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Full Bayesian inference with hazard mixture models

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  • Arbel, Julyan
  • Lijoi, Antonio
  • Nipoti, Bernardo

Abstract

Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical problems, these methods may suffer from some limitations if used to estimate non-linear functionals of the posterior distribution. The main goal is to develop a novel methodology that extends a well-established marginal procedure designed for hazard mixture models, in order to draw approximate inference on survival functions that is not limited to the posterior mean but includes, as remarkable examples, credible intervals and median survival time. The proposed approach relies on a characterization of the posterior moments that, in turn, is used to approximate the posterior distribution by means of a technique based on Jacobi polynomials. The inferential performance of this methodology is analyzed by means of an extensive study of simulated data and real data consisting of leukemia remission times. Although tailored to the survival analysis context, the proposed procedure can be adapted to a range of other models for which moments of the posterior distribution can be estimated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:359-372
    DOI: 10.1016/j.csda.2014.12.003
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    References listed on IDEAS

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    1. Antonio Lijoi & Igor Pruenster & Stephen G. Walker, 2008. "Posterior analysis for some classes of nonparametric models," ICER Working Papers - Applied Mathematics Series 05-2008, ICER - International Centre for Economic Research.
    2. 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.
    3. Pierpaolo De Blasi & Giovanni Peccati & Igor Prünster, 2009. "Asymptotics for posterior hazards," Carlo Alberto Notebooks 122, Collegio Carlo Alberto.
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    5. 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.
    6. Nieto-Barajas, Luis E., 2014. "Bayesian semiparametric analysis of short- and long-term hazard ratios with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 477-490.
    7. Albert Lo & Chung-Sing Weng, 1989. "On a class of Bayesian nonparametric estimates: II. Hazard rate estimates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(2), pages 227-245, June.
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    Cited by:

    1. Moya, Blake & Walker, Stephen G., 2024. "Full uncertainty analysis for Bayesian nonparametric mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    2. Corradin, Riccardo & Nieto-Barajas, Luis Enrique & Nipoti, Bernardo, 2022. "Optimal stratification of survival data via Bayesian nonparametric mixtures," Econometrics and Statistics, Elsevier, vol. 22(C), pages 17-38.

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