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Bootstrap confidence bands for sojourn distributions in multistate semi-Markov models with right censoring

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  • Ronald W. Butler
  • Douglas A. Bronson

Abstract

Transient semi-Markov processes have traditionally been used to describe the transitions of a patient through the various states of a multistate survival model. A survival distribution in this context is a sojourn through the states until passage to a fatal absorbing state or certain endpoint states. Using complete sojourn data, this paper shows how such survival distributions and associated hazard functions can be estimated nonparametrically and also how nonparametric bootstrap pointwise confidence bands can be constructed for them when patients are subject to independent right censoring from each state during the sojourn. Limitations to the estimability of such survival distributions that result from random censoring with bounded support are clarified. The methods are applicable to any sort of sojourn through any finite state process of arbitrary complexity involving feedback into previously occupied states. Copyright 2012, Oxford University Press.

Suggested Citation

  • Ronald W. Butler & Douglas A. Bronson, 2012. "Bootstrap confidence bands for sojourn distributions in multistate semi-Markov models with right censoring," Biometrika, Biometrika Trust, vol. 99(4), pages 959-972.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:4:p:959-972
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    File URL: http://hdl.handle.net/10.1093/biomet/ass036
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    Cited by:

    1. Salim Bouzebda & Chrysanthi Papamichail & Nikolaos Limnios, 2018. "On a multidimensional general bootstrap for empirical estimator of continuous-time semi-Markov kernels with applications," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(1), pages 49-86, January.
    2. Ronald W. Butler & Douglas A. Bronson, 2014. "Multistate Survival Models as Transient Electrical Networks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 167-186, March.

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