IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v37y2022i2d10.1007_s00180-021-01139-7.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-021-01139-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-021-01139-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Patrick Royston & Gareth Ambler, 1999. "Multivariable fractional polynomials," Stata Technical Bulletin, StataCorp LLC, vol. 8(43).
    3. repec:bla:biomet:v:71:y:2015:i:4:p:1034-1041 is not listed on IDEAS
    4. Hans C. Van Houwelingen, 2007. "Dynamic Prediction by Landmarking in Event History Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(1), pages 70-85, March.
    5. 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.
    6. 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.
    7. Jacobo de Uña-Álvarez & Luís Meira-Machado, 2015. "Nonparametric estimation of transition probabilities in the non-Markov illness-death model: A comparative study," Biometrics, The International Biometric Society, vol. 71(2), pages 364-375, June.
    8. Chiou, Sy Han & Qian, Jing & Mormino, Elizabeth & Betensky, Rebecca A., 2018. "Permutation tests for general dependent truncation," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 308-324.
    9. W. Sauerbrei & P. Royston, 1999. "Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional polynomials," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(1), pages 71-94.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gustavo Soutinho & Luís Meira-Machado, 2023. "Nonparametric estimation of the distribution of gap times for recurrent events," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 103-128, March.
    2. Niklas Maltzahn & Rune Hoff & Odd O. Aalen & Ingrid S. Mehlum & Hein Putter & Jon Michael Gran, 2021. "A hybrid landmark Aalen-Johansen estimator for transition probabilities in partially non-Markov multi-state models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 737-760, October.
    3. Geweke, John & Petrella, Lea, 2014. "Likelihood-based inference for regular functions with fractional polynomial approximations," Journal of Econometrics, Elsevier, vol. 183(1), pages 22-30.
    4. Marco Caliendo & Stefan Tübbicke, 2020. "New evidence on long-term effects of start-up subsidies: matching estimates and their robustness," Empirical Economics, Springer, vol. 59(4), pages 1605-1631, October.
    5. Annalisa Orenti & Patrizia Boracchi & Giuseppe Marano & Elia Biganzoli & Federico Ambrogi, 2022. "A pseudo-values regression model for non-fatal event free survival in the presence of semi-competing risks," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(3), pages 709-727, September.
    6. Strasak, Alexander M. & Umlauf, Nikolaus & Pfeiffer, Ruth M. & Lang, Stefan, 2011. "Comparing penalized splines and fractional polynomials for flexible modelling of the effects of continuous predictor variables," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1540-1551, April.
    7. Dennis Dobler & Andrew Titman, 2020. "Dynamic inference for non‐Markov transition probabilities under random right censoring," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 572-586, June.
    8. Stefanie Hieke & Harald Binder & Alexandra Nieters & Martin Schumacher, 2014. "minPtest: a resampling based gene region-level testing procedure for genetic case-control studies," Computational Statistics, Springer, vol. 29(1), pages 51-63, February.
    9. Marisa Rifada & Vita Ratnasari & Purhadi Purhadi, 2023. "Parameter Estimation and Hypothesis Testing of The Bivariate Polynomial Ordinal Logistic Regression Model," Mathematics, MDPI, vol. 11(3), pages 1-12, January.
    10. Guibert, Quentin & Planchet, Frédéric, 2018. "Non-parametric inference of transition probabilities based on Aalen–Johansen integral estimators for acyclic multi-state models: application to LTC insurance," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 21-36.
    11. Patrick Royston, 2006. "Explained variation for survival models," Stata Journal, StataCorp LLC, vol. 6(1), pages 83-96, March.
    12. Patrick Royston, 2012. "Tools to simulate realistic censored survival-time distributions," Stata Journal, StataCorp LLC, vol. 12(4), pages 639-654, December.
    13. Schäfer, Dorothea & Werwatz, Axel & Zimmermann, Volker, 2004. "The Determinants of Debt and (Private) Equity Financing : The Case of Young, Innovative SMEs from Germany," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 11(3), pages 225-248.
    14. Rune Hoff & Hein Putter & Ingrid Sivesind Mehlum & Jon Michael Gran, 2019. "Landmark estimation of transition probabilities in non-Markov multi-state models with covariates," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(4), pages 660-680, October.
    15. Farber, Steven & Li, Xiao, 2013. "Urban sprawl and social interaction potential: an empirical analysis of large metropolitan regions in the United States," Journal of Transport Geography, Elsevier, vol. 31(C), pages 267-277.
    16. Nießl, Alexandra & Allignol, Arthur & Beyersmann, Jan & Mueller, Carina, 2023. "Statistical inference for state occupation and transition probabilities in non-Markov multi-state models subject to both random left-truncation and right-censoring," Econometrics and Statistics, Elsevier, vol. 25(C), pages 110-124.
    17. Armando Rungi & Davide Del Prete, 2017. "The 'Smile Curve': where Value is Added along Supply Chains," Working Papers 05/2017, IMT School for Advanced Studies Lucca, revised Mar 2017.
    18. Sauerbrei, W. & Meier-Hirmer, C. & Benner, A. & Royston, P., 2006. "Multivariable regression model building by using fractional polynomials: Description of SAS, STATA and R programs," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3464-3485, August.
    19. Sauerbrei, Willi & Royston, Patrick & Zapien, Karina, 2007. "Detecting an interaction between treatment and a continuous covariate: A comparison of two approaches," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 4054-4063, May.
    20. Binder, Harald & Sauerbrei, Willi, 2008. "Increasing the usefulness of additive spline models by knot removal," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5305-5318, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:37:y:2022:i:2:d:10.1007_s00180-021-01139-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.