Skip to main content

Advertisement

SpringerLink
Log in

Bayes factors for choosing among six common survival models

  • Published:
Lifetime Data Analysis Aims and scope Submit manuscript

Abstract

A super model that includes proportional hazards, proportional odds, accelerated failure time, accelerated hazards, and extended hazards models, as well as the model proposed in Diao et al. (Biometrics 69(4):840–849, 2013) accounting for crossed survival as special cases is proposed for the purpose of testing and choosing among these popular semiparametric models. Efficient methods for fitting and computing fast, approximate Bayes factors are developed using a nonparametric baseline survival function based on a transformed Bernstein polynomial. All manner of censoring is accommodated including right, left, and interval censoring, as well as data that are observed exactly and mixtures of all of these; current status data are included as a special case. The method is tested on simulated data and two real data examples. The approach is easily carried out via a new function in the spBayesSurv R package.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Beadle GF, Come S, Henderson IC, Silver B, Hellman S, Harris JR (1984) The effect of adjuvant chemotherapy on the cosmetic results after primary radiation treatment for early stage breast cancer. Int J Radiat Oncol Biol Phys 10(11):2131–2137

    Article  Google Scholar 

  • Chen YQ, Jewell NP (2001) On a general class of semiparametric hazards regression models. Biometrika 88(3):687–702

    Article  MathSciNet  MATH  Google Scholar 

  • Chen YQ, Wang M-C (2000) Analysis of accelerated hazards models. J Am Stat Assoc 95(450):608–618

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng S, Wei L, Ying Z (1995) Analysis of transformation models with censored data. Biometrika 82(4):835–845

    Article  MathSciNet  MATH  Google Scholar 

  • Chen Y, Hanson T, Zhang J (2014) Accelerated hazards model based on parametric families generalized with Bernstein polynomials. Biometrics 70(1):192–201

    Article  MathSciNet  MATH  Google Scholar 

  • Cox DR (1992) Regression models and life-tables. In: Breakthroughs in statistics. Springer, New York, NY, pp 527–541

  • De Iorio M, Johnson WO, Müller P, Rosner GL (2009) Bayesian nonparametric nonproportional hazards survival modeling. Biometrics 65(3):762–771

    Article  MathSciNet  MATH  Google Scholar 

  • Devarajan K, Ebrahimi N (2011) A semi-parametric generalization of the Cox proportional hazards regression model: inference and applications. Comput Stat Data Anal 55(1):667–676

    Article  MathSciNet  MATH  Google Scholar 

  • Diao G, Zeng D, Yang S (2013) Efficient semiparametric estimation of short-term and long-term hazard ratios with right-censored data. Biometrics 69(4):840–849

    Article  MathSciNet  MATH  Google Scholar 

  • Etezadi-Amoli J, Ciampi A (1987) Extended hazard regression for censored survival data with covariates: a spline approximation for the baseline hazard function. Biometrics 43(2):181–192

    Article  MATH  Google Scholar 

  • Ferguson TS (1973) A Bayesian analysis of some nonparametric problems. Ann Stat 1(2):209–230

    Article  MathSciNet  MATH  Google Scholar 

  • Ghosal S (2001) Convergence rates for density estimation with Bernstein polynomials. Ann Stat 29(5):1264–1280

    Article  MathSciNet  MATH  Google Scholar 

  • Green PJ (1995) Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82(4):711–732

    Article  MathSciNet  MATH  Google Scholar 

  • Haario H, Saksman E, Tamminen J (2001) An adaptive Metropolis algorithm. Bernoulli 7(2):223–242

    Article  MathSciNet  MATH  Google Scholar 

  • Hanson TE (2006) Inference for mixtures of finite Polya tree models. J Am Stat Assoc 101(476):1548–1565

    Article  MathSciNet  MATH  Google Scholar 

  • Hanson T, Yang M (2007) Bayesian semiparametric proportional odds models. Biometrics 63(1):88–95

    Article  MathSciNet  MATH  Google Scholar 

  • Hanson TE, Branscum AJ, Johnson WO et al (2014) Informative \( g \)-priors for logistic regression. Bayesian Anal 9(3):597–612

