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Lifetime Data Analysis

, Volume 25, Issue 1, pp 52–78 | Cite as

Robust estimation in accelerated failure time models

  • Sanjoy K. SinhaEmail author
Article
  • 130 Downloads

Abstract

The accelerated failure time model is widely used for analyzing censored survival times often observed in clinical studies. It is well-known that the ordinary maximum likelihood estimators of the parameters in the accelerated failure time model are generally sensitive to potential outliers or small deviations from the underlying distributional assumptions. In this paper, we propose and explore a robust method for fitting the accelerated failure time model to survival data by bounding the influence of outliers in both the outcome variable and associated covariates. We also develop a sandwich-type variance–covariance function for approximating the variances of the proposed robust estimators. The finite-sample properties of the estimators are investigated based on empirical results from an extensive simulation study. An application is provided using actual data from a clinical study of primary breast cancer patients.

Keywords

Failure time model Hazard function Outliers Robust estimation Survival data 

References

  1. Bednarski T (1993) Robust estimation in Cox’s regression model. Scand J Stat 20:213–225MathSciNetzbMATHGoogle Scholar
  2. Bednarski T, Nowak M (2003) Robustness and efficiency of Sasieni-type estimators in the Cox model. J Stat Plan Inference 115:261–272MathSciNetCrossRefzbMATHGoogle Scholar
  3. Cantoni E, Ronchetti E (2001) Robust inference for generalized linear models. J Am Stat Assoc 96:1022–1030MathSciNetCrossRefzbMATHGoogle Scholar
  4. Chanrion M, Negre V, Fontaine H, Salvetat N, Bibeau F, Grogan GM, Mauriac L, Katsaros D, Molina F, Theillet C, Darbon JM (2008) A gene expression signature that can predict the recurrence of tamoxifen-treated primary breast cancer. Clin Cancer Res 14:1744–1752CrossRefGoogle Scholar
  5. Collett D (2014) Modelling survival data in medical research, 3rd edn. Chapman and Hall/CRC, New YorkGoogle Scholar
  6. de Jongh PJ, de Wet T, Welsh AH (1988) Mallows-type bounded-influence-regression trimmed means. J Am Stat Assoc 83:805–810MathSciNetzbMATHGoogle Scholar
  7. Farcomeni A, Viviani S (2011) Robust estimation for the Cox regression model based on trimming. Biom J 53:956–973MathSciNetCrossRefzbMATHGoogle Scholar
  8. Grambsch PM, Therneau TM (1994) Proportional hazards tests and diagnostics based on weighted residuals. Biometrika 81:515–526MathSciNetCrossRefzbMATHGoogle Scholar
  9. Hampel FR, Ronchetti EM, Rousseeuw PJ, Stahel WA (1986) Robust statistics: the approach based on influence functions. Wiley, New YorkzbMATHGoogle Scholar
  10. Huber PJ (1973) Robust regression: asymptotics, conjectures and Monte Carlo. Ann Stat 1:799–821MathSciNetCrossRefzbMATHGoogle Scholar
  11. Huber PJ (1981) Robust statistics. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  12. Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data, 2nd edn. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  13. Lin DY, Wei LJ (1989) The robust inference for the Cox proportional hazards model. J Am Stat Assoc 84:1074–1078MathSciNetCrossRefzbMATHGoogle Scholar
  14. Locatelli I, Marazzi A, Yohai VJ (2011) Robust accelerated failure time regression. Comput Stat Data Anal 55:874–887MathSciNetCrossRefzbMATHGoogle Scholar
  15. Minder CE, Bednarski T (1996) A robust method for proportional hazards regression. Stat Med 15:1033–1047CrossRefGoogle Scholar
  16. Nardi A, Schemper M (1999) New residuals for Cox regression and their application to outlier screening. Biometrics 55:523–529CrossRefzbMATHGoogle Scholar
  17. Pinto JD, Carvalho AM, Vinga S (2015) Outlier detection in Cox proportional hazards models based on the concordance c-index. In: Machine learning, optimization, and big data: lecture notes in computer science, pp 252–256Google Scholar
  18. Reid N, Crepeau H (1985) Influence functions for proportional hazards regression. Biometrika 72:1–9MathSciNetCrossRefGoogle Scholar
  19. Rousseeuw PJ, van Zomeren BC (1990) Unmasking multivariate outliers and leverage points. J Am Stat Assoc 85:633–639CrossRefGoogle Scholar
  20. Sasieni PD (1993a) Some new estimators for Cox regression. Ann Stat 21:1721–1759MathSciNetCrossRefzbMATHGoogle Scholar
  21. Sasieni PD (1993b) Maximum weighted partial likelihood estimators for the Cox model. J Am Stat Assoc 88:144–152zbMATHGoogle Scholar
  22. Sinha SK (2004) Robust analysis of generalized linear mixed models. J Am Stat Assoc 99:451–460MathSciNetCrossRefzbMATHGoogle Scholar
  23. Sinha SK, Rao JNK (2009) Robust small area estimation. Can J Stat 37:381–399MathSciNetCrossRefzbMATHGoogle Scholar
  24. Wei LJ (1992) The accelerated failure time model: a useful alternative to the Cox regression model in survival analysis. Stat Med 11:1871–1879CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsCarleton UniversityOttawaCanada

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