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Addition of time-dependent covariates to a survival model significantly improved predictions for daily risk of hospital death

Authors

  • Jenna Wong MSc,

    1. Methodologist, Department of Clinical Epidemiology, Ottawa Hospital Research Institute, Ottawa, ON, Canada and Institute for Clinical Evaluative Sciences, Ottawa, ON, Canada
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  • Monica Taljaard PhD,

    1. Scientist, Department of Clinical Epidemiology, Ottawa Hospital Research Institute, Ottawa, ON, Canada
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  • Alan J. Forster MD FRCPC MSc,

    1. Senior Scientist and General Internist, Department of Clinical Epidemiology, Ottawa Hospital Research Institute, Ottawa, ON, Canada; Institute for Clinical Evaluative Sciences, Ottawa, ON, Canada; and Department of Medicine, University of Ottawa, Ottawa, ON, Canada
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  • Gabriel J. Escobar MD,

    1. Regional Director for Hospital Operations Research and Director of Systems Research Initiative, Kaiser Permanente Division of Research, Oakland, CA, USA
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  • Carl van Walraven MD FRCPC MSc

    Corresponding author
    1. Senior Scientist and General Internist, Department of Clinical Epidemiology, Ottawa Hospital Research Institute, Ottawa, ON, Canada; Institute for Clinical Evaluative Sciences, Ottawa, ON, Canada; and Department of Medicine, University of Ottawa, Ottawa, ON, Canada
      Dr Carl van Walraven, 1053 Carling Avenue, Administrative Services Building, 1st Floor, Room 1003, Ottawa, ON, Canada K1Y 4E9, E-mail: carlv@ohri.ca
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Dr Carl van Walraven, 1053 Carling Avenue, Administrative Services Building, 1st Floor, Room 1003, Ottawa, ON, Canada K1Y 4E9, E-mail: carlv@ohri.ca

Abstract

Rational, aims and objectives  The study aims to determine the extent to which the addition of post-admission information via time-dependent covariates improved the ability of a survival model to predict the daily risk of hospital death.

Method  Using administrative and laboratory data from adult inpatient hospitalizations at our institution between 1 April 2004 and 31 March 2009, we fit both a time-dependent and a time-fixed Cox model for hospital mortality on a randomly chosen 66% of hospitalizations. We compared the predictive performance of these models on the remaining hospitalizations.

Results  All comparative measures clearly indicated that the addition of time-dependent covariates improved model discrimination and prominently improved model calibration. The time-dependent model had a significantly higher concordance probability (0.879 versus 0.811) and predicted significantly closer to the number of observed deaths within all risk deciles. Over the first 32 admission days, the integrated discrimination improvement (IDI) and net reclassification improvement (NRI) were consistently above zero (average IDI of +0.0200 and average NRI of 62.7% over the first 32 days).

Conclusions  The addition of time-dependent covariates significantly improved the ability of a survival model to predict a patient's daily risk of hospital death. Researchers should consider adding time-dependent covariates when seeking to improve the performance of survival models.

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