IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v81y2011i7p797-806.html
   My bibliography  Save this article

Presmoothing the transition probabilities in the illness-death model

Author

Listed:
  • Amorim, Ana Paula
  • de Uña-Álvarez, Jacobo
  • Meira-Machado, Luís

Abstract

One major goal in clinical applications of multi-state models is the estimation of transition probabilities. In a recent paper, Meira-Machado et al. (2006) introduce a substitute for the Aalen-Johansen estimator in the case of a non-Markov illness-death model. The idea behind their estimator is to weight the data by the Kaplan-Meier weights pertaining to the distribution of the total survival time of the process. In this paper we propose a modification of Meira-Machado et al. (2006) estimator based on presmoothing. Consistency is established. We investigate the finite sample performance of the new estimator through simulations. Data from a study on colon cancer are used for illustration purposes.

Suggested Citation

  • Amorim, Ana Paula & de Uña-Álvarez, Jacobo & Meira-Machado, Luís, 2011. "Presmoothing the transition probabilities in the illness-death model," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 797-806, July.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:7:p:797-806
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(11)00063-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Stute, W., 1993. "Consistent Estimation Under Random Censorship When Covariables Are Present," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 89-103, April.
    2. Ming Yuan, 2005. "Semiparametric censorship model with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(2), pages 489-514, December.
    3. de Uña-Álvarez, Jacobo & Meira-Machado, Luis F., 2008. "A simple estimator of the bivariate distribution function for censored gap times," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2440-2445, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Luís Meira-Machado & Jacobo Uña-Álvarez & Somnath Datta, 2015. "Nonparametric estimation of conditional transition probabilities in a non-Markov illness-death model," Computational Statistics, Springer, vol. 30(2), pages 377-397, June.
    2. Jacobo de Uña-Álvarez & Luís Meira-Machado, 2015. "Nonparametric estimation of transition probabilities in the non-Markov illness-death model: A comparative study," Biometrics, The International Biometric Society, vol. 71(2), pages 364-375, June.
    3. Rotolo, Federico & Legrand, Catherine & Van Keilegom, Ingrid, 2011. "Simulation of clustered multi-state survival data based on a copula model," LIDAM Discussion Papers ISBA 2011040, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    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. Zhiping Qiu & Jing Qin & Yong Zhou, 2016. "Composite Estimating Equation Method for the Accelerated Failure Time Model with Length-biased Sampling Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 396-415, June.
    2. Ruoqing Zhu & Ying-Qi Zhao & Guanhua Chen & Shuangge Ma & Hongyu Zhao, 2017. "Greedy outcome weighted tree learning of optimal personalized treatment rules," Biometrics, The International Biometric Society, vol. 73(2), pages 391-400, June.
    3. Guessoum Zohra & Ould-Said Elias, 2009. "On nonparametric estimation of the regression function under random censorship model," Statistics & Risk Modeling, De Gruyter, vol. 26(3), pages 159-177, April.
    4. Sungwan Bang & Soo-Heang Eo & Yong Mee Cho & Myoungshic Jhun & HyungJun Cho, 2016. "Non-crossing weighted kernel quantile regression with right censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(1), pages 100-121, January.
    5. Wenceslao González Manteiga & Cédric Heuchenne & César Sánchez Sellero & Alessandro Beretta, 2020. "Goodness-of-fit tests for censored regression based on artificial data points," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 599-615, June.
    6. 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.
    7. Jacobo Uña-Álvarez & Noël Veraverbeke, 2013. "Generalized copula-graphic estimator," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 343-360, June.
    8. Zhang, Chun-Xia & Mei, Chang-Lin & Zhang, Jiang-She, 2007. "An empirical study of a test for polynomial relationships in randomly right censored regression models," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6543-6556, August.
    9. Xiaochao Xia & Binyan Jiang & Jialiang Li & Wenyang Zhang, 2016. "Low-dimensional confounder adjustment and high-dimensional penalized estimation for survival analysis," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 547-569, October.
    10. Khan Md Hasinur Rahaman & Bhadra Anamika & Howlader Tamanna, 2019. "Stability selection for lasso, ridge and elastic net implemented with AFT models," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 18(5), pages 1-14, October.
    11. Subramanian, Sundarraman, 2016. "Bootstrap likelihood ratio confidence bands for survival functions under random censorship and its semiparametric extension," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 58-81.
    12. Pedro H. C. Sant’Anna, 2021. "Nonparametric Tests for Treatment Effect Heterogeneity With Duration Outcomes," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(3), pages 816-832, July.
    13. Ma, Shuangge & Dai, Ying & Huang, Jian & Xie, Yang, 2012. "Identification of breast cancer prognosis markers via integrative analysis," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2718-2728.
    14. Hu, Jianwei & Chai, Hao, 2013. "Adjusted regularized estimation in the accelerated failure time model with high dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 96-114.
    15. Dong, Yan & Li, Daoji & Zheng, Zemin & Zhou, Jia, 2022. "Reproducible feature selection in high-dimensional accelerated failure time models," Statistics & Probability Letters, Elsevier, vol. 181(C).
    16. Nassira Menni & Abdelkader Tatachak, 2018. "A note on estimating the conditional expectation under censoring and association: strong uniform consistency," Statistical Papers, Springer, vol. 59(3), pages 1009-1030, September.
    17. Ouimet, Frédéric, 2021. "Asymptotic properties of Bernstein estimators on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    18. Svetlana Gribkova & Olivier Lopez, 2015. "Non-parametric Copula Estimation Under Bivariate Censoring," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 925-946, December.
    19. Pedro H. C. Sant'Anna, 2016. "Program Evaluation with Right-Censored Data," Papers 1604.02642, arXiv.org.
    20. Svetlana K. Eden & Chun Li & Bryan E. Shepherd, 2022. "Nonparametric estimation of Spearman's rank correlation with bivariate survival data," Biometrics, The International Biometric Society, vol. 78(2), pages 421-434, June.

    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:eee:stapro:v:81:y:2011:i:7:p:797-806. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.