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Estimating summary functionals in multistate models with an application to hospital infection data

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Abstract

Inhomogeneous Markov chains are a relevant framework for analysing event histories. The fundamental estimator in the presence of incompletely observed data is the Nelson-Aalen estimator of the multivariate cumulative hazards. It may be summarised in terms of probability estimates via the empirical transition matrix. The empirical transition matrix has only slowly entered applications, one reason being previous lack of software. In a number of applications, further summary measures are desired. We illustrate how they may be computed from the empirical transition matrix and why bootstrapping their variance works. In contrast, computing such summaries outside the present framework has typically led to biased results. As an example, we consider in more detail hospital stay following infectious complication. This summary quantity is often considered by clinical decision makers, but reliable estimates require modelling the timing of infection as in the present set-up. In this context, we also derive new summary measures that further distinguish between patients discharged and patients deceased.

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Authors and Affiliations

  1. Freiburg Center for Data Analysis and Modeling, University of Freiburg, Eckerstr. 1, 79104, Freiburg, Germany

    Arthur Allignol & Jan Beyersmann

  2. Institute of Medical Biometry and Medical Informatics, University Medical Center Freiburg, Stefan-Meier-Str. 26, 79104, Freiburg, Germany

    Arthur Allignol, Martin Schumacher & Jan Beyersmann

Authors
  1. Arthur Allignol
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  2. Martin Schumacher
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  3. Jan Beyersmann
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Correspondence to Arthur Allignol.

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Supported by Deutsche Forschungsgemeinschaft (FOR 534).

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Allignol, A., Schumacher, M. & Beyersmann, J. Estimating summary functionals in multistate models with an application to hospital infection data. Comput Stat 26, 181–197 (2011). https://doi.org/10.1007/s00180-010-0200-x

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