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Bayesian Semiparametric Regression for Median Residual Life

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  • Alan E. Gelfand
  • Athanasios Kottas

Abstract

. With survival data there is often interest not only in the survival time distribution but also in the residual survival time distribution. In fact, regression models to explain residual survival time might be desired. Building upon recent work of Kottas & Gelfand [J. Amer. Statist. Assoc. 96 (2001) 1458], we formulate a semiparametric median residual life regression model induced by a semiparametric accelerated failure time regression model. We utilize a Bayesian approach which allows full and exact inference. Classical work essentially ignores covariates and is either based upon parametric assumptions or is limited to asymptotic inference in non‐parametric settings. No regression modelling of median residual life appears to exist. The Bayesian modelling is developed through Dirichlet process mixing. The models are fitted using Gibbs sampling. Residual life inference is implemented extending the approach of Gelfand & Kottas [J. Comput. Graph. Statist. 11 (2002) 289]. Finally, we present a fairly detailed analysis of a set of survival times with moderate censoring for patients with small cell lung cancer.

Suggested Citation

  • Alan E. Gelfand & Athanasios Kottas, 2003. "Bayesian Semiparametric Regression for Median Residual Life," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 651-665, December.
    • Handle: RePEc:bla:scjsta:v:30:y:2003:i:4:p:651-665
    DOI: 10.1111/1467-9469.00356
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    Cited by:

    1. Jong-Hyeon Jeong & Sin-Ho Jung & Joseph P. Costantino, 2008. "Nonparametric Inference on Median Residual Life Function," Biometrics, The International Biometric Society, vol. 64(1), pages 157-163, March.
    2. Yun Yang & Surya T. Tokdar, 2017. "Joint Estimation of Quantile Planes Over Arbitrary Predictor Spaces," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1107-1120, July.
    3. Yimeng Liu & Liwen Wu & Gong Tang & Abdus S. Wahed, 2023. "A series of two-sample non-parametric tests for quantile residual life time," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 234-252, January.
    4. 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.
    5. Das, Priyam & Ghosal, Subhashis, 2017. "Bayesian quantile regression using random B-spline series prior," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 121-143.
    6. Franco Pereira, Alba María & Lillo Rodríguez, Rosa Elvira & Romo, Juan & Shaked, Moshe, 2008. "Percentile residual life orders," DES - Working Papers. Statistics and Econometrics. WS ws086422, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Luis Alexander Crouch & Susanne May & Ying Qing Chen, 2016. "On estimation of covariate-specific residual time quantiles under the proportional hazards model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(2), pages 299-319, April.
    8. Volf, P. & Timková, J., 2014. "On selection of optimal stochastic model for accelerated life testing," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 291-297.
    9. Athanasios Kottas & Milovan Krnjajić, 2009. "Bayesian Semiparametric Modelling in Quantile Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 297-319, June.
    10. Sin-Ho Jung & Jong-Hyeon Jeong & Hanna Bandos, 2009. "Regression on Quantile Residual Life," Biometrics, The International Biometric Society, vol. 65(4), pages 1203-1212, December.

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