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Recent Developments in Censored, Non-Markov Multi-State Models

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Combining Soft Computing and Statistical Methods in Data Analysis

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 77))

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Abstract

Nonparametric estimation of transition probabilities for a censored multi-state model is traditionally performed under a Markov assumption. However, this assumption may (and will) fail in some applications, leading to the inconsistency of the time-honoured Aalen-Johansen estimator. In such a case, alternative (non-Markov) estimators are needed. In this work we review some recent developments in this area. We also review the key problem of testing if a given (censored) multi-state model is Markov, giving modern ideas for the construction of an omnibus test statistic.

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Authors and Affiliations

  1. Department of Statistics and OR, University of Vigo, Spain

    Jacobo de Uña-Álvarez

Authors
  1. Jacobo de Uña-Álvarez
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Editors and Affiliations

  1. Research Unit on Intelligent Data Analysis and Graphical Models, European Centre for Soft Computing Edificio Científico-Tecnológico. 3a Planta, C/ Gonzalo Gutiérrez Quirós s/n, 33600, Mieres, Spain

    Christian Borgelt , Gil González-Rodríguez  & Wolfgang Trutschnig ,  & 

  2. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, Facultad de Ciencias, C/ Calvo Sotelo s/n, 33007, Oviedo, Spain

    María Asunción Lubiano

  3. Departamento de Estadística e I.O. yD.M., Universidad de Oviedo, Facultad de Ciencias, C/ Calvo Sotelo s/n, 33007, Oviedo, Spain

    María Ángeles Gil

  4. Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Przemysław Grzegorzewski

  5. Systems Research Institute, Polish Academy of Science, Newelska 6, 01-447, Warsaw, Poland

    Olgierd Hryniewicz

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de Uña-Álvarez, J. (2010). Recent Developments in Censored, Non-Markov Multi-State Models. In: Borgelt, C., et al. Combining Soft Computing and Statistical Methods in Data Analysis. Advances in Intelligent and Soft Computing, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14746-3_22

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  • DOI: https://doi.org/10.1007/978-3-642-14746-3_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14745-6

  • Online ISBN: 978-3-642-14746-3

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