IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v109y2014i506p802-814.html
   My bibliography  Save this article

A Class of Hazard Rate Mixtures for Combining Survival Data From Different Experiments

Author

Listed:
  • Antonio Lijoi
  • Bernardo Nipoti

Abstract

Mixture models for hazard rate functions are widely used tools for addressing the statistical analysis of survival data subject to a censoring mechanism. The present article introduced a new class of vectors of random hazard rate functions that are expressed as kernel mixtures of dependent completely random measures. This leads to define dependent nonparametric prior processes that are suitably tailored to draw inferences in the presence of heterogenous observations. Besides its flexibility, an important appealing feature of our proposal is analytical tractability: we are, indeed, able to determine some relevant distributional properties and a posterior characterization that is also the key for devising an efficient Markov chain Monte Carlo sampler. For illustrative purposes, we specialize our general results to a class of dependent extended gamma processes. We finally display a few numerical examples, including both simulated and real two-sample datasets: these allow us to identify the effect of a borrowing strength phenomenon and provide evidence of the effectiveness of the prior to deal with datasets for which the proportional hazards assumption does not hold true. Supplementary materials for this article are available online.

Suggested Citation

  • Antonio Lijoi & Bernardo Nipoti, 2014. "A Class of Hazard Rate Mixtures for Combining Survival Data From Different Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 802-814, June.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:506:p:802-814
    DOI: 10.1080/01621459.2013.869499
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2013.869499
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01621459.2013.869499?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. De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
    2. Sangbum Choi & Xuelin Huang, 2012. "A General Class of Semiparametric Transformation Frailty Models for Nonproportional Hazards Survival Data," Biometrics, The International Biometric Society, vol. 68(4), pages 1126-1135, December.
    3. Paul Damien & Stephen Walker, 2002. "A Bayesian Non‐parametric Comparison of Two Treatments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 51-56, March.
    4. Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
    5. Maria De Iorio & Wesley O. Johnson & Peter Müller & Gary L. Rosner, 2009. "Bayesian Nonparametric Nonproportional Hazards Survival Modeling," Biometrics, The International Biometric Society, vol. 65(3), pages 762-771, September.
    6. A. Jara & T. E. Hanson, 2011. "A class of mixtures of dependent tail-free processes," Biometrika, Biometrika Trust, vol. 98(3), pages 553-566.
    7. Pierpaolo De Blasi & Giovanni Peccati & Igor Prünster, 2009. "Asymptotics for posterior hazards," Carlo Alberto Notebooks 122, Collegio Carlo Alberto.
    8. Ishwaran, Hemant & James, Lancelot F., 2004. "Computational Methods for Multiplicative Intensity Models Using Weighted Gamma Processes: Proportional Hazards, Marked Point Processes, and Panel Count Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 175-190, January.
    9. Lorenzo Trippa & Peter Müller & Wesley Johnson, 2011. "The multivariate beta process and an extension of the Polya tree model," Biometrika, Biometrika Trust, vol. 98(1), pages 17-34.
    10. Griffiths, R. C. & Milne, R. K., 1978. "A class of bivariate Poisson processes," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 380-395, September.
    11. J. E. Griffin & M. Kolossiatis & M. F. J. Steel, 2013. "Comparing distributions by using dependent normalized random-measure mixtures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 499-529, June.
    12. Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
    13. 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.
    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. Weixuan Zhu & Fabrizio Leisen, 2015. "A multivariate extension of a vector of two-parameter Poisson-Dirichlet processes," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 89-105, March.
    2. Jim E. Griffin & Fabrizio Leisen, 2017. "Compound random measures and their use in Bayesian non-parametrics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 525-545, March.
    3. Riva Palacio, Alan & Leisen, Fabrizio, 2018. "Integrability conditions for compound random measures," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 32-37.
    4. Arbel, Julyan & Lijoi, Antonio & Nipoti, Bernardo, 2016. "Full Bayesian inference with hazard mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 359-372.

