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Extended Cox and Accelerated Models in Reliability, with General Censoring and Truncation

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Statistical Models and Methods for Biomedical and Technical Systems

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

We review recent developments in reliability or survival analysis. We consider various models for the time to failure or survival time, by a law on IR + that may depend on one or more factors. Inhomogeneity is taken into account by way of frailty models. The presence of censoring and truncation of a general type, more complex than the usual simple case of right censoring, induced the most recent developments on these topics. In the case of clusters of items or families of patients implying a possible dependence between multiple failure times, shared frailty models or hierarchical dependency models are considered.

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References

  1. Alioum, A. and Commenges, D. (1996). A proportional hazards model for arbitrarily censored and truncated data, Biometrics, 52, 512–524.

    Article  MATH  Google Scholar 

  2. Bagdonavicius, V. and Nikulin, M. (1997). Transfer functionals and semiparametric regression models, Biometrika, 84, 365–378.

    Article  MATH  MathSciNet  Google Scholar 

  3. Bagdonavicius, V. and Nikulin, M. (1998). Additive and multiplicative semiparametric models in accelerated life testing and survival analysis, Queen’s papers in Pure and Applied Mathematics, Queen’s University, Kingston, Ontario, Canada.

    MATH  Google Scholar 

  4. Bagdonavicius, V. and Nikulin, M. (1999). Generalized proportional hazards model based on modified partial likelihood, LIDA, 5, 323–344.

    MathSciNet  Google Scholar 

  5. Bagdonavicius, V. and Nikulin, M. (2000a). On goodness of fit for the linear transformation and frailty models, Statistics and Probability Letters, 47, 177–188.

    Article  MATH  MathSciNet  Google Scholar 

  6. Bagdonavicius, V. and Nikulin, M. (2000b). On nonparametric estimation in accelerated experiments with step stresses, Statistics, 33, 349–365.

    Article  MATH  MathSciNet  Google Scholar 

  7. Bagdonavicius, V. and Nikulin, M. (2002). Accelerated Life Models. Modeling and Statistical Analysis, Chapman and Hall, Boca Raton, FL.

    MATH  Google Scholar 

  8. Bagdonavicius, V. and Nikulin, M. (2005). Statistical analysis of survival and reliability data with multiple crossings of survival functions, Comptes Rendus de l’Academie des Sciences de Paris, Series I, 340, 377–382.

    MATH  MathSciNet  Google Scholar 

  9. Bretagnolle, J. and Huber, C. (1988). Effects of omitting covariates in Cox’s model for survival data, Scandinavian Journal of Statistics, 15, 125–138.

    MATH  Google Scholar 

  10. Cheng, S. C., Wei, L. J., and Ying Z. (1995). Analysis of transformation models with censored data, Biometrika, 82, 835–846.

    Article  MATH  MathSciNet  Google Scholar 

  11. Clayton, D. G. and Cuzick, J. (1985). Multivariate generalization of the proportional hazards model (with discussion), Journal of the Royal Statistical Society, Series A, 148, 82–117.

    Article  MATH  MathSciNet  Google Scholar 

  12. Dabrowska, D. (2005). Quantile regression in transformation models, Sankhya, 67, 153–187.

    MathSciNet  Google Scholar 

  13. Dabrowska, D. (2006). Information bounds and efficient estimation in a class of censored transformation models, Web page: arXiv:math.ST/0608088 v1 3 Aug 2006.

    Google Scholar 

  14. Dabrowska, D. (2006). Estimation in a class of semi-parametric transformation models, In Second Eric L. Lehmann Symposium – Optimality (Ed., J. Rojo), Institute of Mathematical Statistics, Lecture Notes and Monograph Series, 49, 166–216.

    Google Scholar 

  15. Dabrowska, D. M. and Doksum, K. A. (1988). Partial likelihood in transformation model with censored data, Scandinavian Journal of Statistics, 15, 1–23.

    MATH  MathSciNet  Google Scholar 

  16. Finkelstein, D. M., Moore, D. F., and Shoenfeld, D. A. (1993). A proportional hazards model for truncated AIDS data, Biometrics, 49, 731–740.

    Article  MATH  MathSciNet  Google Scholar 

  17. Frydman, H. (1994). A note on nonparametric estimation of the distribution function from interval-censored and truncated observations, Journal of the Royal Statistical Society, Series B, 56, 71–74.

    MATH  MathSciNet  Google Scholar 

  18. Gross, S. and Huber, C. (1992). Regression models for truncated survival data, Scandinavian Journal of Statistics, 19, 193–213.

    MATH  Google Scholar 

  19. Gross, S. and Huber, C. (2002). A new family of multivariate distributions for survival data, In Goodness of Fit Tests and Model Validity, pp. 255–266, Birkhaüser, Boston.

    Google Scholar 

  20. Hsieh, F. (2001). On heteroscedastic hazards regression models: Theory and application, Journal of the Royal Statistical Society, Series B, 63, 63–79.

    Article  MATH  MathSciNet  Google Scholar 

  21. Huber-Carol, C. and Vonta, F. (2004). Frailty models for arbitrarily censored and truncated data, Lifetime Data Analysis, 10, 369–388.

    Article  MATH  MathSciNet  Google Scholar 

  22. Huber-Carol, C., Solev, V., and Vonta, F. (2006). Estimation of density for arbitrarily censored and truncated data, In Probability, Statistics and Modelling in Public Health (Eds., M. Nikulin, D. Commenges, C. Huber), pp. 246–265, Springer-Verlag, New York.

