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Inference for transition probabilities in non-Markov multi-state models

Author

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  • Per Kragh Andersen

    (University of Copenhagen)

  • Eva Nina Sparre Wandall

    (University of Copenhagen)

  • Maja Pohar Perme

    (University of Ljubljana)

Abstract

Multi-state models are frequently used when data come from subjects observed over time and where focus is on the occurrence of events that the subjects may experience. A convenient modeling assumption is that the multi-state stochastic process is Markovian, in which case a number of methods are available when doing inference for both transition intensities and transition probabilities. The Markov assumption, however, is quite strict and may not fit actual data in a satisfactory way. Therefore, inference methods for non-Markov models are needed. In this paper, we review methods for estimating transition probabilities in such models and suggest ways of doing regression analysis based on pseudo observations. In particular, we will compare methods using land-marking with methods using plug-in. The methods are illustrated using simulations and practical examples from medical research.

Suggested Citation

  • Per Kragh Andersen & Eva Nina Sparre Wandall & Maja Pohar Perme, 2022. "Inference for transition probabilities in non-Markov multi-state models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(4), pages 585-604, October.
    • Handle: RePEc:spr:lifeda:v:28:y:2022:i:4:d:10.1007_s10985-022-09560-w
    DOI: 10.1007/s10985-022-09560-w
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    References listed on IDEAS

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    1. Andrew C. Titman, 2015. "Transition probability estimates for non-Markov multi-state models," Biometrics, The International Biometric Society, vol. 71(4), pages 1034-1041, December.
    2. Per Kragh Andersen, 2003. "Generalised linear models for correlated pseudo-observations, with applications to multi-state models," Biometrika, Biometrika Trust, vol. 90(1), pages 15-27, March.
    3. Thomas H. Scheike & Mei‐Jie Zhang, 2007. "Direct Modelling of Regression Effects for Transition Probabilities in Multistate Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(1), pages 17-32, March.
    4. Mitton,Lavinia & Sutherland,Holly & Weeks,Melvyn (ed.), 2000. "Microsimulation Modelling for Policy Analysis," Cambridge Books, Cambridge University Press, number 9780521790062.
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