IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v99y2015i3p259-280.html
   My bibliography  Save this article

Bayesian accelerated failure time models based on penalized mixtures of Gaussians: regularization and variable selection

Author

Listed:
  • Susanne Konrath
  • Ludwig Fahrmeir
  • Thomas Kneib

Abstract

In many biostatistical applications concerned with the analysis of duration times and especially those including high-dimensional genetic information, the following three extensions of classical accelerated failure time (AFT) models are required: (1) a flexible, nonparametric estimate of the survival time distribution, (2) a structured additive predictor including linear as well as nonlinear effects of continuous covariates and possibly further types of effects such as random or spatial effects, and (3) regularization and variable selection of high-dimensional effect vectors. Although a lot of research has dealt with these features separately, the development of AFT models combining them in a unified framework has not been considered yet. We present a Bayesian approach for modeling and inference in such flexible AFT models, incorporating a penalized Gaussian mixture error distribution, a structured additive predictor with Bayesian P-splines as a main ingredient, and Bayesian versions of ridge and LASSO as well as a spike and slab priors to enforce sparseness. Priors for regression coefficients are conditionally Gaussian, facilitating Markov chain Monte Carlo inference. The proposed model class is extensively tested in simulation studies and applied in the analysis of acute myeloid leukemia survival times considering microarray information as well as clinical covariates as prognostic factors. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Susanne Konrath & Ludwig Fahrmeir & Thomas Kneib, 2015. "Bayesian accelerated failure time models based on penalized mixtures of Gaussians: regularization and variable selection," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(3), pages 259-280, July.
    • Handle: RePEc:spr:alstar:v:99:y:2015:i:3:p:259-280
    DOI: 10.1007/s10182-014-0240-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10182-014-0240-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10182-014-0240-6?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. Lee Anthony & Caron Francois & Doucet Arnaud & Holmes Chris, 2012. "Bayesian Sparsity-Path-Analysis of Genetic Association Signal using Generalized t Priors," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(2), pages 1-31, January.
    2. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    3. Thomas Kneib & Ludwig Fahrmeir, 2007. "A Mixed Model Approach for Geoadditive Hazard Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(1), pages 207-228, March.
    4. Komarek, Arnost & Lesaffre, Emmanuel, 2008. "Bayesian Accelerated Failure Time Model With Multivariate Doubly Interval-Censored Data and Flexible Distributional Assumptions," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 523-533, June.
    5. Hennerfeind, Andrea & Brezger, Andreas & Fahrmeir, Ludwig, 2006. "Geoadditive Survival Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1065-1075, September.
    6. Stephen Walker & Bani K. Mallick, 1999. "A Bayesian Semiparametric Accelerated Failure Time Model," Biometrics, The International Biometric Society, vol. 55(2), pages 477-483, June.
    7. Brezger, Andreas & Lang, Stefan, 2006. "Generalized structured additive regression based on Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 967-991, February.
    8. Fahrmeir, Ludwig & Kneib, Thomas, 2011. "Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data," OUP Catalogue, Oxford University Press, number 9780199533022.
    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. Wenjing Yin & Sihai Dave Zhao & Feng Liang, 2022. "Bayesian penalized Buckley-James method for high dimensional bivariate censored regression models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(2), pages 282-318, April.

    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. Ezra Gayawan & Samson B. Adebayo, 2013. "A Bayesian semiparametric multilevel survival modelling of age at first birth in Nigeria," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 28(45), pages 1339-1372.
    2. Rui Martins, 2022. "A flexible link for joint modelling longitudinal and survival data accounting for individual longitudinal heterogeneity," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(1), pages 41-61, March.
    3. Seongil Jo & Taeyoung Roh & Taeryon Choi, 2016. "Bayesian spectral analysis models for quantile regression with Dirichlet process mixtures," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 177-206, March.
    4. Nikolaus Umlauf & Nadja Klein & Achim Zeileis, 2017. "BAMLSS: Bayesian Additive Models for Location, Scale and Shape (and Beyond)," Working Papers 2017-05, Faculty of Economics and Statistics, Universität Innsbruck.
    5. Ezra Gayawan & Samson B. Adebayo, 2014. "Spatial Pattern and Determinants of Age at Marriage in Nigeria Using a Geo-Additive Survival Model," Mathematical Population Studies, Taylor & Francis Journals, vol. 21(2), pages 112-124, June.
    6. Costa, M.J. & Shaw, J.E.H., 2009. "Parametrization and penalties in spline models with an application to survival analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(3), pages 657-670, January.
    7. Damien Rousselière, 2019. "A Flexible Approach to Age Dependence in Organizational Mortality: Comparing the Life Duration for Cooperative and Non-Cooperative Enterprises Using a Bayesian Generalized Additive Discrete Time Survi," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(4), pages 829-855, December.
    8. Alexander März & Nadja Klein & Thomas Kneib & Oliver Musshoff, 2016. "Analysing farmland rental rates using Bayesian geoadditive quantile regression," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 43(4), pages 663-698.
    9. Ji, Yonggang & Lin, Nan & Zhang, Baoxue, 2012. "Model selection in binary and tobit quantile regression using the Gibbs sampler," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 827-839.
    10. Elisabeth Waldmann & Thomas Kneib & Yu Ryan Yu & Stefan Lang, 2012. "Bayesian semiparametric additive quantile regression," Working Papers 2012-06, Faculty of Economics and Statistics, Universität Innsbruck.
    11. 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.
    12. Li Li & Timothy Hanson & Jiajia Zhang, 2015. "Spatial extended hazard model with application to prostate cancer survival," Biometrics, The International Biometric Society, vol. 71(2), pages 313-322, June.
    13. Bernardi, Mauro & Bottone, Marco & Petrella, Lea, 2018. "Bayesian quantile regression using the skew exponential power distribution," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 92-111.
    14. Prabhash Kumar & Patil Vijay M & Noronha Vanita & Joshi Amit & Bhattacharjee Atanu, 2016. "Bayesian Accelerated Failure Time and its Application in Chemotherapy Drug Treatment Trial," Statistics in Transition New Series, Polish Statistical Association, vol. 17(4), pages 671-690, December.
    15. Stefan Lang & Nikolaus Umlauf & Peter Wechselberger & Kenneth Harttgen & Thomas Kneib, 2012. "Multilevel structured additive regression," Working Papers 2012-07, Faculty of Economics and Statistics, Universität Innsbruck.
    16. Jiajia Zhang & Andrew B. Lawson, 2011. "Bayesian parametric accelerated failure time spatial model and its application to prostate cancer," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(3), pages 591-603, November.
    17. Fabian Scheipl & Thomas Kneib & Ludwig Fahrmeir, 2013. "Penalized likelihood and Bayesian function selection in regression models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 349-385, October.
    18. Kumar Prabhash & Vijay M Patil & Vanita Noronha & Amit Joshi & Atanu Bhattacharjee, 2016. "Bayesian Accelerated Failure Time And Its Application In Chemotherapy Drug Treatment Trial," Statistics in Transition New Series, Polish Statistical Association, vol. 17(4), pages 671-690, December.
    19. Thomas Kneib & Nadja Klein & Stefan Lang & Nikolaus Umlauf, 2019. "Modular regression - a Lego system for building structured additive distributional regression models with tensor product interactions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 1-39, March.
    20. Thomas Kneib & Bernhard Baumgartner & Winfried Steiner, 2007. "Semiparametric multinomial logit models for analysing consumer choice behaviour," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 91(3), pages 225-244, October.

    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:alstar:v:99:y:2015:i:3:p:259-280. 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.