IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i6p1303-1318.html
   My bibliography  Save this article

Frailty modeling via the empirical Bayes–Hastings sampler

Author

Listed:
  • Levine, Richard A.
  • Fan, Juanjuan
  • Strickland, Pamela Ohman
  • Demirel, Shaban

Abstract

Studies of ocular disease and analyses of time to disease onset are complicated by the correlation expected between the two eyes from a single patient. We overcome these statistical modeling challenges through a nonparametric Bayesian frailty model. While this model suggests itself as a natural one for such complex data structures, model fitting routines become overwhelmingly complicated and computationally intensive given the nonparametric form assumed for the frailty distribution and baseline hazard function. We consider empirical Bayesian methods to alleviate these difficulties through a routine that iterates between frequentist, data-driven estimation of the cumulative baseline hazard and Markov chain Monte Carlo estimation of the frailty and regression coefficients. We show both in theory and through simulation that this approach yields consistent estimators of the parameters of interest. We then apply the method to the short-wave automated perimetry (SWAP) data set to study risk factors of glaucomatous visual field deficits.

Suggested Citation

  • Levine, Richard A. & Fan, Juanjuan & Strickland, Pamela Ohman & Demirel, Shaban, 2012. "Frailty modeling via the empirical Bayes–Hastings sampler," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1303-1318.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1303-1318
    DOI: 10.1016/j.csda.2011.09.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311003239
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2011.09.004?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. Hanson, Timothy E., 2006. "Inference for Mixtures of Finite Polya Tree Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1548-1565, December.
    2. Stephen G. Walker & Bani K. Mallick, 1997. "Hierarchical Generalized Linear Models and Frailty Models with Bayesian Nonparametric Mixing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 845-860.
    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. Zhuang, Haoxin & Diao, Liqun & Yi, Grace Y., 2023. "Polya tree Monte Carlo method," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    2. Chen, Yuhui & Hanson, Timothy E., 2014. "Bayesian nonparametric k-sample tests for censored and uncensored data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 335-346.
    3. Ernesto San Martín & Alejandro Jara & Jean-Marie Rolin & Michel Mouchart, 2011. "On the Bayesian Nonparametric Generalization of IRT-Type Models," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 385-409, July.
    4. Jianjun Zhang & Lei Yang & Xianyi Wu, 2019. "Polya tree priors and their estimation with multi-group data," Statistical Papers, Springer, vol. 60(3), pages 849-875, June.
    5. Komárek, Arnost & Lesaffre, Emmanuel, 2008. "Generalized linear mixed model with a penalized Gaussian mixture as a random effects distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3441-3458, March.
    6. Adam Branscum & Timothy Hanson & Ian Gardner, 2008. "Bayesian non-parametric models for regional prevalence estimation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(5), pages 567-582.
    7. Antonio Lijoi & Igor Pruenster, 2009. "Models beyond the Dirichlet process," ICER Working Papers - Applied Mathematics Series 23-2009, ICER - International Centre for Economic Research.
    8. Luping Zhao & Timothy E. Hanson, 2011. "Spatially Dependent Polya Tree Modeling for Survival Data," Biometrics, The International Biometric Society, vol. 67(2), pages 391-403, June.
    9. Thomas A. Murray & Peter F. Thall & Ying Yuan & Sarah McAvoy & Daniel R. Gomez, 2017. "Robust Treatment Comparison Based on Utilities of Semi-Competing Risks in Non-Small-Cell Lung Cancer," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 11-23, January.
    10. Nalini Ravishanker & Dipak K. Dey, 2000. "Multivariate Survival Models with a Mixture of Positive Stable Frailties," Methodology and Computing in Applied Probability, Springer, vol. 2(3), pages 293-308, September.
    11. Angela Schörgendorfer & Adam J. Branscum & Timothy E. Hanson, 2013. "A Bayesian Goodness of Fit Test and Semiparametric Generalization of Logistic Regression with Measurement Data," Biometrics, The International Biometric Society, vol. 69(2), pages 508-519, June.
    12. Shinya Sugawara, 2017. "Firm‐Driven Management of Longevity Risk: Analysis of Lump‐Sum Forward Payments in Japanese Nursing Homes," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 26(1), pages 169-204, February.
    13. Song Zhang & Peter Müller & Kim-Anh Do, 2010. "A Bayesian Semiparametric Survival Model with Longitudinal Markers," Biometrics, The International Biometric Society, vol. 66(2), pages 435-443, June.
    14. Haiming Zhou & Timothy Hanson & Jiajia Zhang, 2017. "Generalized accelerated failure time spatial frailty model for arbitrarily censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(3), pages 495-515, July.
    15. Meijuan Li & Cavan Reilly & Tim Hanson, 2010. "Association Tests for a Censored Quantitative Trait and Candidate Genes in Structured Populations with Multilevel Genetic Relatedness," Biometrics, The International Biometric Society, vol. 66(3), pages 925-933, September.
    16. Cipolli III, William & Hanson, Timothy & McLain, Alexander C., 2016. "Bayesian nonparametric multiple testing," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 64-79.
    17. Antonio Lijoi & Igor Prunster, 2009. "Models beyond the Dirichlet process," Quaderni di Dipartimento 103, University of Pavia, Department of Economics and Quantitative Methods.
    18. Jiajia Zhang & Timothy Hanson & Haiming Zhou, 2019. "Bayes factors for choosing among six common survival models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(2), pages 361-379, April.
    19. Zhang, Jianjun & Qiu, Chunjuan & Wu, Xianyi, 2018. "Bayesian ratemaking with common effects modeled by mixture of Polya tree processes," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 87-94.
    20. Kyu Ha Lee & Virginie Rondeau & Sebastien Haneuse, 2017. "Accelerated failure time models for semi‐competing risks data in the presence of complex censoring," Biometrics, The International Biometric Society, vol. 73(4), pages 1401-1412, 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:eee:csdana:v:56:y:2012:i:6:p:1303-1318. 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.