Association Structures in Bayesian Joint Models of Longitudinal Markers and Survival Outcomes: Application to Cardiac Data

Tayu Nigusie Abebe

doi:doi:10.11648/j.bsi.20261103.12

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Association Structures in Bayesian Joint Models of Longitudinal Markers and Survival Outcomes: Application to Cardiac Data

Tayu Nigusie Abebe^*

Published in Biomedical Statistics and Informatics (Volume 11, Issue 3)

Received: 1 August 2026 Accepted: 4 September 2026 Published: 20 September 2026

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Abstract

In clinical research, longitudinal biomarkers and time-to-event outcomes are often correlated. Standard separate modeling of these processes leads to biased estimates due to the failure to account for endogeneity. This study investigates the application of the Bayesian joint modeling framework to quantify the association between pulse rate trajectories and mortality risk in cardiac patients. A primary focus is placed on comparing various association structures to determine the most effective parameterization for medical inference. Data from cardiac patients at an Ethiopian cardiac center were analyzed using a linear mixed model for pulse rate and a Cox PH model for time-to-death. Three distinct association structures current value, current value plus slope, and shared random effects were estimated via Markov chain Monte Carlo (MCMC) algorithms. The current value plus slope association structure provided the best model fit, demonstrating that both the current level of pulse rate and its instantaneous rate of change are significant predictors of mortality. Clinical findings also indicated that underweight status and pulmonary complications significantly increase the hazard of death, while corrective surgery serves as a protective factor. Joint modeling offers a robust unified approach for medical research, yielding more efficient and less biased estimates than separate analyses. The choice of association structure is critical; specifically, incorporating the trajectory's slope alongside its current value enhances the predictive performance and interpretability of clinical biomarkers in survival analysis.

Published in	Biomedical Statistics and Informatics (Volume 11, Issue 3)
DOI	10.11648/j.bsi.20261103.12
Page(s)	74-85
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Joint Modeling, Association Structures, Bayesian Inference, Longitudinal Data, Survival Analysis, Cardiac Data

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Abebe, T. N. (2026). Association Structures in Bayesian Joint Models of Longitudinal Markers and Survival Outcomes: Application to Cardiac Data. Biomedical Statistics and Informatics, 11(3), 74-85. https://doi.org/10.11648/j.bsi.20261103.12

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ACS Style

Abebe, T. N. Association Structures in Bayesian Joint Models of Longitudinal Markers and Survival Outcomes: Application to Cardiac Data. Biomed. Stat. Inform. 2026, 11(3), 74-85. doi: 10.11648/j.bsi.20261103.12

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AMA Style

Abebe TN. Association Structures in Bayesian Joint Models of Longitudinal Markers and Survival Outcomes: Application to Cardiac Data. Biomed Stat Inform. 2026;11(3):74-85. doi: 10.11648/j.bsi.20261103.12

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@article{10.11648/j.bsi.20261103.12,
  author = {Tayu Nigusie Abebe},
  title = {Association Structures in Bayesian Joint Models of Longitudinal Markers and Survival Outcomes: Application to Cardiac Data},
  journal = {Biomedical Statistics and Informatics},
  volume = {11},
  number = {3},
  pages = {74-85},
  doi = {10.11648/j.bsi.20261103.12},
  url = {https://doi.org/10.11648/j.bsi.20261103.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.bsi.20261103.12},
  abstract = {In clinical research, longitudinal biomarkers and time-to-event outcomes are often correlated. Standard separate modeling of these processes leads to biased estimates due to the failure to account for endogeneity. This study investigates the application of the Bayesian joint modeling framework to quantify the association between pulse rate trajectories and mortality risk in cardiac patients. A primary focus is placed on comparing various association structures to determine the most effective parameterization for medical inference. Data from cardiac patients at an Ethiopian cardiac center were analyzed using a linear mixed model for pulse rate and a Cox PH model for time-to-death. Three distinct association structures current value, current value plus slope, and shared random effects were estimated via Markov chain Monte Carlo (MCMC) algorithms. The current value plus slope association structure provided the best model fit, demonstrating that both the current level of pulse rate and its instantaneous rate of change are significant predictors of mortality. Clinical findings also indicated that underweight status and pulmonary complications significantly increase the hazard of death, while corrective surgery serves as a protective factor. Joint modeling offers a robust unified approach for medical research, yielding more efficient and less biased estimates than separate analyses. The choice of association structure is critical; specifically, incorporating the trajectory's slope alongside its current value enhances the predictive performance and interpretability of clinical biomarkers in survival analysis.},
 year = {2026}
}

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TY  - JOUR
T1  - Association Structures in Bayesian Joint Models of Longitudinal Markers and Survival Outcomes: Application to Cardiac Data
AU  - Tayu Nigusie Abebe
Y1  - 2026/09/20
PY  - 2026
N1  - https://doi.org/10.11648/j.bsi.20261103.12
DO  - 10.11648/j.bsi.20261103.12
T2  - Biomedical Statistics and Informatics
JF  - Biomedical Statistics and Informatics
JO  - Biomedical Statistics and Informatics
SP  - 74
EP  - 85
PB  - Science Publishing Group
SN  - 2578-8728
UR  - https://doi.org/10.11648/j.bsi.20261103.12
AB  - In clinical research, longitudinal biomarkers and time-to-event outcomes are often correlated. Standard separate modeling of these processes leads to biased estimates due to the failure to account for endogeneity. This study investigates the application of the Bayesian joint modeling framework to quantify the association between pulse rate trajectories and mortality risk in cardiac patients. A primary focus is placed on comparing various association structures to determine the most effective parameterization for medical inference. Data from cardiac patients at an Ethiopian cardiac center were analyzed using a linear mixed model for pulse rate and a Cox PH model for time-to-death. Three distinct association structures current value, current value plus slope, and shared random effects were estimated via Markov chain Monte Carlo (MCMC) algorithms. The current value plus slope association structure provided the best model fit, demonstrating that both the current level of pulse rate and its instantaneous rate of change are significant predictors of mortality. Clinical findings also indicated that underweight status and pulmonary complications significantly increase the hazard of death, while corrective surgery serves as a protective factor. Joint modeling offers a robust unified approach for medical research, yielding more efficient and less biased estimates than separate analyses. The choice of association structure is critical; specifically, incorporating the trajectory's slope alongside its current value enhances the predictive performance and interpretability of clinical biomarkers in survival analysis.
VL  - 11
IS  - 3
ER  -

