IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v33y2018i1d10.1007_s00180-017-0728-0.html
   My bibliography  Save this article

Bayesian estimation of generalized gamma shared frailty model

Author

Listed:
  • Sukhmani Sidhu

    (Panjab University)

  • Kanchan Jain

    (Panjab University)

  • Suresh Kumar Sharma

    (Panjab University)

Abstract

Multivariate survival analysis comprises of event times that are generally grouped together in clusters. Observations in each of these clusters relate to data belonging to the same individual or individuals with a common factor. Frailty models can be used when there is unaccounted association between survival times of a cluster. The frailty variable describes the heterogeneity in the data caused by unknown covariates or randomness in the data. In this article, we use the generalized gamma distribution to describe the frailty variable and discuss the Bayesian method of estimation for the parameters of the model. The baseline hazard function is assumed to follow the two parameter Weibull distribution. Data is simulated from the given model and the Metropolis–Hastings MCMC algorithm is used to obtain parameter estimates. It is shown that increasing the size of the dataset improves estimates. It is also shown that high heterogeneity within clusters does not affect the estimates of treatment effects significantly. The model is also applied to a real life dataset.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:1:d:10.1007_s00180-017-0728-0
    DOI: 10.1007/s00180-017-0728-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-017-0728-0
    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/s00180-017-0728-0?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. 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.
    2. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    3. Golightly, A. & Wilkinson, D.J., 2008. "Bayesian inference for nonlinear multivariate diffusion models observed with error," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1674-1693, January.
    4. Julian P. T. Higgins & Simon G. Thompson & David J. Spiegelhalter, 2009. "A re‐evaluation of random‐effects meta‐analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(1), pages 137-159, January.
    5. Koop, Gary & Osiewalski, Jacek & Steel, Mark F. J., 1997. "Bayesian efficiency analysis through individual effects: Hospital cost frontiers," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 77-105.
    6. Philip Heidelberger & Peter D. Welch, 1983. "Simulation Run Length Control in the Presence of an Initial Transient," Operations Research, INFORMS, vol. 31(6), pages 1109-1144, December.
    7. 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.
    8. 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.
    9. Allenby, Greg M. & Rossi, Peter E., 1998. "Marketing models of consumer heterogeneity," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 57-78, November.
    10. 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.
    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. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    2. Zellner, Arnold & Ando, Tomohiro, 2010. "A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model," Journal of Econometrics, Elsevier, vol. 159(1), pages 33-45, November.
    3. Han Shang, 2014. "Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density," Computational Statistics, Springer, vol. 29(3), pages 829-848, June.
    4. 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.
    5. Elizabeth Wrigley-Field, 2020. "Multidimensional Mortality Selection: Why Individual Dimensions of Frailty Don’t Act Like Frailty," Demography, Springer;Population Association of America (PAA), vol. 57(2), pages 747-777, April.
    6. William Griffiths & Xiaohui Zhang & Xueyan Zhao, 2010. "A Stochastic Frontier Model for Discrete Ordinal Outcomes: A Health Production Function," Monash Econometrics and Business Statistics Working Papers 3/10, Monash University, Department of Econometrics and Business Statistics.
    7. Andreas Wienke & Konstantin G. Arbeev & Isabella Locatelli & Anatoli I. Yashin, 2003. "A simulation study of different correlated frailty models and estimation strategies," MPIDR Working Papers WP-2003-018, Max Planck Institute for Demographic Research, Rostock, Germany.
    8. Guohua Feng & Todd Jewell, 2021. "Productivity and efficiency at english football clubs: a random coefficient approach," Scottish Journal of Political Economy, Scottish Economic Society, vol. 68(5), pages 571-604, November.
    9. Steven M. Shugan, 2006. "Editorial: Errors in the Variables, Unobserved Heterogeneity, and Other Ways of Hiding Statistical Error," Marketing Science, INFORMS, vol. 25(3), pages 203-216, 05-06.
    10. Y. K. Tse & Xibin Zhang & Jun Yu, 2004. "Estimation of hyperbolic diffusion using the Markov chain Monte Carlo method," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 158-169.
    11. Yu, Jun, 2012. "A semiparametric stochastic volatility model," Journal of Econometrics, Elsevier, vol. 167(2), pages 473-482.
    12. 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.
    13. David B. Dunson & Zhen Chen, 2004. "Selecting Factors Predictive of Heterogeneity in Multivariate Event Time Data," Biometrics, The International Biometric Society, vol. 60(2), pages 352-358, June.
    14. Il Do Ha & Maengseok Noh & Youngjo Lee, 2010. "Bias Reduction of Likelihood Estimators in Semiparametric Frailty Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 307-320, June.
    15. Loaiza-Maya, Rubén & Smith, Michael Stanley & Nott, David J. & Danaher, Peter J., 2022. "Fast and accurate variational inference for models with many latent variables," Journal of Econometrics, Elsevier, vol. 230(2), pages 339-362.
    16. Guohua Feng & Chuan Wang & Xibin Zhang, 2019. "Estimation of inefficiency in stochastic frontier models: a Bayesian kernel approach," Journal of Productivity Analysis, Springer, vol. 51(1), pages 1-19, February.
    17. Jing Wang, 2019. "Weighted estimation for multivariate shared frailty models for complex surveys," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 469-479, July.
    18. Sicsic, Jonathan & Krucien, Nicolas & Franc, Carine, 2016. "What are GPs' preferences for financial and non-financial incentives in cancer screening? Evidence for breast, cervical, and colorectal cancers," Social Science & Medicine, Elsevier, vol. 167(C), pages 116-127.
    19. Djeundje, Viani Biatat & Crook, Jonathan, 2018. "Incorporating heterogeneity and macroeconomic variables into multi-state delinquency models for credit cards," European Journal of Operational Research, Elsevier, vol. 271(2), pages 697-709.
    20. Xiaohui Zhang & Katharina Hauck & Xueyan Zhao, 2013. "Patient Safety In Hospitals – A Bayesian Analysis Of Unobservable Hospital And Specialty Level Risk Factors," Health Economics, John Wiley & Sons, Ltd., vol. 22(9), pages 1158-1174, September.

    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:compst:v:33:y:2018:i:1:d:10.1007_s00180-017-0728-0. 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.