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A wild bootstrap approach for the Aalen–Johansen estimator

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Listed:
  • Tobias Bluhmki
  • Claudia Schmoor
  • Dennis Dobler
  • Markus Pauly
  • Juergen Finke
  • Martin Schumacher
  • Jan Beyersmann

Abstract

We suggest a wild bootstrap resampling technique for nonparametric inference on transition probabilities in a general time‐inhomogeneous Markov multistate model. We first approximate the limiting distribution of the Nelson–Aalen estimator by repeatedly generating standard normal wild bootstrap variates, while the data is kept fixed. Next, a transformation using a functional delta method argument is applied. The approach is conceptually easier than direct resampling for the transition probabilities. It is used to investigate a non‐standard time‐to‐event outcome, currently being alive without immunosuppressive treatment, with data from a recent study of prophylactic treatment in allogeneic transplanted leukemia patients. Due to non‐monotonic outcome probabilities in time, neither standard survival nor competing risks techniques apply, which highlights the need for the present methodology. Finite sample performance of time‐simultaneous confidence bands for the outcome probabilities is assessed in an extensive simulation study motivated by the clinical trial data. Example code is provided in the web‐based Supplementary Materials.

Suggested Citation

  • Tobias Bluhmki & Claudia Schmoor & Dennis Dobler & Markus Pauly & Juergen Finke & Martin Schumacher & Jan Beyersmann, 2018. "A wild bootstrap approach for the Aalen–Johansen estimator," Biometrics, The International Biometric Society, vol. 74(3), pages 977-985, September.
  • Handle: RePEc:bla:biomet:v:74:y:2018:i:3:p:977-985
    DOI: 10.1111/biom.12861
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    References listed on IDEAS

    as
    1. Allignol, Arthur & Schumacher, Martin & Beyersmann, Jan, 2011. "Empirical Transition Matrix of Multi-State Models: The etm Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 38(i04).
    2. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    3. D. Dobler & J. Beyersmann & M. Pauly, 2017. "Non-strange weird resampling for complex survival data," Biometrika, Biometrika Trust, vol. 104(3), pages 699-711.
    4. Jan Beyersmann & Susanna Di Termini & Markus Pauly, 2013. "Weak Convergence of the Wild Bootstrap for the Aalen–Johansen Estimator of the Cumulative Incidence Function of a Competing Risk," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 387-402, September.
    5. Thomas H. Scheike & Mei-Jie Zhang, 2003. "Extensions and Applications of the Cox-Aalen Survival Model," Biometrics, The International Biometric Society, vol. 59(4), pages 1036-1045, December.
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    Cited by:

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