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Confidence intervals for survival quantiles in the Cox regression model

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Abstract

Median survival times and their associated confidence intervals are often used to summarize the survival outcome of a group of patients in clinical trials with failure-time endpoints. Although there is an extensive literature on this topic for the case in which the patients come from a homogeneous population, few papers have dealt with the case in which covariates are present as in the proportional hazards model. In this paper we propose a new approach to this problem and demonstrate its advantages over existing methods, not only for the proportional hazards model but also for the widely studied cases where covariates are absent and where there is no censoring. As an illustration, we apply it to the Stanford Heart Transplant data. Asymptotic theory and simulation studies show that the proposed method indeed yields confidence intervals and bands with accurate coverage errors.

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References

  • Andersen PK, Gill RD (1982) Cox’s regression model for counting processes: a large sample study. Ann Statist 10:1100–1120

    MathSciNet  Google Scholar 

  • Andersen PK, Borgan O, Gill RD, Keiding N (1993) Statistical models based on counting processes. Springer, New York

    MATH  Google Scholar 

  • Beran R, Hall P (1993) Interpolated nonparametric prediction intervals and confidence intervals. J R Stat Soc Ser B 55:643–652

    MathSciNet  Google Scholar 

  • Breslow NE (1974) Covariance analysis of censored survival data. Biometrics 30:89–99

    Article  Google Scholar 

  • Brookmeyer R, Crowley J (1982) A confidence interval for the median survival time. Biometrics 38:29–41

    Article  Google Scholar 

  • Burr D, Doss H (1993) Confidence bands for the median survival time as a function of the covariates in the Cox model. J Am Stat Assoc 88:1330–1340

    Article  MathSciNet  Google Scholar 

  • Chen X, Hall P (1993) Smoothed empirical likelihood confidence intervals for quantiles. Ann Statist 21:1166–1181

    MathSciNet  Google Scholar 

  • Cox DR (1972) Regression models and life-tables (with discussion). J R Stat Soc Ser B 34:187–220

    Google Scholar 

  • Dabrowska D, Doksum K (1987) Estimates and confidence intervals for median and mean life in the proportional hazard model. Biometrika 74:799–807

    Article  MathSciNet  Google Scholar 

  • Efron B (1979) Bootstrap methods: another look at the jackknife. Ann Statist 7:1–21

    MathSciNet  Google Scholar 

  • Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. Chapman & Hall, New York

    MATH  Google Scholar 

  • Gross S, Lai TL (1996) Bootstrap methods for truncated and censored data. Statist Sin 6:509–530

    MathSciNet  Google Scholar 

  • Gu M (1992) On the Edgeworth expansion and bootstrap approximation for the Cox regression model under random censorship. Can J Statist 20:399–414

    Google Scholar 

  • Hall P (1992) The bootstrap and Edgeworth expansion. Springer, New York

    Google Scholar 

  • Helmers R (1991) On the Edgeworth expansion and the bootstrap approximation for a Studentized U-statistic. Ann Statist 19:470–484

    MathSciNet  Google Scholar 

  • Ho Y, Lee M (2005) Iterated smoothed bootstrap confidence intervals for population quantiles. Ann Statist 33:437–462

    Article  MathSciNet  Google Scholar 

  • Lai TL, Wang Q (1993) Edgeworth expansions for symmetric statistics with applications to bootstrap methods. Statist Sin 3:517–542

    MathSciNet  Google Scholar 

  • Li G, Hollander M, McKeague IW, Yang J (1996) Nonparametric likelihood ratio confidence bands for quantile functions from incomplete data. Ann Statist 24:628–640

    Article  MathSciNet  Google Scholar 

  • Miller R, Halpern J (1982) Regression with censored data. Biometrika 69:521–531

    Article  MathSciNet  Google Scholar 

  • Strawderman RL, Parzen MI, Wells MT (1997) Accurate confidence limits for quantiles under random censoring. Biometrics 53:1399–1415

    Article  Google Scholar 

  • Tsiatis AA (1981) A large sample study of Cox’s regression model. Ann Statist 9:93–108

    MathSciNet  Google Scholar 

Download references

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Correspondence to Tze Leung Lai.

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Lai, T.L., Su, Z. Confidence intervals for survival quantiles in the Cox regression model. Lifetime Data Anal 12, 407–419 (2006). https://doi.org/10.1007/s10985-006-9024-y

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  • DOI: https://doi.org/10.1007/s10985-006-9024-y

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