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Nonparametric estimation of transition probabilities for a general progressive multi‐state model under cross‐sectional sampling

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  • Jacobo de Uña‐Álvarez
  • Micha Mandel

Abstract

Nonparametric estimation of the transition probability matrix of a progressive multi‐state model is considered under cross‐sectional sampling. Two different estimators adapted to possibly right‐censored and left‐truncated data are proposed. The estimators require full retrospective information before the truncation time, which, when exploited, increases efficiency. They are obtained as differences between two survival functions constructed for sub‐samples of subjects occupying specific states at a certain time point. Both estimators correct the oversampling of relatively large survival times by using the left‐truncation times associated with the cross‐sectional observation. Asymptotic results are established, and finite sample performance is investigated through simulations. One of the proposed estimators performs better when there is no censoring, while the second one is strongly recommended with censored data. The new estimators are applied to data on patients in intensive care units (ICUs).

Suggested Citation

  • 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.
    • Handle: RePEc:bla:biomet:v:74:y:2018:i:4:p:1203-1212
    DOI: 10.1111/biom.12874
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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. César Sánchez Sellero & Wenceslao González Manteiga & Ingrid Van Keilegom, 2005. "Uniform Representation of Product‐Limit Integrals with Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 563-581, December.
    3. de Wreede, Liesbeth C. & Fiocco, Marta & Putter, Hein, 2011. "mstate: An R Package for the Analysis of Competing Risks and Multi-State Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 38(i07).
    4. repec:bla:biomet:v:71:y:2015:i:4:p:1034-1041 is not listed on IDEAS
    5. 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.
    6. John P. Klein & Per Kragh Andersen, 2005. "Regression Modeling of Competing Risks Data Based on Pseudovalues of the Cumulative Incidence Function," Biometrics, The International Biometric Society, vol. 61(1), pages 223-229, March.
    7. Zhou, Yong & Yip, Paul S. F., 1999. "A Strong Representation of the Product-Limit Estimator for Left Truncated and Right Censored Data," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 261-280, May.
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    1. 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.
    2. 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.
    3. 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.

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