Lifetime Data Analysis

, Volume 12, Issue 3, pp 325–344 | Cite as

Nonparametric estimation of transition probabilities in a non-Markov illness–death model

  • Luís Meira-MachadoEmail author
  • Jacobo de Uña-Álvarez
  • Carmen Cadarso-Suárez


In this paper we consider nonparametric estimation of transition probabilities for multi-state models. Specifically, we focus on the illness-death or disability model. The main novelty of the proposed estimators is that they do not rely on the Markov assumption, typically assumed to hold in a multi-state model. We investigate the asymptotic properties of the introduced estimators, such as their consistency and their convergence to a normal law. Simulations demonstrate that the new estimators may outperform Aalen–Johansen estimators (the classical nonparametric tool for estimating the transition probabilities) in non-Markov situation. An illustration through real data analysis is included.


Aalen–Johansen estimator Kaplan–Meier estimator Markov process Multi-state Model Survival analysis 



The authors acknowledge finantial support by Spanish Ministry of Education & Science grants BMF2002-03213, MTM2005-01274 and MTM2005-00818 (European FEDER support included). The Authors would also like to thank W. Stute and P.K. Andersen for their helpful comments and views. Thanks to two anonymous referees for comments and suggestions which have improved the presentation of the paper.


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Luís Meira-Machado
    • 1
    Email author
  • Jacobo de Uña-Álvarez
    • 2
  • Carmen Cadarso-Suárez
    • 3
  1. 1.Department of Mathematics for Science and TechnologyUniversity of MinhoGuimaraesPortugal
  2. 2.Department of Statistics and Operations ResearchUniversity of VigoVigoSpain
  3. 3.Department of Statistics and Operations ResearchUniversity of Santiago de CompostelaSantiago de CompostelaSpain

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