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State Occupation Probabilities in Non-Markov Models


The consistency of the Aalen—Johansen-derived estimator of state occupation probabilities in non-Markov multi-state settings is studied and established via a new route. This new route is based on interval functions and relies on a close connection between additive and multiplicative transforms of interval functions, which is established. Under certain assumptions, the consistency follows from explicit expressions of the additive and multiplicative transforms related to the transition probabilities as interval functions, which are obtained, in combination with certain censoring and positivity assumptions

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The author would like to thank Erik Thorlund Parner and Jan Pedersen for discussions and comments on drafts of this paper.

This research is supported by the Novo Nordisk Foundation, grant NNF17OC0028276.

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Correspondence to M. Overgaard.

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Overgaard, M. State Occupation Probabilities in Non-Markov Models. Math. Meth. Stat. 28, 279–290 (2019).

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  • Aalen—Johansen estimator
  • interval function
  • additive transform
  • multiplicative transform
  • product integral

AMS 2010 Subject Classification

  • 62N02
  • 62N05
  • 62F12
  • 62F40