Communications for Statistical Applications and Methods

  • 제24권2호
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  • Pages.115-127
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  • 2017
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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Bayesian test for the differences of survival functions in multiple groups

  • Kim, Gwangsu (Data Science for Knowledge Creation Research Center, Seoul National University)
  • 투고 : 2016.09.26
  • 심사 : 2017.02.04
  • 발행 : 2017.03.31
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초록

This paper proposes a Bayesian test for the equivalence of survival functions in multiple groups. Proposed Bayesian test use the model of Cox's regression with time-varying coefficients. B-spline expansions are used for the time-varying coefficients, and the proposed test use only the partial likelihood, which provides easier computations. Various simulations of the proposed test and typical tests such as log-rank and Fleming and Harrington tests were conducted. This result shows that the proposed test is consistent as data size increase. Specifically, the power of the proposed test is high despite the existence of crossing hazards. The proposed test is based on a Bayesian approach, which is more flexible when used in multiple tests. The proposed test can therefore perform various tests simultaneously. Real data analysis of Larynx Cancer Data was conducted to assess applicability.

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참고문헌

  1. Andersen PK and Gill RD (1982). Cox's regression model for counting processes: a large sample study, The Annals of Statistics, 10, 1100-1120. https://doi.org/10.1214/aos/1176345976
  2. Cox DR (1972). Regression models and life-tables, Journal of the Royal Statistical Society Series B (Methodological), 34, 187-220. https://doi.org/10.1111/j.2517-6161.1972.tb00899.x
  3. Gilks WR andWild P (1992). Adaptive rejection sampling for Gibbs sampling, Applied Statistics, 41, 337-348. https://doi.org/10.2307/2347565
  4. Harrington DP and Fleming TR (1982). A class of rank test procedures for censored survival data, Biometrika, 69, 553-566. https://doi.org/10.1093/biomet/69.3.553
  5. Hastings WK (1970). Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57, 97-109. https://doi.org/10.1093/biomet/57.1.97
  6. Kaplan EL and Meier P (1958). Nonparametric estimation from incomplete observations, Journal of the American Statistical Association, 53, 457-481. https://doi.org/10.1080/01621459.1958.10501452
  7. Kass RE and Raftery AE (1995). Bayes factors, Journal of the American Statistical Association, 90, 773-795. https://doi.org/10.1080/01621459.1995.10476572
  8. Kim G, Kim Y, and Choi T (2017). Bayesian analysis of the proportional hazards model with time-varying coefficients, Scandinavian Journal of Statistics, Advance online publication, doi:10.1111/sjos.12263
  9. Kim G and Lee S (2016). Bayesian test for hazard ratio in survival analysis, SpringerPlus, 5, 649. https://doi.org/10.1186/s40064-016-2210-9
  10. Kim MK, Lee JW, and Huh MH (2001). Random permutation test for comparison of two survival curves, Communications for Statistical Applications and Methods, 8, 137-145.
  11. Kim Y and Lee J (2003). Bayesian bootstrap for proportional hazards models, The Annals of Statistics, 31, 1905-1922. https://doi.org/10.1214/aos/1074290331
  12. Li H, Han D, Hou Y, Chen H, and Chen Z (2015). Statistical inference methods for two crossing survival curves: a comparison of methods, PLoS One, 10, e0116774. https://doi.org/10.1371/journal.pone.0116774
  13. Mantel N (1966). Evaluation of survival data and two new rank order statistics arising in its consideration, Cancer Chemotherapy Reports, 50, 163-170.
  14. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, and Teller E (1953). Equations of state calculations by fast computing machines, Journal of Chemical Physics, 21, 1087-1092. https://doi.org/10.1063/1.1699114
  15. Muggeo VMR and TagliaviaM(2010). A flexible approach to the crossing hazards problem, Statistics in Medicine, 29, 1947-1957. https://doi.org/10.1002/sim.3959
  16. Park SG and Jeong GJ (1995). On combination of several weighted logrank tests, Communications for Statistical Applications and Methods, 2, 213-220.
  17. Tsiatis AA (1981). A large sample study of Cox's regression model, The Annals of Statistics, 9, 93-108. https://doi.org/10.1214/aos/1176345335
  18. Yang S and Prentice R (2005). Semiparametric analysis of short-term and long-term hazard ratios with two-sample survival data, Biometrika, 92, 1-17. https://doi.org/10.1093/biomet/92.1.1