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Validity of the Aalen-Johansen estimators of stage occupation probabilities and Nelson-Aalen estimators of integrated transition hazards for non-Markov models

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  • Datta, Somnath
  • Satten, Glen A.

Abstract

We consider estimation of integrated transition hazard and stage occupation probabilities using right censored i.i.d. data that come from a general multistage model which is not Markov. We show that the Nelson-Aalen estimator for the integrated transition hazard of a Markov process consistently estimates a population quantity even when the underlying process is not Markov. Further, the Aalen-Johansen estimators of the stage occupation probabilities constructed from these integrated hazards via product integration are valid (i.e., consistent) for a general multistage model that is not Markov. These observations appear to have been unnoticed in the literature, where validity of the Aalen-Johansen estimators is only claimed for Markov models.

Suggested Citation

  • Datta, Somnath & Satten, Glen A., 2001. "Validity of the Aalen-Johansen estimators of stage occupation probabilities and Nelson-Aalen estimators of integrated transition hazards for non-Markov models," Statistics & Probability Letters, Elsevier, vol. 55(4), pages 403-411, December.
  • Handle: RePEc:eee:stapro:v:55:y:2001:i:4:p:403-411
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    References listed on IDEAS

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    1. Satten, Glen A. & Datta, Somnath & Robins, James, 2001. "Estimating the marginal survival function in the presence of time dependent covariates," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 397-403, October.
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    Cited by:

    1. Araújo, Artur & Meira-Machado, Luís & Roca-Pardiñas, Javier, 2014. "TPmsm: Estimation of the Transition Probabilities in 3-State Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 62(i04).
    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. Richard J. Cook & Leilei Zeng & Ker-Ai Lee, 2008. "A Multistate Model for Bivariate Interval-Censored Failure Time Data," Biometrics, The International Biometric Society, vol. 64(4), pages 1100-1109, December.
    4. Arthur Allignol & Martin Schumacher & Jan Beyersmann, 2011. "Estimating summary functionals in multistate models with an application to hospital infection data," Computational Statistics, Springer, vol. 26(2), pages 181-197, June.
    5. Bella Vakulenko-Lagun & Micha Mandel & Yair Goldberg, 2017. "Nonparametric estimation in the illness-death model using prevalent data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 25-56, January.
    6. repec:bla:stanee:v:71:y:2017:i:1:p:31-57 is not listed on IDEAS
    7. Jan Beyersmann & Hein Putter, 2014. "A note on computing average state occupation times," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(62), pages 1681-1696, May.
    8. Somnath Datta & Rajeshwari Sundaram, 2006. "Nonparametric Estimation of Stage Occupation Probabilities in a Multistage Model with Current Status Data," Biometrics, The International Biometric Society, vol. 62(3), pages 829-837, September.

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