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Incorporating unobserved heterogeneity in Weibull survival models: A Bayesian approach

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  • Vallejos, Catalina A.
  • Steel, Mark F.J.
Abstract
Outlying observations and other forms of unobserved heterogeneity can distort inference for survival datasets. The family of Rate Mixtures of Weibull distributions includes subject-level frailty terms as a solution to this issue. With a parametric mixing distribution assigned to the frailties, this family generates flexible hazard functions. Covariates are introduced via an Accelerated Failure Time specification for which the interpretation of the regression coefficients does not depend on the choice of mixing distribution. A weakly informative prior is proposed by combining the structure of the Jeffreys prior with a proper prior on some model parameters. This improper prior is shown to lead to a proper posterior distribution under easily satisfied conditions. By eliciting the proper component of the prior through the coefficient of variation of the survival times, prior information is matched for different mixing distributions. Posterior inference on subject-level frailty terms is exploited as a tool for outlier detection. Finally, the proposed methodology is illustrated using two real datasets, one concerning bone marrow transplants and another on cerebral palsy.

Suggested Citation

  • Vallejos, Catalina A. & Steel, Mark F.J., 2017. "Incorporating unobserved heterogeneity in Weibull survival models: A Bayesian approach," Econometrics and Statistics, Elsevier, vol. 3(C), pages 73-88.
    • Handle: RePEc:eee:ecosta:v:3:y:2017:i:c:p:73-88
    DOI: 10.1016/j.ecosta.2017.01.005
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    References listed on IDEAS

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    1. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
    2. G. P. S. Kwong & J. L. Hutton, 2003. "Choice of parametric models in survival analysis: applications to monotherapy for epilepsy and cerebral palsy," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(2), pages 153-168, May.
    3. Catalina A. Vallejos & Mark F. J. Steel, 2015. "Objective Bayesian Survival Analysis Using Shape Mixtures of Log-Normal Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 697-710, June.
    4. Il Do Ha & Maengseok Noh & Youngjo Lee, 2010. "Bias Reduction of Likelihood Estimators in Semiparametric Frailty Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 307-320, June.
    5. Philip Heidelberger & Peter D. Welch, 1983. "Simulation Run Length Control in the Presence of an Initial Transient," Operations Research, INFORMS, vol. 31(6), pages 1109-1144, December.
    6. Jaap H. Abbring & Gerard J. Van Den Berg, 2007. "The unobserved heterogeneity distribution in duration analysis," Biometrika, Biometrika Trust, vol. 94(1), pages 87-99.
    7. J. Heckman & B. Singer, 1984. "The Identifiability of the Proportional Hazard Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(2), pages 231-241.
    8. Fernández, C. & Steel, M.F.J., 1997. "On the Dangers of Modelling through Continuous Distributions : A Bayesian Perspective," Discussion Paper 1997-05, Tilburg University, Center for Economic Research.
    9. Gerda Claeskens & Rosemary Nguti & Paul Janssen, 2008. "One-sided tests in shared frailty models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 69-82, May.
    10. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
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    Cited by:

    1. 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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