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Methods for checking the Markov condition in multi-state survival data

Author

Listed:
  • Gustavo Soutinho

    (Institute of Public Health of the University of Porto (ISPUP))

  • Luís Meira-Machado

    (University of Minho - School of Sciences)

Abstract

The inference in multi-state models is traditionally performed under a Markov assumption that claims that past and future of the process are independent given the present state. This assumption has an important role in the estimation of the transition probabilities. When the multi-state model is Markovian, the Aalen–Johansen estimator gives consistent estimators of the transition probabilities but this is no longer the case when the process is non-Markovian. Usually, this assumption is checked including covariates depending on the history. Since the landmark methods of the transition probabilities are free of the Markov assumption, they can also be used to introduce such tests by measuring their discrepancy to Markovian estimators. In this paper, we introduce tests for the Markov assumption and compare them with the usual approach based on the analysis of covariates depending on history through simulations. The methods are also compared with more recent and competitive approaches. Three real data examples are included for illustration of the proposed methods.

Suggested Citation

  • Gustavo Soutinho & Luís Meira-Machado, 2022. "Methods for checking the Markov condition in multi-state survival data," Computational Statistics, Springer, vol. 37(2), pages 751-780, April.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:2:d:10.1007_s00180-021-01139-7
    DOI: 10.1007/s00180-021-01139-7
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    References listed on IDEAS

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    1. Datta, Somnath & Satten, Glen 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 & Probability Letters, Elsevier, vol. 55(4), pages 403-411, December.
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    7. Luís Meira-Machado & Jacobo Uña-Álvarez & Somnath Datta, 2015. "Nonparametric estimation of conditional transition probabilities in a non-Markov illness-death model," Computational Statistics, Springer, vol. 30(2), pages 377-397, June.
    8. Rafael Pérez‐Ocón & Juan Eloy Ruiz‐Castro & M. Luz Gámiz‐Pérez, 2001. "Non‐homogeneous Markov models in the analysis of survival after breast cancer," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(1), pages 111-124.
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