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Tayu Nigusie Abebe

Department of Statistics, Bule Hora University, Bule Hora, Ethiopia

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http://orcid.org/0009-0009-3602-6484

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APA Style

Abebe, T. N. (2026). Association Structures in Bayesian Joint Models of Longitudinal Markers and Survival Outcomes: Application to Cardiac Data. Biomedical Statistics and Informatics, 11(3), 74-85. https://doi.org/10.11648/j.bsi.20261103.12

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ACS Style

Abebe, T. N. Association Structures in Bayesian Joint Models of Longitudinal Markers and Survival Outcomes: Application to Cardiac Data. Biomed. Stat. Inform. 2026, 11(3), 74-85. doi: 10.11648/j.bsi.20261103.12

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AMA Style

Abebe TN. Association Structures in Bayesian Joint Models of Longitudinal Markers and Survival Outcomes: Application to Cardiac Data. Biomed Stat Inform. 2026;11(3):74-85. doi: 10.11648/j.bsi.20261103.12

Copy | Download

@article{10.11648/j.bsi.20261103.12,
  author = {Tayu Nigusie Abebe},
  title = {Association Structures in Bayesian Joint Models of Longitudinal Markers and Survival Outcomes: Application to Cardiac Data},
  journal = {Biomedical Statistics and Informatics},
  volume = {11},
  number = {3},
  pages = {74-85},
  doi = {10.11648/j.bsi.20261103.12},
  url = {https://doi.org/10.11648/j.bsi.20261103.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.bsi.20261103.12},
  abstract = {In clinical research, longitudinal biomarkers and time-to-event outcomes are often correlated. Standard separate modeling of these processes leads to biased estimates due to the failure to account for endogeneity. This study investigates the application of the Bayesian joint modeling framework to quantify the association between pulse rate trajectories and mortality risk in cardiac patients. A primary focus is placed on comparing various association structures to determine the most effective parameterization for medical inference. Data from cardiac patients at an Ethiopian cardiac center were analyzed using a linear mixed model for pulse rate and a Cox PH model for time-to-death. Three distinct association structures current value, current value plus slope, and shared random effects were estimated via Markov chain Monte Carlo (MCMC) algorithms. The current value plus slope association structure provided the best model fit, demonstrating that both the current level of pulse rate and its instantaneous rate of change are significant predictors of mortality. Clinical findings also indicated that underweight status and pulmonary complications significantly increase the hazard of death, while corrective surgery serves as a protective factor. Joint modeling offers a robust unified approach for medical research, yielding more efficient and less biased estimates than separate analyses. The choice of association structure is critical; specifically, incorporating the trajectory's slope alongside its current value enhances the predictive performance and interpretability of clinical biomarkers in survival analysis.},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Association Structures in Bayesian Joint Models of Longitudinal Markers and Survival Outcomes: Application to Cardiac Data
AU  - Tayu Nigusie Abebe
Y1  - 2026/09/20
PY  - 2026
N1  - https://doi.org/10.11648/j.bsi.20261103.12
DO  - 10.11648/j.bsi.20261103.12
T2  - Biomedical Statistics and Informatics
JF  - Biomedical Statistics and Informatics
JO  - Biomedical Statistics and Informatics
SP  - 74
EP  - 85
PB  - Science Publishing Group
SN  - 2578-8728
UR  - https://doi.org/10.11648/j.bsi.20261103.12
AB  - In clinical research, longitudinal biomarkers and time-to-event outcomes are often correlated. Standard separate modeling of these processes leads to biased estimates due to the failure to account for endogeneity. This study investigates the application of the Bayesian joint modeling framework to quantify the association between pulse rate trajectories and mortality risk in cardiac patients. A primary focus is placed on comparing various association structures to determine the most effective parameterization for medical inference. Data from cardiac patients at an Ethiopian cardiac center were analyzed using a linear mixed model for pulse rate and a Cox PH model for time-to-death. Three distinct association structures current value, current value plus slope, and shared random effects were estimated via Markov chain Monte Carlo (MCMC) algorithms. The current value plus slope association structure provided the best model fit, demonstrating that both the current level of pulse rate and its instantaneous rate of change are significant predictors of mortality. Clinical findings also indicated that underweight status and pulmonary complications significantly increase the hazard of death, while corrective surgery serves as a protective factor. Joint modeling offers a robust unified approach for medical research, yielding more efficient and less biased estimates than separate analyses. The choice of association structure is critical; specifically, incorporating the trajectory's slope alongside its current value enhances the predictive performance and interpretability of clinical biomarkers in survival analysis.
VL  - 11
IS  - 3
ER  -

Copy | Download