Multi-state models: Beware the Markov assumption!

Seminar in Insurance and Economics

Please note that the talk takes place in Auditorium 3 of the August Krogh Building just opposite HCØ. Further details and a map can be found via

SPEAKER: Hein Putter (Leiden University).

TITLE: Multi-state models: Beware the Markov assumption!

ABSTRACT: Multi-state models are useful extensions of classical survival and competing risks models to multiple types of events occurring sequentially in time. The Aalen-Johansen estimator (Aalen & Johansen 1978) plays a central role in multi-state models. While transition hazards form the building blocks in multi-state models, the Aalen-Johansen formula could be seen as the cement that connects the transition hazards with the quantities that are of final interest, namely the state occupation and transition probabilities. The product-limit relation between the transition hazards and transition probabilities that is described by Aalen-Johansen is valid only under the Markov assumption. The Markov assumption is often taken for granted because it enables these mathematical relations between rates and risks, but many situations exist where it does not hold. A remarkable result from Datta & Satten (2000) states that in the absence of covariates the Aalen-Johansen estimator of the state occupation probabilities is nevertheless consistent, even if the Markov assumption is violated. In this talk we discuss how the result of Datta & Satten can be exploited to obtain robust estimators of transition probabilities based on landmarking. We will also study alternative representations of the Aalen-Johansen estimator and show how these alternative representations can be used to derive robust estimators of state occupation probabilities with covariates.


  • Aalen, O. O. & Johansen, S. (1978), `An empirical transition matrix for nonhomogeneous Markov chains based on censored observations', Scandinavian Journal of Statistics 5, 141-150.
  • Datta, S. & Satten, G. A. (2001), `Validity of the Aalen-Johansen estimators of stage occupation probabilities and Nelson-Aalen estimators of integrated transition hazards for non-Markov models', Statistics and Probability Letters 55, 403-411.


Link to Seminar in Insurance and Economics.