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Targeted estimation of state occupation probabilities for the non‐Markov illness‐death model

Author

Listed:
  • Anders Munch
  • Marie Skov Breum
  • Torben Martinussen
  • Thomas A. Gerds

Abstract

We use semi‐parametric efficiency theory to derive a class of estimators for the state occupation probabilities of the continuous‐time irreversible illness‐death model. We consider both the setting with and without additional baseline information available, where we impose no specific functional form on the intensity functions of the model. We show that any estimator in the class is asymptotically linear under suitable assumptions about the estimators of the intensity functions. In particular, the assumptions are weak enough to allow the use of data‐adaptive methods, which is important for making the identifying assumption of coarsening at random plausible in realistic settings. We suggest a flexible method for estimating the transition intensity functions of the illness‐death model based on penalized Poisson regression. We apply this method to estimate the nuisance parameters of an illness‐death model in a simulation study and a real‐world application.

Suggested Citation

  • Anders Munch & Marie Skov Breum & Torben Martinussen & Thomas A. Gerds, 2023. "Targeted estimation of state occupation probabilities for the non‐Markov illness‐death model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 1532-1551, September.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:3:p:1532-1551
    DOI: 10.1111/sjos.12644
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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.
    2. Hidehiko Ichimura & Whitney K. Newey, 2022. "The influence function of semiparametric estimators," Quantitative Economics, Econometric Society, vol. 13(1), pages 29-61, January.
    3. Somnath Datta & Glen A. Satten, 2002. "Estimation of Integrated Transition Hazards and Stage Occupation Probabilities for Non-Markov Systems Under Dependent Censoring," Biometrics, The International Biometric Society, vol. 58(4), pages 792-802, December.
    4. Jinfeng Xu & John D. Kalbfleisch & Beechoo Tai, 2010. "Statistical Analysis of Illness–Death Processes and Semicompeting Risks Data," Biometrics, The International Biometric Society, vol. 66(3), pages 716-725, September.
    5. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    6. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    7. Aaron Fisher & Edward H. Kennedy, 2021. "Visually Communicating and Teaching Intuition for Influence Functions," The American Statistician, Taylor & Francis Journals, vol. 75(2), pages 162-172, May.
    8. van der Laan Mark J. & Rubin Daniel, 2006. "Targeted Maximum Likelihood Learning," The International Journal of Biostatistics, De Gruyter, vol. 2(1), pages 1-40, December.
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