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The International Journal of Biostatistics

Ed. by Chambaz, Antoine / Hubbard, Alan E. / van der Laan, Mark J.

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

Cristian Spitoni
  • Leiden University Medical Centre
/ Marion Verduijn
  • Leiden University Medical Centre
/ Hein Putter
  • Leiden University Medical Centre
Published Online: 2012-08-07 | DOI: https://doi.org/10.1515/1557-4679.1375


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.

This article offers supplementary material which is provided at the end of the article.

Keywords: functional delta–method; semi–markov processes; survival analysis

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Published Online: 2012-08-07

Citation Information: The International Journal of Biostatistics, ISSN (Online) 1557-4679, DOI: https://doi.org/10.1515/1557-4679.1375.

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©2012 Walter de Gruyter GmbH & Co. KG, Berlin/Boston. Copyright Clearance Center

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