Lifetime Data Analysis

, Volume 20, Issue 4, pp 514–537

Nonparametric estimation with recurrent competing risks data

Article

Abstract

Nonparametric estimators of component and system life distributions are developed and presented for situations where recurrent competing risks data from series systems are available. The use of recurrences of components’ failures leads to improved efficiencies in statistical inference, thereby leading to resource-efficient experimental or study designs or improved inferences about the distributions governing the event times. Finite and asymptotic properties of the estimators are obtained through simulation studies and analytically. The detrimental impact of parametric model misspecification is also vividly demonstrated, lending credence to the virtue of adopting nonparametric or semiparametric models, especially in biomedical settings. The estimators are illustrated by applying them to a data set pertaining to car repairs for vehicles that were under warranty.

Keywords

Recurrent events Competing risks Perfect and partial repairs Martingales Survival analysis Repairable systems Nonparametric methods 

References

  1. Andersen PK, Borgan Ø, Gill RD, Keiding N (1993) Statistical models based on counting processes. Springer series in statistics. Springer, New YorkGoogle Scholar
  2. Bedford T, Lindqvist BH (2004) The identifiability problem for repairable systems subject to competing risks. Adv Appl Probab 36(3):774–790MathSciNetCrossRefMATHGoogle Scholar
  3. Chen BE, Cook RJ (2004) Tests for multivariate recurrent events in the presence of a terminal event. Biostatistics 5:129–143CrossRefMATHGoogle Scholar
  4. Cook RJ, Lawless JF (2007) The statistical analysis of recurrent events. Springer, New YorkMATHGoogle Scholar
  5. Dauxois JY, Sencey S (2009) Non-parametric tests for recurrent events under competing risks. Scand J Stat 36(4):649–670MathSciNetCrossRefMATHGoogle Scholar
  6. Fine JP, Jiang H, Chappell R (2001) On semi-competing risks data. Biometrika 88(4):907–919MathSciNetCrossRefMATHGoogle Scholar
  7. Geffray S (2013) Modeling and inferential thoughts for consecutive gap times observed with death and censoring. J Iran Stat Soc 12(1):71–112MathSciNetGoogle Scholar
  8. Ghosh D, Lin DY (2000) Nonparametric analysis of recurrent events and death. Biometrics 56(2):554–562MathSciNetCrossRefMATHGoogle Scholar
  9. Huang CY, Wang MC (2005) Nonparametric estimation of the bivariate recurrence time distribution. Biometrics 61(2):392–402MathSciNetCrossRefMATHGoogle Scholar
  10. Lawless J, Wigg M, Tuli S, Drake J, Lamberti-Pasculli M (2001) Analysis of repeated failures of durations, with application to shunt failures for patients with paediatric hydrocephalus. Appl Stat 50(4):449–465MathSciNetMATHGoogle Scholar
  11. Lindqvist BH (2006) On the statistical modeling and analysis of repairable systems. Stat Sci 21(4):532–551MathSciNetCrossRefMATHGoogle Scholar
  12. Peña EA, Strawderman RL, Hollander M (2000) A weak convergence result relevant in recurrent and renewal models. In: Recent advances in reliability theory (Bordeaux, 2000). Statistics for industry and technology. Birkhäuser Boston, Boston, pp 93–514Google Scholar
  13. Peña EA, Strawderman RL, Hollander M (2001) Nonparametric estimation with recurrent event data. J Am Stat Assoc 96(456):1299–1315CrossRefMATHGoogle Scholar
  14. Peña EA, Slate EH, González JR (2007) Semiparametric inference for a general class of models for recurrent events. J Stat Plan Inference 137(6):1727–1747CrossRefMATHGoogle Scholar
  15. Prentice RL, Williams BJ, Peterson AV (1981) On the regression analysis of multivariate failure time data. Biometrika 68(2):373–379MathSciNetCrossRefMATHGoogle Scholar
  16. Song C, Kuo L (2013) Dynamic frailty and change point models for recurrent events data. J Iran Stat Soc 12(1):127–151MathSciNetGoogle Scholar
  17. Taylor LL, Peña EA (2013) Parametric estimation in a recurrent competing risks model. J Iran Stat Soc 12(1):153–181Google Scholar
  18. Wei LJ, Lin DY, Weissfeld L (1989) Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. J Am Stat Assoc 84(408):1065–1073MathSciNetCrossRefGoogle Scholar
  19. Xu J, Kalbfleisch JD, Tai B (2010) Statistical analysis of illness–death processes and semicompeting risks data. Biometrics 66(3):716–725MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Elon UniversityElonUSA
  2. 2.216 LeConte CollegeUniversity of South CarolinaColumbiaUSA

Personalised recommendations