A note on nonparametric quantile inference for competing risks and more complex multistate models

Authors: Beyersmann, Jan; Schumacher, Martin

Source: Biometrika, Volume 95, Number 4, 26 December 2008 , pp. 1006-1008(3)

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Abstract:

Nonparametric quantile inference for competing risks has recently been studied by Peng & Fine (2007). Their key result establishes uniform consistency and weak convergence of the inverse of the AalenJohansen estimator of the cumulative incidence function, using the representation of the cumulative incidence estimator as a sum of independent and identically distributed random variables. The limit process is of a form similar to that of the standard survival result, but with the cause-specific hazard of interest replacing the all-causes hazard. We show that this fact is not a coincidence, but can be derived from a general Hadamard differentiation result. We discuss a simplified proof and extensions of the approach to more complex multistate models. As a further consequence, we find that the bootstrap works.

Keywords: Cumulative incidence function; Functional delta method; Inverse functional; Survival analysis

Document Type: Research article

DOI: http://dx.doi.org/10.1093/biomet/asn044

Publication date: 2008-12-26