    Article  MathSciNet  MATH  Google Scholar 

  • Kalbfleisch JD, Prentice RL (2011) The statistical analysis of failure time data. Wiley, Hoboken

    MATH  Google Scholar 

  • Li L, Hanson T, Zhang J (2015) Spatial extended hazard model with application to prostate cancer survival. Biometrics 71(2):313–322

    Article  MathSciNet  MATH  Google Scholar 

  • Murphy S, Rossini A, van der Vaart AW (1997) Maximum likelihood estimation in the proportional odds model. J Am Stat Assoc 92(439):968–976

    Article  MathSciNet  MATH  Google Scholar 

  • Petrone S, Wasserman L (2002) Consistency of Bernstein polynomial posteriors. J R Stat Soc Ser B (Stat Methodol) 64(1):79–100

    Article  MathSciNet  MATH  Google Scholar 

  • Prentice RL (1973) Exponential survivals with censoring and explanatory variables. Biometrika 60(2):279–288

    Article  MathSciNet  MATH  Google Scholar 

  • Quantin C, Moreau T, Asselain B, Maccario J, Lellouch J (1996) A regression survival model for testing the proportional hazards hypothesis. Biometrics 52(3):874–885

    Article  MathSciNet  MATH  Google Scholar 

  • Scharfstein DO, Tsiatis AA, Gilbert PB (1998) Semiparametric efficient estimation in the generalized odds-rate class of regression models for right-censored time-to-event data. Lifetime Data Anal 4(4):355–391

    Article  MATH  Google Scholar 

  • Sun J (2006) The statistical analysis of interval-censored failure time data. Springer, Berlin

    MATH  Google Scholar 

  • Turnbull BW (1976) The empirical distribution function with arbitrarily grouped, censored and truncated data. J Roy Stat Soc Ser B (Methodol) 38(3):290–295

    MathSciNet  MATH  Google Scholar 

  • Verdinelli I, Wasserman L (1995) Computing Bayes factors using a generalization of the Savage-Dickey density ratio. J Am Stat Assoc 90(430):614–618

    Article  MathSciNet  MATH  Google Scholar 

  • Yang S, Prentice RL (1999) Semiparametric inference in the proportional odds regression model. J Am Stat Assoc 94(445):125–136

    Article  MathSciNet  MATH  Google Scholar 

  • Yang S, Prentice R (2005) Semiparametric analysis of short-term and long-term hazard ratios with two-sample survival data. Biometrika 92(1):1–17

    Article  MathSciNet  MATH  Google Scholar 

  • Yin G, Ibrahim JG (2005) Bayesian frailty models based on Box-Cox transformed hazards. Statistica Sinica 15(3):781–794

    MathSciNet  MATH  Google Scholar 

  • Zellner A (1983) Applications of Bayesian analysis in econometrics. J R Stat Soc Ser D (Stat) 32:23–34

    Google Scholar 

  • Zeng D, Lin D (2007) Semiparametric transformation models with random effects for recurrent events. J Am Stat Assoc 102(477):167–180

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang J, Peng Y (2009) Crossing hazard functions in common survival models. Stat Probab Lett 79(20):2124–2130

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou H, Hanson T (2015) Bayesian spatial survival models. In: Nonparametric Bayesian inference in biostatistics. Springer, Cham, pp 215–246

  • Zhou H, Hanson T, Zhang J (2017) Generalized accelerated failure time spatial frailty model for arbitrarily censored data. Lifetime Data Anal 23(3):495–515

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Epidemiology and Biostatistics, University of South Carolina, Columbia, SC, 29208, USA

    Jiajia Zhang

  2. Medtronic Inc., Minneapolis, MN, USA

    Timothy Hanson

  3. Division of Statistics, Northern Illinois University, DeKalb, IL, 60115, USA

    Haiming Zhou

Authors
  1. Jiajia Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Timothy Hanson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haiming Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiajia Zhang.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 179 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, J., Hanson, T. & Zhou, H. Bayes factors for choosing among six common survival models. Lifetime Data Anal 25, 361–379 (2019). https://doi.org/10.1007/s10985-018-9429-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10985-018-9429-4

Keywords

Search

Navigation