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Nonparametric estimation of transition probabilities in the non-Markov illness-death model: A comparative study

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  • Jacobo de Uña-Álvarez
  • Luís Meira-Machado

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  • 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.
    • Handle: RePEc:bla:biomet:v:71:y:2015:i:2:p:364-375
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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. Luís Meira-Machado & Javier Roca-Pardiñas & Ingrid Van Keilegom & Carmen Cadarso-Suárez, 2013. "Bandwidth selection for the estimation of transition probabilities in the location-scale progressive three-state model," Computational Statistics, Springer, vol. 28(5), pages 2185-2210, October.
    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. Stute, W., 1993. "Consistent Estimation Under Random Censorship When Covariables Are Present," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 89-103, April.
    5. Glen A. Satten, 1999. "Estimating the Extent of Tracking in Interval-Censored Chain-Of-Events Data," Biometrics, The International Biometric Society, vol. 55(4), pages 1228-1231, December.
    6. David V. Glidden, 2002. "Robust Inference for Event Probabilities with Non-Markov Event Data," Biometrics, The International Biometric Society, vol. 58(2), pages 361-368, June.
    7. Amorim, Ana Paula & de Uña-Álvarez, Jacobo & Meira-Machado, Luís, 2011. "Presmoothing the transition probabilities in the illness-death model," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 797-806, July.
    8. Spitoni Cristian & Verduijn Marion & Putter Hein, 2012. "Estimation and Asymptotic Theory for Transition Probabilities in Markov Renewal Multi-State Models," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-39, August.
    9. Halina Frydman & Michael Szarek, 2009. "Nonparametric Estimation in a Markov “Illness–Death” Process from Interval Censored Observations with Missing Intermediate Transition Status," Biometrics, The International Biometric Society, vol. 65(1), pages 143-151, March.
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    Cited by:

    1. Giorgos Bakoyannis & Dipankar Bandyopadhyay, 2022. "Nonparametric tests for multistate processes with clustered data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 837-867, October.
    2. 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.
    3. 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.
    4. Arthur Berg & Dimitris Politis & Kagba Suaray & Hui Zeng, 2020. "Reduced bias nonparametric lifetime density and hazard estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 704-727, September.
    5. 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.
    6. Fuino, Michel & Wagner, Joël, 2018. "Long-term care models and dependence probability tables by acuity level: New empirical evidence from Switzerland," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 51-70.
    7. Ritesh Ramchandani & Dianne M. Finkelstein & David A. Schoenfeld, 2020. "Estimation for an accelerated failure time model with intermediate states as auxiliary information," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 1-20, January.
    8. 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.
    9. 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.
    10. 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.
    11. Jacobo de Uña‐Álvarez & Micha Mandel, 2018. "Nonparametric estimation of transition probabilities for a general progressive multi‐state model under cross‐sectional sampling," Biometrics, The International Biometric Society, vol. 74(4), pages 1203-1212, December.

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