IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v24y2012i3p733-752.html
   My bibliography  Save this article

Semiparametric estimation with recurrent event data under informative monitoring

Author

Listed:
  • Akim Adekpedjou
  • Edsel Peña

Abstract

Consider a study where the times of occurrences of a recurrent event for n units are monitored. For the ith unit, Ti1, Ti2, …, denote the successive event inter-occurrence times and this unit is monitored over a random period [0, τi] with τi independent of the Tijs. Over this monitoring period, is the random number of event occurrences. The Tijs are independent and identically distributed (IID) from an unknown continuous distribution function F and the τis are IID from a distribution function G. A generalised Koziol–Green (GKG) structure wherein 1−G=(1−F)β for some β>0 is assumed. Under this model, Nelson–Aalen and product-limit type estimators of Λ=−log(1−F) and F are obtained, as well as an estimator of β. Asymptotic and small-sample properties of these estimators are obtained and the estimator of F is compared to the fully nonparametric estimator in Peña et al. [(2001), ‘Nonparametric Estimation with Recurrent Event Data’, Journal of the American Statistical Association, 96, 1299–1315] in terms of their finite-sample and asymptotic efficiency. The performance of the estimators of F are also examined when the GKG structure does not hold through a simulation study.

Suggested Citation

  • Akim Adekpedjou & Edsel Peña, 2012. "Semiparametric estimation with recurrent event data under informative monitoring," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 733-752.
  • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:733-752
    DOI: 10.1080/10485252.2012.698281
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485252.2012.698281
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/10485252.2012.698281?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cheng, Philip E. & Lin, Gwo Dong, 1987. "Maximum likelihood estimation of a survival function under the koziol-green proportional hazards model," Statistics & Probability Letters, Elsevier, vol. 5(1), pages 75-80, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Uña-Álvarez, Jacobo de & González-Manteiga, Wenceslao, 1999. "Strong consistency under proportional censorship when covariables are present," Statistics & Probability Letters, Elsevier, vol. 42(3), pages 283-292, April.
    2. Jean-Yves Dauxois & Agathe Guilloux & Syed N. U. A. Kirmani, 2004. "Estimation in a Competing Risks Proportional Hazards Model Under Length-biased Sampling with Censoring," Working Papers 2004-02, Center for Research in Economics and Statistics.
    3. M. A. Jácome & R. Cao, 2008. "Strong representation of the presmoothed quantile function estimator for censored data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(4), pages 425-440, November.
    4. Zhang, Haimeng & Rao, M. Bhaskara, 2006. "A note on the generalized maximum likelihood estimator in partial Koziol-Green model," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 813-820, April.
    5. Wen, Xuerong Meggie, 2010. "On sufficient dimension reduction for proportional censorship model with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1975-1982, August.
    6. Kirmani, Syed N. U. A. & Dauxois, Jean-Yves, 2004. "Testing the Koziol-Green model against monotone conditional odds for censoring," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 327-334, February.
    7. Ghorai, J. K. & Schmitter, J., 1999. "The asymptotic distribution of the suprema of the standardized empirical processes under the Koziol-Green model," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 303-313, February.
    8. Noel Veraverbeke & Carmen Cadarso-Suárez, 2000. "Estimation of the conditional distribution in a conditional Koziol-green model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(1), pages 97-122, June.
    9. Uttam Bandyopadhyay & Atanu Biswas & Rahul Bhattacharya, 2010. "A covariate‐adjusted adaptive design for two‐stage clinical trials with survival data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(2), pages 202-226, May.
    10. Zheng, Gang & Gastwirth, Joseph L., 2001. "On the Fisher information in randomly censored data," Statistics & Probability Letters, Elsevier, vol. 52(4), pages 421-426, May.
    11. Adekpedjou, Akim & Stocker, Russell & De Mel, Withanage A., 2013. "A class of inference procedures for validating the generalized Koziol–Green model with recurrent events," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 83-92.
    12. Winfried Stute, 2008. "Almost sure representations of weighted -statistics with applications," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(3), pages 191-205.
    13. Sun, Liuquan & Zhu, Lixing, 2000. "A semiparametric model for truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 217-227, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:733-752. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.