis of Socioeconomic Differences in Health and Mortality," European Journal of Population, Springer;European Association for Population Studies, vol. 32(1), pages 55-72, February.
    17. Timothy Hanson & Mingan Yang, 2007. "Bayesian Semiparametric Proportional Odds Models," Biometrics, The International Biometric Society, vol. 63(1), pages 88-95, March.
    18. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2014. "Beta-product dependent Pitman–Yor processes for Bayesian inference," Journal of Econometrics, Elsevier, vol. 180(1), pages 49-72.
    19. Balakrishnan, N. & Pal, Suvra, 2013. "Lognormal lifetimes and likelihood-based inference for flexible cure rate models based on COM-Poisson family," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 41-67.
    20. Wensheng Zhu & Yuan Jiang & Heping Zhang, 2012. "Nonparametric Covariate-Adjusted Association Tests Based on the Generalized Kendall's Tau," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 1-11, March.

    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:testjl:v:25:y:2016:i:4:d:10.1007_s11749-015-0468-9. 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.