Skip to main content
SpringerLink
Log in

Bayesian Approach for Interval-Censored Survival Data with Time-Varying Coefficients

  • Chapter
  • First Online:
Bayesian Inference and Computation in Reliability and Survival Analysis

Part of the book series: Emerging Topics in Statistics and Biostatistics ((ETSB))

  • 519 Accesses

Abstract

Interval-censored data arise when the failure time cannot be observed exactly but can only be determined to lie within an interval. Interval-censored data are very common in medical and epidemiological studies. In this chapter, we discuss a Bayesian approach for correlated interval-censored data under a dynamic Cox regression model. Some methods that incorporate right censoring have been developed for time-to-event data with temporal covariate effects. However, interval-censored data analysis under the same circumstance is much less developed. In this chapter, we introduce a piecewise constant coefficients estimate based on a dynamic Cox regression model under the Bayesian framework. The dimensions of coefficients are automatically determined by the reversible jump Markov chain Monte Carlo algorithm. Meanwhile, we use a shared frailty factor for unobserved heterogeneity or for statistical dependence between observations. Two illustrative examples are given to demonstrate the methods’ performance. A summary is provided to discuss the methods introduced in this chapter.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Besag, J., Kooperberg, C.: On conditional and intrinsic autoregressions. Biometrika 82(4), 733–746 (1995)

    MathSciNet  MATH  Google Scholar 

  2. Brezger, A., Lang, S.: Generalized structured additive regression based on Bayesian P-splines. Comput. Stat. Data Anal. 50(4), 967–991 (2006)

    Article  MathSciNet  Google Scholar 

  3. Carlin, B.P., Louis, T.A.: Bayes and empirical Bayes methods for data analysis. Stat. Comput. 7(2), 153–154 (1997)

    Article  Google Scholar 

  4. De Gruttola, V., Lagakos, S.W.: Analysis of doubly-censored survival data, with application to AIDS. Biometrics 45, 1–11 (1989)

    Article  MathSciNet  Google Scholar 

  5. Diamond, I.D., McDonald, J.W., Shah, I.H.: Proportional hazards models for current status data: application to the study of differentials in age at weaning in Pakistan. Demography 23(4), 607–620 (1986)

    Article  Google Scholar 

  6. Fahrmeir, L., Lang, S.: Bayesian semiparametric regression analysis of multicategorical time-space data. Ann. Inst. Stat. Math. 53(1), 11–30 (2001)

    Article  MathSciNet  Google Scholar 

  7. Finkelstein, D.M.: A proportional hazards model for interval-censored failure time data. Biometrics 42, 845–854 (1986)

    Article  MathSciNet  Google Scholar 

  8. Finkelstein, D.M., Wolfe, R.A.: A semiparametric model for regression analysis of interval-censored failure time data. Biometrics 41, 933–945 (1985)

    Article  MathSciNet  Google Scholar 

  9. Gilks, W.R., Wild, P.: Adaptive rejection sampling for Gibbs sampling. Appl. Stat. 41, 337–348 (1992)

    Article  Google Scholar 

  10. Gómez, G., Calle, M.L., Oller, R., Langohr, K.: Tutorial on methods for interval-censored data and their implementation in R. Stat. Model. 9(4), 259–297 (2009)

    Article  MathSciNet  Google Scholar 

  11. Green, P.J.: Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82(4), 711–732 (1995)

    Article  MathSciNet  Google Scholar 

  12. Higle, J.L., Sen, S.: Stochastic decomposition: an algorithm for two-stage linear programs with recourse. Math. Oper. Res. 16(3), 650–669 (1991)

    Article  MathSciNet  Google Scholar 

  13. Hoel, D.G., Walburg, H.: Statistical analysis of survival experiments. J. Nat. Cancer Inst. 49(2), 361–372 (1972)

    Google Scholar 

  14. Ibrahim, J.G., Chen, M.-H., Sinha, D.: Bayesian Survival Analysis. Wiley, London (2005)

    MATH  Google Scholar 

  15. Jewell, N.P., Malani, H.M., Vittinghoff, E.: Nonparametric estimation for a form of doubly censored data, with application to two problems in AIDS. J. Am. Stat. Assoc. 89(425), 7–18 (1994)

    Article  Google Scholar 

  16. Kim, M.Y., De Gruttola, V.G., Lagakos, S.W.: Analyzing doubly censored data with covariates, with application to AIDS. Biometrics 49, 13–22 (1993)

    Article  Google Scholar 

  17. Kim, S., Chen, M.-H., Dey, D.K., Gamerman, D.: Bayesian dynamic models for survival data with a cure fraction. Lifetime Data Anal. 13(1), 17–35 (2007)

