Landmark estimation of transition probabilities in non-Markov multi-state models with covariates

  • Rune HoffEmail author
  • Hein Putter
  • Ingrid Sivesind Mehlum
  • Jon Michael Gran


In non-Markov multi-state models, the traditional Aalen–Johansen (AJ) estimator for state transition probabilities is generally not valid. An alternative, suggested by Putter and Spitioni, is to analyse a subsample of the full data, consisting of the individuals present in a specific state at a given landmark time-point. The AJ estimator of occupation probabilities is then applied to the landmark subsample. Exploiting the result by Datta and Satten, that the AJ estimator is consistent for state occupation probabilities even in non-Markov models given that censoring is independent of state occupancy and times of transition between states, the landmark Aalen–Johansen (LMAJ) estimator provides consistent estimates of transition probabilities. So far, this approach has only been studied for non-parametric estimation without covariates. In this paper, we show how semi-parametric regression models and inverse probability weights can be used in combination with the LMAJ estimator to perform covariate adjusted analyses. The methods are illustrated by a simulation study and an application to population-wide registry data on work, education and health-related absence in Norway. Results using the traditional AJ estimator and the LMAJ estimator are compared, and show large differences in estimated transition probabilities for highly non-Markov multi-state models.


Multi-state models The Markov property Transition probabilities Landmarking Aalen–Johansen estimator 



This work was financially supported by the Research Council of Norway (Grant Nos. 237831, 218368 and 273674).

Supplementary material

10985_2019_9474_MOESM1_ESM.pdf (703 kb)
Supplementary material 1 (pdf 702 KB)


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Oslo Centre for Biostatistics and EpidemiologyUniversity of Oslo and Oslo University HospitalOsloNorway
  2. 2.National Institute of Occupational HealthOsloNorway
  3. 3.Department of Medical Statistics and BioinformaticsLeiden University Medical CenterLeidenThe Netherlands

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