    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. Antonio Lijoi & Bernardo Nipoti, 2013. "A class of hazard rate mixtures for combining survival data from different experiments," DEM Working Papers Series 059, University of Pavia, Department of Economics and Management.
    2. Andrés F. Barrientos & Alejandro Jara & Fernando A. Quintana, 2017. "Fully Nonparametric Regression for Bounded Data Using Dependent Bernstein Polynomials," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 806-825, April.
    3. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2014. "Beta-product dependent Pitman–Yor processes for Bayesian inference," Journal of Econometrics, Elsevier, vol. 180(1), pages 49-72.
    4. Michael L. Pennell & David B. Dunson, 2008. "Nonparametric Bayes Testing of Changes in a Response Distribution with an Ordinal Predictor," Biometrics, The International Biometric Society, vol. 64(2), pages 413-423, June.
    5. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2016. "Random density functions with common atoms and pairwise dependence," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 236-249.
    6. Chen, Kunzhi & Shen, Weining & Zhu, Weixuan, 2023. "Covariate dependent Beta-GOS process," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    7. Hatjispyros, Spyridon J. & Merkatas, Christos & Nicoleris, Theodoros & Walker, Stephen G., 2018. "Dependent mixtures of geometric weights priors," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 1-18.
    8. Igor Prünster & Matteo Ruggiero, 2011. "A Bayesian nonparametric approach to modeling market share dynamics," Carlo Alberto Notebooks 217, Collegio Carlo Alberto.
    9. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2011. "Beta-product Poisson-Dirichlet Processes," DES - Working Papers. Statistics and Econometrics. WS 12160, Universidad Carlos III de Madrid. Departamento de Estadística.
    10. Ilenia Epifani & Antonio Lijoi, 2009. "Nonparametric Priors for Vectors of Survival Functions," Quaderni di Dipartimento 098, University of Pavia, Department of Economics and Quantitative Methods.
    11. Jin, Xin & Maheu, John M., 2016. "Bayesian semiparametric modeling of realized covariance matrices," Journal of Econometrics, Elsevier, vol. 192(1), pages 19-39.
    12. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "On the stick–breaking representation of normalized inverse Gaussian priors," DEM Working Papers Series 008, University of Pavia, Department of Economics and Management.
    13. Pati, Debdeep & Dunson, David B. & Tokdar, Surya T., 2013. "Posterior consistency in conditional distribution estimation," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 456-472.
    14. Fuentes-García, Ruth & Mena, Ramsés H. & Walker, Stephen G., 2009. "A nonparametric dependent process for Bayesian regression," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1112-1119, April.
    15. Weixuan Zhu & Fabrizio Leisen, 2015. "A multivariate extension of a vector of two-parameter Poisson-Dirichlet processes," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 89-105, March.
    16. Arbel, Julyan & Lijoi, Antonio & Nipoti, Bernardo, 2016. "Full Bayesian inference with hazard mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 359-372.
    17. Trippa, Lorenzo & Muliere, Pietro, 2009. "Bayesian nonparametric binary regression via random tessellations," Statistics & Probability Letters, Elsevier, vol. 79(21), pages 2273-2280, November.
    18. Bruno Scarpa & David B. Dunson, 2009. "Bayesian Hierarchical Functional Data Analysis Via Contaminated Informative Priors," Biometrics, The International Biometric Society, vol. 65(3), pages 772-780, September.
    19. Yushu Shi & Purushottam Laud & Joan Neuner, 2021. "A dependent Dirichlet process model for survival data with competing risks," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 156-176, January.
    20. Shamsi Zamenjani, Azam, 2021. "Do financial variables help predict the conditional distribution of the market portfolio?," Journal of Empirical Finance, Elsevier, vol. 62(C), pages 327-345.

    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:taf:jnlasa:v:109:y:2014:i:506:p:802-814. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    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.