    Article  MathSciNet  Google Scholar 

  18. Kneib, T.: Mixed model based inference in structured additive regression. Ph.D. Thesis, LMU (2006)

    Google Scholar 

  19. Martinussen, T., Scheike, T.H.: A flexible additive multiplicative hazard model. Biometrika 89(2), 283–298 (2002)

    Article  MathSciNet  Google Scholar 

  20. Martinussen, T., Scheike, T.H., Skovgaard, I.M.: Efficient estimation of fixed and time-varying covariate effects in multiplicative intensity models. Scand. J. Stat. 29(1), 57–74 (2002)

    Article  MathSciNet  Google Scholar 

  21. Murray, R.P., Anthonisen, N.R., Connett, J.E., Wise, R.A., Lindgren, P.G., Greene, P.G., Nides, M.A., Group, L.H.S.R., et al.: Effects of multiple attempts to quit smoking and relapses to smoking on pulmonary function. J. Clin. Epidemiol. 51(12), 1317–1326 (1998)

    Article  Google Scholar 

  22. Self, S.G., Grossman, E.A.: Linear rank tests for interval-censored data with application to PCB levels in adipose tissue of transformer repair workers. Biometrics 42, 521–530 (1986)

    Article  Google Scholar 

  23. Shiboski, S.C., Jewell, N.P.: Statistical analysis of the time dependence of HIV infectivity based on partner study data. J. Am. Stat. Assoc. 87(418), 360–372 (1992)

    Article  Google Scholar 

  24. Sinha, D., Chen, M.-H., Ghosh, S.K.: Bayesian analysis and model selection for interval-censored survival data. Biometrics 55, 585–590 (1999)

    Article  MathSciNet  Google Scholar 

  25. Sun, J.: A non-parametric test for interval-censored failure time data with application to AIDS studies. Stat. Med. 15(13), 1387–1395 (1996)

    Article  Google Scholar 

  26. Sun, J., Kalbfleisch, J.D.: Nonparametric tests of tumor prevalence data. Biometrics 52, 726–731 (1996)

    Article  Google Scholar 

  27. Vanobbergen, J., Martens, L., Lesaffre, E., Declerck, D.: The signal-Tandmobiel project a longitudinal intervention health promotion study in Flanders (Belgium): baseline and first year results. Eur. J. Paediatr. Dent. 2, 87–96 (2000)

    Google Scholar 

  28. Wang, X., Chen, M.-H., Yan, J.: Bayesian dynamic regression models for interval censored survival data with application to children dental health. Lifetime Data Anal. 19(3), 297–316 (2013)

    Article  MathSciNet  Google Scholar 

  29. Zhang, Y., Wang, X., Zhang, B.: Bayesian approach for clustered interval-censored data with time-varying covariate effects. Stat. Interface 12(3), 457–465 (2019)

    Article  MathSciNet  Google Scholar 

  30. Zhang, Y., Zhang, B.: Semiparametric spatial model for interval-censored data with time-varying covariate effects. Comput. Stat. Data Anal. 123(C), 146–156 (2018)

    Article  MathSciNet  Google Scholar 

  31. Zucker, D.M., Karr, A.F.: Nonparametric survival analysis with time-dependent covariate effects: a penalized partial likelihood approach. Ann. Stat. 18, 329–353 (1990)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Bioinformatics and Biostatistics, School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, Shanghai, PR China

    Yue Zhang

  2. Division of Biostatistics and Epidemiology, Cincinnati Children’s Hospital Medical Center, Cincinnati, OH, USA

    Bin Zhang

Authors
  1. Yue Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yue Zhang .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of South Dakota, Vermillion, SD, USA

    Yuhlong Lio

  2. College of Health Solutions, Arizona State University, Phoenix, AZ, USA

    Ding-Geng Chen

  3. Department of Mathematical Sciences, Bentley University, Waltham, MA, USA

    Hon Keung Tony Ng

  4. Department of Statistics, Tamkang University, New Taipei City, Taiwan

    Tzong-Ru Tsai

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Zhang, Y., Zhang, B. (2022). Bayesian Approach for Interval-Censored Survival Data with Time-Varying Coefficients. In: Lio, Y., Chen, DG., Ng, H.K.T., Tsai, TR. (eds) Bayesian Inference and Computation in Reliability and Survival Analysis. Emerging Topics in Statistics and Biostatistics . Springer, Cham. https://doi.org/10.1007/978-3-030-88658-5_15

Download citation

Publish with us

Policies and ethics

Search

Navigation