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Nonparametric estimation of the distribution of gap times for recurrent events

Author

Listed:
  • Gustavo Soutinho

    (University of Porto)

  • Luís Meira-Machado

    (University of Minho)

Abstract

In many longitudinal studies, information is collected on the times of different kinds of events. Some of these studies involve repeated events, where a subject or sample unit may experience a well-defined event several times throughout their history. Such events are called recurrent events. In this paper, we introduce nonparametric methods for estimating the marginal and joint distribution functions for recurrent event data. New estimators are introduced and their extensions to several gap times are also given. Nonparametric inference conditional on current or past covariate measures is also considered. We study by simulation the behavior of the proposed estimators in finite samples, considering two or three gap times. Our proposed methods are applied to the study of (multiple) recurrence times in patients with bladder tumors. Software in the form of an R package, called survivalREC, has been developed, implementing all methods.

Suggested Citation

  • Gustavo Soutinho & Luís Meira-Machado, 2023. "Nonparametric estimation of the distribution of gap times for recurrent events," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 103-128, March.
    • Handle: RePEc:spr:stmapp:v:32:y:2023:i:1:d:10.1007_s10260-022-00641-6
    DOI: 10.1007/s10260-022-00641-6
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    References listed on IDEAS

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    1. Moreira, Ana Cristina & Machado, Luís Filipe Meira, 2012. "survivalBIV: Estimation of the Bivariate Distribution Function for Sequentially Ordered Events Under Univariate Censoring," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 46(i13).
    2. 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.
    3. Hans C. Van Houwelingen, 2007. "Dynamic Prediction by Landmarking in Event History Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(1), pages 70-85, March.
    4. 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.
    5. 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.
    6. van der Laan M.J. & Hubbard A.E. & Robins J.M., 2002. "Locally Efficient Estimation of a Multivariate Survival Function in Longitudinal Studies," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 494-507, June.
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