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Flexible objective Bayesian linear regression with applications in survival analysis

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  • Francisco J. Rubio
  • Keming Yu

Abstract

We study objective Bayesian inference for linear regression models with residual errors distributed according to the class of two-piece scale mixtures of normal distributions. These models allow for capturing departures from the usual assumption of normality of the errors in terms of heavy tails, asymmetry, and certain types of heteroscedasticity. We propose a general non-informative, scale-invariant, prior structure and provide sufficient conditions for the propriety of the posterior distribution of the model parameters, which cover cases when the response variables are censored. These results allow us to apply the proposed models in the context of survival analysis. This paper represents an extension to the Bayesian framework of the models proposed in [16]. We present a simulation study that shows good frequentist properties of the posterior credible intervals as well as point estimators associated to the proposed priors. We illustrate the performance of these models with real data in the context of survival analysis of cancer patients.

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  • Francisco J. Rubio & Keming Yu, 2017. "Flexible objective Bayesian linear regression with applications in survival analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(5), pages 798-810, April.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:5:p:798-810
    DOI: 10.1080/02664763.2016.1182138
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    References listed on IDEAS

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    1. 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.
    2. Nuttanan Wichitaksorn & Joanna J. J. Wang & S. T. Boris Choy & Richard Gerlach, 2015. "Analyzing return asymmetry and quantiles through stochastic volatility models using asymmetric Laplace error via uniform scale mixtures," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(5), pages 584-608, September.
    3. Jianchang Lin & Debajyoti Sinha & Stuart Lipsitz & Adriano Polpo, 2012. "Semiparametric Bayesian Survival Analysis using Models with Log-linear Median," Biometrics, The International Biometric Society, vol. 68(4), pages 1136-1145, December.
    4. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    5. Juárez, Miguel A. & Steel, Mark F. J., 2010. "Model-Based Clustering of Non-Gaussian Panel Data Based on Skew-t Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 52-66.
    6. Adelchi Azzalini & Marc G. Genton, 2008. "Robust Likelihood Methods Based on the Skew‐t and Related Distributions," International Statistical Review, International Statistical Institute, vol. 76(1), pages 106-129, April.
    7. Brian J. Reich & Luke B. Smith, 2013. "Bayesian Quantile Regression for Censored Data," Biometrics, The International Biometric Society, vol. 69(3), pages 651-660, September.
    8. Debajyoti Sinha & Ming-Hui Chen & Sujit K. Ghosh, 1999. "Bayesian Analysis and Model Selection for Interval-Censored Survival Data," Biometrics, The International Biometric Society, vol. 55(2), pages 585-590, June.
    9. Francisco J. Rubio & Yili Hong, 2016. "Survival and lifetime data analysis with a flexible class of distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(10), pages 1794-1813, August.
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    Cited by:

    1. Saverio Ranciati & Giuliano Galimberti & Gabriele Soffritti, 2019. "Bayesian variable selection in linear regression models with non-normal errors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 323-358, June.
    2. Worku Biyadgie Ewnetu & Irène Gijbels & Anneleen Verhasselt, 2024. "Two-piece distribution based semi-parametric quantile regression for right censored data," Statistical Papers, Springer, vol. 65(5), pages 2775-2810, July.
    3. Fabrizio Leisen & Luca Rossini & Cristiano Villa, 2020. "Loss-based approach to two-piece location-scale distributions with applications to dependent data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 309-333, June.

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