Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Bayesian Semi-Parametric Regression for Quantile Residual Lifetime

  • Park, Taeyoung (Department of Applied Statistics, Yonsei University) ;
  • Bae, Wonho (Department of Applied Statistics, Yonsei University)
  • Received : 2014.04.11
  • Accepted : 2014.06.16
  • Published : 2014.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

The quantile residual life function has been effectively used to interpret results from the analysis of the proportional hazards model for censored survival data; however, the quantile residual life function is not always estimable with currently available semi-parametric regression methods in the presence of heavy censoring. A parametric regression approach may circumvent the difficulty of heavy censoring, but parametric assumptions on a baseline hazard function can cause a potential bias. This article proposes a Bayesian semi-parametric regression approach for inference on an unknown baseline hazard function while adjusting for available covariates. We consider a model-based approach but the proposed method does not suffer from strong parametric assumptions, enjoying a closed-form specification of the parametric regression approach without sacrificing the flexibility of the semi-parametric regression approach. The proposed method is applied to simulated data and heavily censored survival data to estimate various quantile residual lifetimes and adjust for important prognostic factors.

Keywords

References

  1. Carlin, B. P. and Hodges, J. S. (1999). Hierarchical proportional hazards models for highly stratified data, Biometrics, 55, 1162-1170. https://doi.org/10.1111/j.0006-341X.1999.01162.x
  2. Cox, D. R. (1972). Regression models and life-tables (with discussion), Journal of the Royal Statistical Society, Series B, 34, 187-220.
  3. Cox, D. R. (1975). Partial likelihood, Biometrika, 62, 269-276. https://doi.org/10.1093/biomet/62.2.269
  4. Gelfand, A. E. and Kottas, A. (2003). Bayesian semiparametric regression for median residual life, Scandinavian Journal of Statistics, 30, 651-665. https://doi.org/10.1111/1467-9469.00356
  5. Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulations using multiple sequences (with discussion), Statistical Science, 7, 457-472. https://doi.org/10.1214/ss/1177011136
  6. Gilks, W. R. and Wild, P. (1992). Adaptive rejection sampling for Gibbs sampling, Applied Statistics, 41, 337-348. https://doi.org/10.2307/2347565
  7. Hjort, N. L. and Petrone, S. (2007). Nonparametric quantile inference using Dirichlet processes. In Nair, V., editor, Advances in Statistical Modeling and Inference: Essays in Honor of Kjell A. Doksum, 463-492. World Scientific Publishing Company, Singapore.
  8. Ishwaran, H. and James, L. F. (2001). Gibbs sampling methods for stick-breaking priors, Journal of the American Statistical Association, 96, 161-173. https://doi.org/10.1198/016214501750332758
  9. Jeong, J. H., Jung, S. H. and Costantino, J. P. (2008). Nonparametric inference on median residual life function, Biometrics, 64, 157-163. https://doi.org/10.1111/j.1541-0420.2007.00826.x
  10. Kim, M.-O., Zhou, M., and Jeong, J.-H. (2012). Censored quantile regression for residual lifetimes, Lifetime Data Analysis, 18, 177-194. https://doi.org/10.1007/s10985-011-9212-2
  11. Kottas, A. (2006). Nonparametric Bayesian survival analysis using mixtures of Weibull distributions, Journal of Statistical Planning and Inference, 136, 578-596. https://doi.org/10.1016/j.jspi.2004.08.009
  12. Kottas, A. and Gelfand, A. E. (2001). Bayesian semiparametric median regression modeling, Journal of the American Statistical Association, 96, 1458-1468. https://doi.org/10.1198/016214501753382363
  13. Kottas, A. and Krnjajic, M. (2009). Bayesian semiparametric modelling in quantile regression, Scandinavian Journal of Statistics, 36, 297-319. https://doi.org/10.1111/j.1467-9469.2008.00626.x
  14. Kottas, A., Krnjajic, M. and Taddy, M. (2007). Model-based approaches to nonparametric Bayesian quantile regression, In Proceedings of the 2007 Joint Statistical Meetings, 1137-1148.
  15. Kuo, L. and Mallick, B. (1997). Bayesian semiparametric inference for the accelerated failure-time model, Canadian Journal of Statistics, 25, 457-472. https://doi.org/10.2307/3315341
  16. Park, T. (2011). Bayesian analysis of individual choice behavior with aggregate data, Journal of Computational and Graphical Statistics, 20, 158-173. https://doi.org/10.1198/jcgs.2010.10006
  17. Park, T., Jeong, J. and Lee, J. (2012a). Bayesian nonparametric inference on quantile residual life function: Application to breast cancer data, Statistics In Medicine, 31, 1972-1985. https://doi.org/10.1002/sim.5353
  18. Park, T., Krafty, R. T. and Sanchez, A. I. (2012b). Bayesian semi-parametric analysis of Poisson change-point regression models: Application to policy making in Cali, Colombia, Journal of Applied Statistics, 39, 2285-2298. https://doi.org/10.1080/02664763.2012.709227
  19. Park, T. and van Dyk, D. A. (2009). Partially collapsed Gibbs samplers: Illustrations and applications, Journal of Computational and Graphical Statistics, 18, 283-305. https://doi.org/10.1198/jcgs.2009.08108
  20. Park, T., van Dyk, D. A. and Siemiginowska, A. (2008). Searching for narrow emission lines in X-ray spectra: Computation and methods, The Astrophysical Journal, 688, 807-825. https://doi.org/10.1086/591631
  21. Sethuraman, J. A. (1994). A constructive definition of Dirichlet priors, Statistica Sinica, 4, 639-650.
  22. van Dyk, D. A. and Park, T. (2008). Partially collapsed Gibbs samplers: Theory and methods, Journal of the American Statistical Association, 103, 790-796. https://doi.org/10.1198/016214508000000409

Cited by

  1. Efficient Bayesian Inference on Asymmetric Jump-Diffusion Models vol.27, pp.6, 2014, https://doi.org/10.5351/KJAS.2014.27.6.959