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Estimation and Asymptotic Theory for Transition Probabilities in Markov Renewal Multi-State Models

Author

Listed:
  • Spitoni Cristian

    (Leiden University Medical Centre)

  • Verduijn Marion

    (Leiden University Medical Centre)

  • Putter Hein

    (Leiden University Medical Centre)

Abstract

In this paper we discuss estimation of transition probabilities for semi–Markov multi–state models. Non–parametric and semi–parametric estimators of the transition probabilities for a large class of models (forward going models) are proposed. Large sample theory is derived using the functional delta method and the use of resampling is proposed to derive confidence bands for the transition probabilities. The last part of the paper concerns the presentation of the main ideas of the R implementation of the proposed estimators, and data from a renal replacement study are used to illustrate the behavior of the estimators proposed.

Suggested Citation

  • Spitoni Cristian & Verduijn Marion & Putter Hein, 2012. "Estimation and Asymptotic Theory for Transition Probabilities in Markov Renewal Multi-State Models," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-39, August.
    • Handle: RePEc:bpj:ijbist:v:8:y:2012:i:1:n:23
    DOI: 10.1515/1557-4679.1375
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    References listed on IDEAS

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    1. Jinfeng Xu & John D. Kalbfleisch & Beechoo Tai, 2010. "Statistical Analysis of Illness–Death Processes and Semicompeting Risks Data," Biometrics, The International Biometric Society, vol. 66(3), pages 716-725, September.
    2. Jackson, Christopher, 2011. "Multi-State Models for Panel Data: The msm Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 38(i08).
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    Cited by:

    1. 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.
    2. 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.
    3. Oliver Lunding Sandqvist, 2023. "A multistate approach to disability insurance reserving with information delays," Papers 2312.14324, arXiv.org, revised Jan 2025.

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