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Updated: May 1, 2026

Establishing a Competing Risk Regression Nomogram Model for Survival Data
Published on: October 23, 2020
Joint modeling of two longitudinal outcomes and competing risk data
Eleni-Rosalina Andrinopoulou1, Dimitris Rizopoulos, Johanna J M Takkenberg
1Department of Biostatistics, Erasmus MC, Rotterdam, The Netherlands; Department of Cardiothoracic Surgery, Erasmus MC, Rotterdam, The Netherlands.
This study introduces a joint statistical model to analyze aortic valve function markers, such as aortic gradient and regurgitation, alongside patient outcomes like death and reoperation. The novel graphical approach aids in interpreting complex longitudinal data for better clinical insights.
Area of Science:
- Cardiovascular Medicine
- Biostatistics
- Medical Imaging
Background:
- Aortic gradient and aortic regurgitation are key echocardiographic markers of aortic valve function.
- These biomarkers are repeatedly measured in patients with valve abnormalities, suggesting a biological interrelation.
- Analyzing these outcomes jointly is crucial due to potential loss to follow-up from events like death or reoperation.
Purpose of the Study:
- To propose and apply a flexible joint statistical model for analyzing longitudinal echocardiographic data and time-to-event outcomes.
- To investigate the relationship between aortic gradient, aortic regurgitation, death, and reoperation in patients with human tissue aortic valves.
- To introduce a graphical approach for interpreting complex joint models with non-linear structures.
Main Methods:
- Development of a joint model incorporating two longitudinal outcomes (continuous aortic gradient, ordinal aortic regurgitation) and two time-to-event outcomes (death, reoperation).
- Utilized B-splines for flexible modeling of the average and subject-specific profiles of the continuous longitudinal outcome.
- Applied the proposed joint models within a Bayesian framework using serial echocardiographic data.
Main Results:
- The study demonstrates the application of a novel joint model for analyzing complex cardiovascular data.
- A graphical approach was proposed to facilitate the interpretation of results from non-linear joint models.
- The model was applied to a dataset of patients with human tissue aortic valves, examining echocardiographic markers and clinical outcomes.
Conclusions:
- Joint models offer a powerful framework for analyzing interrelated longitudinal and time-to-event data in cardiovascular research.
- The proposed flexible joint model and graphical interpretation method enhance the understanding of aortic valve disease progression and patient outcomes.
- This approach provides valuable insights for managing patients with aortic valve abnormalities.
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