IDEAS home Printed from https://ideas.repec.org/a/ben/tostpj/v9y2018i1p1-17.html
   My bibliography  Save this article

Consistency of the Kaplan-Meier Estimator of the Survival Function in Competiting Risks

Author

Listed:
  • Didier Alain Njamen Njomen

    (Department of Mathematics and Computer Sciences, Faculty of Science, University of Maroua, Maroua, Cameroon)

  • Joseph Wandji Ngatchou

    (Institut Elie Cartan de Lorraine, University of Lorraine, Nancy, France)

Abstract

Introduction : In this article, we only focus on the probability distributions of the breakdown time whose causes are known, and we consider a partition of the observations into subgroups according to each of the causes as defined in Njamen and Ngatchou [1]. By adapting the stochastic processes developed by Aalen [2, 3], we derive a Kaplan-Meier [4] nonparametric estimator for the survival function in competiting risks. Result & Discussion : In a region where there is at least one observation, we prove on one hand that this new nonparametric estimator is unbiased in competiting risk and on the other hand, using the Lenglart inequality, we establish its uniform consistency in competiting risks.

Suggested Citation

  • Didier Alain Njamen Njomen & Joseph Wandji Ngatchou, 2018. "Consistency of the Kaplan-Meier Estimator of the Survival Function in Competiting Risks," The Open Statistics and Probability Journal, Bentham Open, vol. 9(1), pages 1-17, April.
    • Handle: RePEc:ben:tostpj:v:9:y:2018:i:1:p:1-17
    DOI: 10.2174/1876527001809010001
    as

    Download full text from publisher

    File URL: https://benthamopen.com/DOWNLOAD-PDF/TOSPJ-9-1/
    Download Restriction: no
    File URL: https://benthamopen.com/ABSTRACT/TOSPJ-9-1/
    Download Restriction: no
    File URL: https://libkey.io/10.2174/1876527001809010001?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
    ---><---

    References listed on IDEAS

    as
    1. R.D. Gill, 1980. "Censoring and Stochastic Integrals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 34(2), pages 124-124, June.
    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. Erica Brittain & Dean Follmann & Song Yang, 2008. "Dynamic Comparison of Kaplan–Meier Proportions: Monitoring a Randomized Clinical Trial with a Long-Term Binary Endpoint," Biometrics, The International Biometric Society, vol. 64(1), pages 189-197, March.
    2. Xiaofeng Lv & Gupeng Zhang & Guangyu Ren, 2017. "Gini index estimation for lifetime data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 275-304, April.
    3. Phadia, Eswar G. & Shao, Peter Yi-Shi, 1999. "Exact moments of the product limit estimator," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 277-286, February.
    4. Yi Wu & Wei Yu & Xuejun Wang, 2022. "Strong representations of the Kaplan–Meier estimator and hazard estimator with censored widely orthant dependent data," Computational Statistics, Springer, vol. 37(1), pages 383-402, March.
    5. Han-Ying Liang & Jacobo Uña-Álvarez, 2011. "Asymptotic properties of conditional quantile estimator for censored dependent observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 267-289, April.
    6. Ganesh B. Malla, 2022. "A Monte Carlo Simulation Comparison of Some Nonparametric Survival Functions for Incomplete Data," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 14(5), pages 1-1, November.
    7. Imbens, G.W., 1989. "Duration models with time-varying coefficients," Other publications TiSEM 8432944f-1cfc-4403-bcbe-4, Tilburg University, School of Economics and Management.
    8. Lee, Seung-Hwan & Lee, Eun-Joo & Omolo, Bernard Oguna, 2008. "Using integrated weighted survival difference for the two-sample censored data problem," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4410-4416, May.
    9. Gang Li & Somnath Datta, 2001. "A Bootstrap Approach to Nonparametric Regression for Right Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 708-729, December.
    10. Li, Gang & Sun, Yanqing, 2000. "A simulation-based goodness-of-fit test for survival data," Statistics & Probability Letters, Elsevier, vol. 47(4), pages 403-410, May.
    11. Morten Overgaard & Stefan Nygaard Hansen, 2021. "On the assumption of independent right censoring," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1234-1255, December.
    12. Hongwei Zhao & Anastasios A. Tsiatis, 2001. "Testing Equality of Survival Functions of Quality-Adjusted Lifetime," Biometrics, The International Biometric Society, vol. 57(3), pages 861-867, September.
    13. Kevin Hasegawa Eng & Michael R. Kosorok, 2005. "A Sample Size Formula for the Supremum Log-Rank Statistic," Biometrics, The International Biometric Society, vol. 61(1), pages 86-91, March.
    14. Sun, Liuquan & Zhou, Yong, 1998. "Sequential confidence bands for densities under truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 31-41, September.
    15. Yang, Song, 1996. "Weighted empiricals and the product-limit estimator in the multiplicative hazard and time transfer regression model," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 17-24, September.
    16. Su, Pei-Fang & Chi, Yunchan & Li, Chung-I & Shyr, Yu & Liao, Yi-De, 2011. "Analyzing survival curves at a fixed point in time for paired and clustered right-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1617-1628, April.
    17. Thomas DeLeire & Shakeeb Khan & Christopher Timmins, 2013. "Roy Model Sorting And Nonrandom Selection In The Valuation Of A Statistical Life," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(1), pages 279-306, February.
    18. Mashayekhi, Mostafa, 2002. "Compound estimation of a monotone sequence," Statistics & Probability Letters, Elsevier, vol. 60(1), pages 7-15, November.
    19. Yu-Mei Chang & Chun-Shu Chen & Pao-Sheng Shen, 2012. "A jackknife-based versatile test for two-sample problems with right-censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 267-277, April.
    20. Darilay, Annie Tordilla & Naranjo, Joshua D., 2011. "A pretest for using logrank or Wilcoxon in the two-sample problem," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2400-2409, July.

    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:ben:tostpj:v:9:y:2018:i:1:p:1-17. 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: Rehana Raza (email available below). General contact details of provider: .

    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.