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Multiple-Imputation-Based Residuals and Diagnostic Plots for Joint Models of Longitudinal and Survival Outcomes

Authors

  • Dimitris Rizopoulos,

    Corresponding author
    1. Department of Biostatistics, Erasmus Medical Center, PO Box 2040, 3000 CA Rotterdam, The Netherlands
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  • Geert Verbeke,

    1. Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Katholieke Universiteit Leuven, Kapucijnenvoer 35, Blok D, bus 7001, B3000 Leuven, Belgium and Universiteit Hasselt, Agoralaan 1, B3590 Diepenbeek, Belgium
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  • Geert Molenberghs

    1. Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Katholieke Universiteit Leuven, Kapucijnenvoer 35, Blok D, bus 7001, B3000 Leuven, Belgium and Universiteit Hasselt, Agoralaan 1, B3590 Diepenbeek, Belgium
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email: d.rizopoulos@erasmusmc.nl

Abstract

Summary The majority of the statistical literature for the joint modeling of longitudinal and time-to-event data has focused on the development of models that aim at capturing specific aspects of the motivating case studies. However, little attention has been given to the development of diagnostic and model-assessment tools. The main difficulty in using standard model diagnostics in joint models is the nonrandom dropout in the longitudinal outcome caused by the occurrence of events. In particular, the reference distribution of statistics, such as the residuals, in missing data settings is not directly available and complex calculations are required to derive it. In this article, we propose a multiple-imputation-based approach for creating multiple versions of the completed data set under the assumed joint model. Residuals and diagnostic plots for the complete data model can then be calculated based on these imputed data sets. Our proposals are exemplified using two real data sets.

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