IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v79y2023i4p3023-3037.html
   My bibliography  Save this article

Nonparametric failure time: Time‐to‐event machine learning with heteroskedastic Bayesian additive regression trees and low information omnibus Dirichlet process mixtures

Author

Listed:
  • Rodney A. Sparapani
  • Brent R. Logan
  • Martin J. Maiers
  • Purushottam W. Laud
  • Robert E. McCulloch

Abstract

Many popular survival models rely on restrictive parametric, or semiparametric, assumptions that could provide erroneous predictions when the effects of covariates are complex. Modern advances in computational hardware have led to an increasing interest in flexible Bayesian nonparametric methods for time‐to‐event data such as Bayesian additive regression trees (BART). We propose a novel approach that we call nonparametric failure time (NFT) BART in order to increase the flexibility beyond accelerated failure time (AFT) and proportional hazard models. NFT BART has three key features: (1) a BART prior for the mean function of the event time logarithm; (2) a heteroskedastic BART prior to deduce a covariate‐dependent variance function; and (3) a flexible nonparametric error distribution using Dirichlet process mixtures (DPM). Our proposed approach widens the scope of hazard shapes including nonproportional hazards, can be scaled up to large sample sizes, naturally provides estimates of uncertainty via the posterior and can be seamlessly employed for variable selection. We provide convenient, user‐friendly, computer software that is freely available as a reference implementation. Simulations demonstrate that NFT BART maintains excellent performance for survival prediction especially when AFT assumptions are violated by heteroskedasticity. We illustrate the proposed approach on a study examining predictors for mortality risk in patients undergoing hematopoietic stem cell transplant (HSCT) for blood‐borne cancer, where heteroskedasticity and nonproportional hazards are likely present.

Suggested Citation

  • Rodney A. Sparapani & Brent R. Logan & Martin J. Maiers & Purushottam W. Laud & Robert E. McCulloch, 2023. "Nonparametric failure time: Time‐to‐event machine learning with heteroskedastic Bayesian additive regression trees and low information omnibus Dirichlet process mixtures," Biometrics, The International Biometric Society, vol. 79(4), pages 3023-3037, December.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:4:p:3023-3037
    DOI: 10.1111/biom.13857
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13857
    Download Restriction: no
    File URL: https://libkey.io/10.1111/biom.13857?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
    ---><---

    References listed on IDEAS

    as
    1. Yi Liu & Veronika Ročková, 2023. "Variable Selection Via Thompson Sampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(541), pages 287-304, January.
    2. Antonio R. Linero, 2018. "Bayesian Regression Trees for High-Dimensional Prediction and Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 626-636, April.
    3. P. Richard Hahn & Carlos M. Carvalho, 2015. "Decoupling Shrinkage and Selection in Bayesian Linear Models: A Posterior Summary Perspective," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 435-448, March.
    4. Yang, Mingan & Dunson, David B. & Baird, Donna, 2010. "Semiparametric Bayes hierarchical models with mean and variance constraints," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2172-2186, September.
    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. Donelli, Nicola & Peluso, Stefano & Mira, Antonietta, 2021. "A Bayesian semiparametric vector Multiplicative Error Model," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    2. Sarah Brown & Pulak Ghosh & Bhuvanesh Pareek & Karl Taylor, 2017. "Financial Hardship and Saving Behaviour: Bayesian Analysis of British Panel Data," Working Papers 2017011, The University of Sheffield, Department of Economics.
    3. Cai, Jing-Heng & Song, Xin-Yuan & Lam, Kwok-Hap & Ip, Edward Hak-Sing, 2011. "A mixture of generalized latent variable models for mixed mode and heterogeneous data," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2889-2907, November.
    4. Song, Xin-Yuan & Chen, Fei & Lu, Zhao-Hua, 2013. "A Bayesian semiparametric dynamic two-level structural equation model for analyzing non-normal longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 87-108.
    5. Huber, Florian & Koop, Gary & Onorante, Luca & Pfarrhofer, Michael & Schreiner, Josef, 2023. "Nowcasting in a pandemic using non-parametric mixed frequency VARs," Journal of Econometrics, Elsevier, vol. 232(1), pages 52-69.
    6. Tang, Nian-Sheng & Tang, An-Min & Pan, Dong-Dong, 2014. "Semiparametric Bayesian joint models of multivariate longitudinal and survival data," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 113-129.
    7. Florian Huber & Luca Rossini, 2020. "Inference in Bayesian Additive Vector Autoregressive Tree Models," Papers 2006.16333, arXiv.org, revised Mar 2021.
    8. Robert B. Gramacy, 2020. "Discussion," International Statistical Review, International Statistical Institute, vol. 88(2), pages 326-329, August.
    9. Daniel R. Kowal, 2023. "Subset selection for linear mixed models," Biometrics, The International Biometric Society, vol. 79(3), pages 1853-1867, September.
    10. Niko Hauzenberger & Michael Pfarrhofer & Luca Rossini, 2020. "Sparse time-varying parameter VECMs with an application to modeling electricity prices," Papers 2011.04577, arXiv.org, revised Apr 2023.
    11. Xueying Tang & Xiaofan Xu & Malay Ghosh & Prasenjit Ghosh, 2018. "Bayesian Variable Selection and Estimation Based on Global-Local Shrinkage Priors," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 215-246, August.
    12. Falco J. Bargagli Stoffi & Kenneth De Beckker & Joana E. Maldonado & Kristof De Witte, 2021. "Assessing Sensitivity of Machine Learning Predictions.A Novel Toolbox with an Application to Financial Literacy," Papers 2102.04382, arXiv.org.
    13. Mingan Yang & Min Wang & Guanghui Dong, 2020. "Bayesian variable selection for mixed effects model with shrinkage prior," Computational Statistics, Springer, vol. 35(1), pages 227-243, March.
    14. Byron Botha & Rulof Burger & Kevin Kotzé & Neil Rankin & Daan Steenkamp, 2023. "Big data forecasting of South African inflation," Empirical Economics, Springer, vol. 65(1), pages 149-188, July.
    15. Deshpande Sameer K. & Evans Katherine, 2020. "Expected hypothetical completion probability," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 16(2), pages 85-94, June.
    16. Billio, Monica & Casarin, Roberto & Costola, Michele & Veggente, Veronica, 2023. "Learning from experts: Energy efficiency in residential buildings," SAFE Working Paper Series 403, Leibniz Institute for Financial Research SAFE.
    17. Braun, Robin, 2021. "The importance of supply and demand for oil prices: evidence from non-Gaussianity," Bank of England working papers 957, Bank of England.
    18. Horiguchi, Akira & Pratola, Matthew T. & Santner, Thomas J., 2021. "Assessing variable activity for Bayesian regression trees," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    19. Yaojun Zhang & Lanpeng Ji & Georgios Aivaliotis & Charles Taylor, 2023. "Bayesian CART models for insurance claims frequency," Papers 2303.01923, arXiv.org, revised Dec 2023.
    20. Tang, Niansheng & Wu, Ying & Chen, Dan, 2018. "Semiparametric Bayesian analysis of transformation linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 225-240.

    More about this item

    Statistics

    Access and download statistics

    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:bla:biomet:v:79:y:2023:i:4:p:3023-3037. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    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.