Estimating summary functionals in multistate models with an application to hospital infection data |
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Authors: | Arthur Allignol Martin Schumacher Jan Beyersmann |
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Institution: | (1) Institute of Medical Biometry and Medical Informatics, University Medical Center Freiburg, Stefan-Meier-Stra?e 26, 79104 Freiburg, Germany;(2) Freiburg Centre for Data Analysis and Modelling, University of Freiburg, Eckerstra?e 1, 79104 Freiburg, Germany;(3) Institute of Hygiene and Environmental Medicine, Charit?-University Medicine Berlin, Heubnerweg 6, 14059 Berlin, Germany |
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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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