SpringerLink
Log in

Nonparametric estimation with recurrent competing risks data

  • Published:
Lifetime Data Analysis Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

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

  • Bedford T, Lindqvist BH (2004) The identifiability problem for repairable systems subject to competing risks. Adv Appl Probab 36(3):774–790

    Article  MathSciNet  MATH  Google Scholar 

  • Chen BE, Cook RJ (2004) Tests for multivariate recurrent events in the presence of a terminal event. Biostatistics 5:129–143

    Article  MATH  Google Scholar 

  • Cook RJ, Lawless JF (2007) The statistical analysis of recurrent events. Springer, New York

    MATH  Google Scholar 

  • Dauxois JY, Sencey S (2009) Non-parametric tests for recurrent events under competing risks. Scand J Stat 36(4):649–670

    Article  MathSciNet  MATH  Google Scholar 

  • Fine JP, Jiang H, Chappell R (2001) On semi-competing risks data. Biometrika 88(4):907–919

    Article  MathSciNet  MATH  Google Scholar 

  • Geffray S (2013) Modeling and inferential thoughts for consecutive gap times observed with death and censoring. J Iran Stat Soc 12(1):71–112

    MathSciNet  Google Scholar 

  • Ghosh D, Lin DY (2000) Nonparametric analysis of recurrent events and death. Biometrics 56(2):554–562

    Article  MathSciNet  MATH  Google Scholar 

  • Huang CY, Wang MC (2005) Nonparametric estimation of the bivariate recurrence time distribution. Biometrics 61(2):392–402

    Article  MathSciNet  MATH  Google Scholar 

  • 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):449–465

    MathSciNet  MATH  Google Scholar 

  • Lindqvist BH (2006) On the statistical modeling and analysis of repairable systems. Stat Sci 21(4):532–551

    Article  MathSciNet  MATH  Google Scholar 

  • 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 93–514

  • Peña EA, Strawderman RL, Hollander M (2001) Nonparametric estimation with recurrent event data. J Am Stat Assoc 96(456):1299–1315

    Article  MATH  Google Scholar 

  • Peña EA, Slate EH, González JR (2007) Semiparametric inference for a general class of models for recurrent events. J Stat Plan Inference 137(6):1727–1747

    Article  MATH  Google Scholar 

  • Prentice RL, Williams BJ, Peterson AV (1981) On the regression analysis of multivariate failure time data. Biometrika 68(2):373–379

    Article  MathSciNet  MATH  Google Scholar 

  • Song C, Kuo L (2013) Dynamic frailty and change point models for recurrent events data. J Iran Stat Soc 12(1):127–151

    MathSciNet  Google Scholar 

  • Taylor LL, Peña EA (2013) Parametric estimation in a recurrent competing risks model. J Iran Stat Soc 12(1):153–181

    Google Scholar 

  • 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):1065–1073

    Article  MathSciNet  Google Scholar 

  • Xu J, Kalbfleisch JD, Tai B (2010) Statistical analysis of illness–death processes and semicompeting risks data. Biometrics 66(3):716–725

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to thank Professor Ananda Sen of the University of Michigan for providing the car warranty data. The authors thank the Reviewers, Associate Editor, and Editor for their comments that led to improvements. They are also grateful to Professors Jason Fine and Bo Lindqvist for inviting them to contribute to this special issue. Research partially supported by NSF Grant DMS1106435 and NIH Grants R01 CA154731 and P20 RR17698.

Author information

Authors and Affiliations

  1. Elon University, Campus Box 2320, Elon, NC, 27244, USA

    Laura L. Taylor

  2. 216 LeConte College, University of South Carolina, Columbia, SC, 29208, USA

    Edsel A. Peña

Authors
  1. Laura L. Taylor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edsel A. Peña
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Laura L. Taylor.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Taylor, L.L., Peña, E.A. Nonparametric estimation with recurrent competing risks data. Lifetime Data Anal 20, 514–537 (2014). https://doi.org/10.1007/s10985-013-9280-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10985-013-9280-6

Keywords

Search

Navigation