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Bayes factors for choosing among six common survival models

  • Jiajia Zhang
  • Timothy Hanson
  • Haiming Zhou
Article
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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.

Keywords

Interval censoring Model choice Bernstein polynomial Bayes factor 
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Supplementary material

10985_2018_9429_MOESM1_ESM.pdf (179 kb)
Supplementary material 1 (pdf 179 KB)

References

  1. 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):2131–2137CrossRefGoogle Scholar
  2. Chen YQ, Jewell NP (2001) On a general class of semiparametric hazards regression models. Biometrika 88(3):687–702MathSciNetCrossRefzbMATHGoogle Scholar
  3. Chen YQ, Wang M-C (2000) Analysis of accelerated hazards models. J Am Stat Assoc 95(450):608–618MathSciNetCrossRefzbMATHGoogle Scholar
  4. Cheng S, Wei L, Ying Z (1995) Analysis of transformation models with censored data. Biometrika 82(4):835–845MathSciNetCrossRefzbMATHGoogle Scholar
  5. Chen Y, Hanson T, Zhang J (2014) Accelerated hazards model based on parametric families generalized with Bernstein polynomials. Biometrics 70(1):192–201MathSciNetCrossRefzbMATHGoogle Scholar
  6. Cox DR (1992) Regression models and life-tables. In: Breakthroughs in statistics. Springer, New York, NY, pp 527–541Google Scholar
  7. De Iorio M, Johnson WO, Müller P, Rosner GL (2009) Bayesian nonparametric nonproportional hazards survival modeling. Biometrics 65(3):762–771MathSciNetCrossRefzbMATHGoogle Scholar
  8. 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):667–676MathSciNetCrossRefzbMATHGoogle Scholar
  9. 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):840–849MathSciNetCrossRefzbMATHGoogle Scholar
  10. 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):181–192CrossRefzbMATHGoogle Scholar
  11. Ferguson TS (1973) A Bayesian analysis of some nonparametric problems. Ann Stat 1(2):209–230MathSciNetCrossRefzbMATHGoogle Scholar
  12. Ghosal S (2001) Convergence rates for density estimation with Bernstein polynomials. Ann Stat 29(5):1264–1280MathSciNetCrossRefzbMATHGoogle Scholar
  13. Green PJ (1995) Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82(4):711–732MathSciNetCrossRefzbMATHGoogle Scholar
  14. Haario H, Saksman E, Tamminen J (2001) An adaptive Metropolis algorithm. Bernoulli 7(2):223–242MathSciNetCrossRefzbMATHGoogle Scholar
  15. Hanson TE (2006) Inference for mixtures of finite Polya tree models. J Am Stat Assoc 101(476):1548–1565MathSciNetCrossRefzbMATHGoogle Scholar
  16. Hanson T, Yang M (2007) Bayesian semiparametric proportional odds models. Biometrics 63(1):88–95MathSciNetCrossRefzbMATHGoogle Scholar
  17. Hanson TE, Branscum AJ, Johnson WO et al (2014) Informative \( g \)-priors for logistic regression. Bayesian Anal 9(3):597–612MathSciNetCrossRefzbMATHGoogle Scholar
  18. Kalbfleisch JD, Prentice RL (2011) The statistical analysis of failure time data. Wiley, HobokenzbMATHGoogle Scholar
  19. Li L, Hanson T, Zhang J (2015) Spatial extended hazard model with application to prostate cancer survival. Biometrics 71(2):313–322MathSciNetCrossRefzbMATHGoogle Scholar
  20. Murphy S, Rossini A, van der Vaart AW (1997) Maximum likelihood estimation in the proportional odds model. J Am Stat Assoc 92(439):968–976MathSciNetCrossRefzbMATHGoogle Scholar
  21. Petrone S, Wasserman L (2002) Consistency of Bernstein polynomial posteriors. J R Stat Soc Ser B (Stat Methodol) 64(1):79–100MathSciNetCrossRefzbMATHGoogle Scholar
  22. Prentice RL (1973) Exponential survivals with censoring and explanatory variables. Biometrika 60(2):279–288MathSciNetCrossRefzbMATHGoogle Scholar
  23. Quantin C, Moreau T, Asselain B, Maccario J, Lellouch J (1996) A regression survival model for testing the proportional hazards hypothesis. Biometrics 52(3):874–885MathSciNetCrossRefzbMATHGoogle Scholar
  24. 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):355–391CrossRefzbMATHGoogle Scholar
  25. Sun J (2006) The statistical analysis of interval-censored failure time data. Springer, BerlinzbMATHGoogle Scholar
  26. Turnbull BW (1976) The empirical distribution function with arbitrarily grouped, censored and truncated data. J Roy Stat Soc Ser B (Methodol) 38(3):290–295MathSciNetzbMATHGoogle Scholar
  27. Verdinelli I, Wasserman L (1995) Computing Bayes factors using a generalization of the Savage-Dickey density ratio. J Am Stat Assoc 90(430):614–618MathSciNetCrossRefzbMATHGoogle Scholar
  28. Yang S, Prentice RL (1999) Semiparametric inference in the proportional odds regression model. J Am Stat Assoc 94(445):125–136MathSciNetCrossRefzbMATHGoogle Scholar
  29. Yang S, Prentice R (2005) Semiparametric analysis of short-term and long-term hazard ratios with two-sample survival data. Biometrika 92(1):1–17MathSciNetCrossRefzbMATHGoogle Scholar
  30. Yin G, Ibrahim JG (2005) Bayesian frailty models based on Box-Cox transformed hazards. Statistica Sinica 15(3):781–794MathSciNetzbMATHGoogle Scholar
  31. Zellner A (1983) Applications of Bayesian analysis in econometrics. J R Stat Soc Ser D (Stat) 32:23–34Google Scholar
  32. Zeng D, Lin D (2007) Semiparametric transformation models with random effects for recurrent events. J Am Stat Assoc 102(477):167–180MathSciNetCrossRefzbMATHGoogle Scholar
  33. Zhang J, Peng Y (2009) Crossing hazard functions in common survival models. Stat Probab Lett 79(20):2124–2130MathSciNetCrossRefzbMATHGoogle Scholar
  34. Zhou H, Hanson T (2015) Bayesian spatial survival models. In: Nonparametric Bayesian inference in biostatistics. Springer, Cham, pp 215–246Google Scholar
  35. Zhou H, Hanson T, Zhang J (2017) Generalized accelerated failure time spatial frailty model for arbitrarily censored data. Lifetime Data Anal 23(3):495–515MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Epidemiology and BiostatisticsUniversity of South CarolinaColumbiaUSA
  2. 2.Medtronic Inc.MinneapolisUSA
  3. 3.Division of StatisticsNorthern Illinois UniversityDeKalbUSA

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