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Proportional reversed hazard and frailty models

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Abstract

Reversed hazard rates are found to be very useful in survival analysis and reliability especially in study on parallel systems and in the analysis of left censored lifetime data. In this paper, we derive a class of bivariate distributions having marginal proportional reversed hazard rates. We, then, introduce a class of proportional reversed hazard rates frailty models and propose a multivariate correlated gamma frailty model. Bivariate reversed hazard rates and association measure are discussed in terms of frailty parameters.

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References

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

    Google Scholar 

  • Bismi G (2005) Bivariate burr distributions. Ph.D. thesis, Cochin University of Science and Technology, India (unpublished)

  • Block HW, Savits TH and Singh H (1998). The reversed hazard rate function. Probab Eng Inform Sci 12: 69–90

    Article  MathSciNet  MATH  Google Scholar 

  • Chen YQ, Wang MC and Huang Y (2004). Semiparametric regression analysis on longitudinal pattern of recurrent gap times. Biostatistics 5(2): 277–290

    Article  MATH  Google Scholar 

  • Clayton DG (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65: 141–151

    Article  MathSciNet  MATH  Google Scholar 

  • Clayton DG and Cuzick J (1985). Multivariate generalizations of the proportional hazards model. J R Stat Soc Ser A 148(2): 82–117

    Article  MathSciNet  MATH  Google Scholar 

  • Di Crescenzo A (2000). Some results on the proportional reversed hazards model. Stat Probab Lett 50: 313–321

    Article  MathSciNet  MATH  Google Scholar 

  • Finkelstein MS (2003). On one class of bivariate distributions. Stat Probab Lett 65: 1–6

    Article  MathSciNet  MATH  Google Scholar 

  • Gupta RD and Nanda AK (2001). Some results on reversed hazard rate ordering. Commun Stat Theory Methods 30: 2447–2457

    Article  MathSciNet  MATH  Google Scholar 

  • Gupta RC and Wu H (2001). Analyzing survival data by proportional reversed hazard model. Int J Reliab Appl 2(1): 1–26

    Google Scholar 

  • Gupta RC, Gupta PL and Gupta RD (1998). Modelling failure time data by Lehman alternative. Commun Stat Theory Methods 27: 887–904

    Article  MATH  Google Scholar 

  • Hougaard P (2000). Analysis of multivariate survival data. Springer, New York

    MATH  Google Scholar 

  • Jones G and Rocke DM (2002). Multivariate survival analysis with doubly censored data: application to the assessment of accutane treatment for fibrodysplasia ossificans progressiva. Stat Med 21: 2547–2562

    Article  Google Scholar 

  • Kalbfleisch JD and Lawless JF (1989). Interface based on retrospective ascertainment: an analysis of the data based on transfusion-related AIDS. J Am Stat Assoc 84: 360–372

    Article  MathSciNet  MATH  Google Scholar 

  • Kaplan EL and Meier P (1958). Nonparametric estimation from incomplete observations. J Am Stat Assoc 53: 457–481

    Article  MathSciNet  MATH  Google Scholar 

  • Keilson J and Sumitha U (1982). Uniform stochastic ordering and related inequalities. Can J Stat 10: 181–198

    Article  MATH  Google Scholar 

  • Lawless JF (2003). Statistical models and methods for lifetime data. Wiley, New York

    MATH  Google Scholar 

  • Nair NU, Sankaran PG and Asha G (2005). Characterizations of distributions using reliability concepts. J Appl Stat Sci 14: 237–242

    Google Scholar 

  • Roy D (2002). A characterization of model approach for generating bivariate life distributions using reversed hazard rates. J Jpn Stat Soc 32(2): 239–245

    MATH  Google Scholar 

  • Sankaran PG and Gleeja VL (2006). On bivariate reversed hazard rates. J Jpn Stat Soc 36(2): 213–224

    MathSciNet  MATH  Google Scholar 

  • Sengupta D, Singh H, Nanda AK (2006) The proportional reversed hazard model. (Personal communication)

  • Vaupel JW, Manton KG and Stallard E (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16: 439–454

    Article  Google Scholar 

  • Yashin AI and Iashine IA (1997). How frailty models can be used for evaluating longevity limits: taking advantage of an interdisciplinary approach. Demography 34(1): 31–48

    Article  Google Scholar 

  • Yashin AI and Iashine IA (1999). Dependent hazards in multivariate survival problems. J Multivariate Anal 71: 241–261

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, Cochin University of Science and Technology, Cochin, 682022, India

    P. G. Sankaran & V. L. Gleeja

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  1. P. G. Sankaran
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  2. V. L. Gleeja
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Correspondence to P. G. Sankaran.

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Sankaran, P.G., Gleeja, V.L. Proportional reversed hazard and frailty models. Metrika 68, 333–342 (2008). https://doi.org/10.1007/s00184-007-0165-0

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  • DOI: https://doi.org/10.1007/s00184-007-0165-0

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