    Chapter  Google Scholar 

  23. Kalbfleisch, J.D. and Lawless, J.F. (1989). Inference on retrospective ascertainment: An analysis of the data on transfusion-related AIDS, Journal of the American Statistical Association, 84, 360–372.

    Article  MATH  MathSciNet  Google Scholar 

  24. Martinussen, T., Scheike, T. (2006). Dynamic Regression Models for Survival Analysis, Springer-Verlag, New York.

    Google Scholar 

  25. Meeker, W. Q. and Escobar L. (1998), Statistical Methods for Reliability Data, John Wiley & Sons, New York.

    MATH  Google Scholar 

  26. Nikulin, M. and Wu, H-D.I. (2006). Flexible regression models for carcinogenesis studies, In Probability and Statistics, 10 (Eds., I. Ibragimov and V. Sudakov), pp. 78–101, Academy of Sciences of Russia, St. Petersburg.

    Google Scholar 

  27. Parner, E. (1998). Asymptotic theory for the correlated gamma-frailty model, Annals of Statistics, 26, 183–214.

    Article  MATH  MathSciNet  Google Scholar 

  28. Pons, O. and Visser, M. (2000). A non-stationary Cox model, Scandinanvia Journal of Statistics, 24, 619–639.

    Article  MathSciNet  Google Scholar 

  29. Pons, O. (2000). Nonparametric estimation in a varying-coefficient Cox model, Mathematical Methods in Statistics, 9, 376–398.

    MATH  MathSciNet  Google Scholar 

  30. Pons, O. (2002a). Inference in extensions of the Cox model for heterogeneous populations, In Goodness-of-fit Tests and Validity of Models (Eds., C. Huber-Carol, N. Balakrishnan, M. S. Nikulin, and M. Mesbah), pp. 211–225, Birkhaüser, Boston.

    Google Scholar 

  31. Pons, O. (2002b). Estimation in a Cox regression model with a change-point at an unknown time, Statistics, 36, 101–124.

    MATH  MathSciNet  Google Scholar 

  32. Scheike, T. (2006). A flexible semiparametric transformation model for survival data, Lifetime Data Analysis, 12, 461–480.

    Article  MATH  MathSciNet  Google Scholar 

  33. Slud, E. V. and Vonta, F. (2004). Consistency of the NPML estimator in the right-censored transformation model, Scandinavian Journal of Statistics, 31, 21–41.

    Article  MATH  MathSciNet  Google Scholar 

  34. Tsiatis, A. A. (1981). A large sample study of Cox’s regression model, Annals of Statistics, 9, 93–108.

    Article  MATH  MathSciNet  Google Scholar 

  35. Turnbull, B. W. (1976). The empirical distribution function with arbitrarily grouped, censored and truncated data, Journal of the Royal Statistical Society, 38, 290–295.

    MATH  MathSciNet  Google Scholar 

  36. Wu, H-D. I. (2004). Effect of ignoring heterogeneity in hazards regression, In Parametric and Semiparametric Models with Applicatiions to Reliability, Survival Analysis, and Quality of Life, pp. 239–252, Birkhaüser, Boston.

    Google Scholar 

  37. Wu, H-D. I. (2006). Statistical inference for two-sample and regression models with heterogeneity effects: A collected-sample perspective, In Probability, Statistics and Modelling in Public Health (Eds., M. Nikulin, D. Commenges, and C. Huber), pp. 452–465, Springer-Verlag, New York.

    Chapter  Google Scholar 

  38. Wu, H-D. I. (2007). A partial score test for difference among heterogeneous populations, Journal of Statistical Planning and Inference, 137, 527–537.

    Article  MATH  MathSciNet  Google Scholar 

  39. Wu, H-D. I., Hsieh, F., and Chen C.-H. (2002). Validation of a heteroscedastic hazards regression model, Lifetime Data Analysis, 8, 21–34.

    Article  MATH  MathSciNet  Google Scholar 

  40. Zeng, D. and Lin, D. (2007). Maximum likelihood estimation in semiparametric regression models with censored data, Journal of the Royal Statistical Society, 69, 1–30.

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Université Paris 5 and Unité INSERM 870, Paris, France

    Catherine Huber-Carol

  2. IMB, Université Victor Segalen, Bordeaux, France

    Mikhail Nikulin

Authors
  1. Catherine Huber-Carol
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  2. Mikhail Nikulin
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Cyprus, CY-1678, Nicosia, Cyprus

    Filia Vonta

  2. UFR Sciences et Modélisation, Université Victor Segalen Bordeaux 2, 33076, Bordeaux Cedex, France

    Mikhail Nikulin

  3. Laboratoire de Mathématiques Appliquées, Université de Technologie de Compiègne, 60205, Compiègne Cedex, France

    Nikolaos Limnios

  4. Université Paris V, 45 rue des Saints-Pères, 75270, Paris Cedex 06, France

    Catherine Huber-Carol

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© 2008 Birkhäuser Boston

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Huber-Carol, C., Nikulin, M. (2008). Extended Cox and Accelerated Models in Reliability, with General Censoring and Truncation. In: Vonta, F., Nikulin, M., Limnios, N., Huber-Carol, C. (eds) Statistical Models and Methods for Biomedical and Technical Systems. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4619-6_1

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