IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v73y2021i5d10.1007_s10463-020-00774-z.html
   My bibliography  Save this article

Generalized inverse-Gaussian frailty models with application to TARGET neuroblastoma data

Author

Listed:
  • Luiza S. C. Piancastelli

    (University College Dublin
    Universidade Federal de Minas Gerais)

  • Wagner Barreto-Souza

    (King Abdullah University of Science and Technology
    Universidade Federal de Minas Gerais)

  • Vinícius D. Mayrink

    (Universidade Federal de Minas Gerais)

Abstract

A new class of survival frailty models based on the generalized inverse-Gaussian (GIG) distributions is proposed. We show that the GIG frailty models are flexible and mathematically convenient like the popular gamma frailty model. A piecewise-exponential baseline hazard function is employed, yielding flexibility for the proposed class. Although a closed-form observed log-likelihood function is available, simulation studies show that employing an EM-algorithm is advantageous concerning the direct maximization of this function. Further simulated results address the comparison of different methods for obtaining standard errors of the estimates and confidence intervals for the parameters. Additionally, the finite-sample behavior of the EM-estimators is investigated and the performance of the GIG models under misspecification assessed. We apply our methodology to a TARGET (Therapeutically Applicable Research to Generate Effective Treatments) data about the survival time of patients with neuroblastoma cancer and show some advantages of the GIG frailties over existing models in the literature.

Suggested Citation

  • Luiza S. C. Piancastelli & Wagner Barreto-Souza & Vinícius D. Mayrink, 2021. "Generalized inverse-Gaussian frailty models with application to TARGET neuroblastoma data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 979-1010, October.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:5:d:10.1007_s10463-020-00774-z
    DOI: 10.1007/s10463-020-00774-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-020-00774-z
    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/s10463-020-00774-z?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. Wagner Barreto-Souza & Vinícius Diniz Mayrink, 2019. "Semiparametric generalized exponential frailty model for clustered survival data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 679-701, June.
    2. 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.
    3. Duchateau, Luc & Janssen, Paul & Lindsey, Patrick & Legrand, Catherine & Nguti, Rosemary & Sylvester, Richard, 2002. "The shared frailty model and the power for heterogeneity tests in multicenter trials," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 603-620, September.
    4. Peng, Mengjiao & Xiang, Liming & Wang, Shanshan, 2018. "Semiparametric regression analysis of clustered survival data with semi-competing risks," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 53-70.
    5. Vu, Hien T. V. & Knuiman, Matthew W., 2002. "A hybrid ML-EM algorithm for calculation of maximum likelihood estimates in semiparametric shared frailty models," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 173-187, July.
    6. Chen, Pengcheng & Zhang, Jiajia & Zhang, Riquan, 2013. "Estimation of the accelerated failure time frailty model under generalized gamma frailty," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 171-180.
    7. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
    8. D. Zeng & D. Y. Lin, 2007. "Maximum likelihood estimation in semiparametric regression models with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 507-564, September.
    9. C. Paddy Farrington & Steffen Unkel & Karim Anaya-Izquierdo, 2012. "The relative frailty variance and shared frailty models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(4), pages 673-696, September.
    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. Bodunrin Brown & Bin Liu & Stuart McIntyre & Matthew Revie, 2023. "Reliability evaluation of repairable systems considering component heterogeneity using frailty model," Journal of Risk and Reliability, , vol. 237(4), pages 654-670, August.

    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. 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.
    2. 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.
    3. Steven Abrams & Marc Aerts & Geert Molenberghs & Niel Hens, 2017. "Parametric overdispersed frailty models for current status data," Biometrics, The International Biometric Society, vol. 73(4), pages 1388-1400, December.
    4. Bo-Hong Wu & Hirofumi Michimae & Takeshi Emura, 2020. "Meta-analysis of individual patient data with semi-competing risks under the Weibull joint frailty–copula model," Computational Statistics, Springer, vol. 35(4), pages 1525-1552, December.
    5. Mojtaba Ganjali & T. Baghfalaki & D. Berridge, 2014. "A Bayesian Analysis of Unobserved Heterogeneity for Unemployment Duration Data in the Presence of Interval Censoring," International Econometric Review (IER), Econometric Research Association, vol. 6(1), pages 24-41, April.
    6. Qiu, Zhiping & Zhou, Yong, 2015. "Partially linear transformation models with varying coefficients for multivariate failure time data," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 144-166.
    7. Li, Shuwei & Hu, Tao & Zhao, Xingqiu & Sun, Jianguo, 2019. "A class of semiparametric transformation cure models for interval-censored failure time data," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 153-165.
    8. Xi Ning & Yinghao Pan & Yanqing Sun & Peter B. Gilbert, 2023. "A semiparametric Cox–Aalen transformation model with censored data," Biometrics, The International Biometric Society, vol. 79(4), pages 3111-3125, December.
    9. Tianxi Cai & Thomas A Gerds & Yingye Zheng & Jinbo Chen, 2011. "Robust Prediction of t-Year Survival with Data from Multiple Studies," Biometrics, The International Biometric Society, vol. 67(2), pages 436-444, June.
    10. Chi-Chung Wen & Yi-Hau Chen, 2014. "Semiparametric analysis of incomplete current status outcome data under transformation models," Biometrics, The International Biometric Society, vol. 70(2), pages 335-345, June.
    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. Lu Mao & D. Y. Lin, 2017. "Efficient estimation of semiparametric transformation models for the cumulative incidence of competing risks," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 573-587, March.
    13. Chia-Hui Huang, 2019. "Mixture regression models for the gap time distributions and illness–death processes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 168-188, January.
    14. Munda, Marco & Rotolo, Federico & Legrand, Catherine, 2012. "parfm: Parametric Frailty Models in R," LIDAM Discussion Papers ISBA 2012005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Sukhmani Sidhu & Kanchan Jain & Suresh Kumar Sharma, 2018. "Bayesian estimation of generalized gamma shared frailty model," Computational Statistics, Springer, vol. 33(1), pages 277-297, March.
    16. Yi‐Hau Chen, 2010. "Semiparametric marginal regression analysis for dependent competing risks under an assumed copula," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 235-251, March.
    17. Abrahantes, Jose Cortinas & Legrand, Catherine & Burzykowski, Tomasz & Janssen, Paul & Ducrocq, Vincent & Duchateau, Luc, 2007. "Comparison of different estimation procedures for proportional hazards model with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3913-3930, May.
    18. Yu‐Jen Cheng & Yen‐Chun Liu & Chang‐Yu Tsai & Chiung‐Yu Huang, 2023. "Semiparametric estimation of the transformation model by leveraging external aggregate data in the presence of population heterogeneity," Biometrics, The International Biometric Society, vol. 79(3), pages 1996-2009, September.
    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. Lu Chen & Li Hsu & Kathleen Malone, 2009. "A Frailty-Model-Based Approach to Estimating the Age-Dependent Penetrance Function of Candidate Genes Using Population-Based Case-Control Study Designs: An Application to Data on the BRCA1 Gene," Biometrics, The International Biometric Society, vol. 65(4), pages 1105-1114, December.

    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:aistmt:v:73:y:2021:i:5:d:10.1007_s10463-020-00774-z. 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.