An Introduction to Mixed Models and Joint Modeling: Analysis of Valve Function Over Time Eleni-Rosalina Andrinopoulou, BS, Dimitris Rizopoulos, PhD,

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Presentation transcript:

An Introduction to Mixed Models and Joint Modeling: Analysis of Valve Function Over Time Eleni-Rosalina Andrinopoulou, BS, Dimitris Rizopoulos, PhD, Ruyun Jin, MD, Ad J.J.C. Bogers, MD, PhD, Emmanuel Lesaffre, PhD, Johanna J.M. Takkenberg, MD, PhD The Annals of Thoracic Surgery Volume 93, Issue 6, Pages 1765-1772 (June 2012) DOI: 10.1016/j.athoracsur.2012.02.049 Copyright © 2012 The Society of Thoracic Surgeons Terms and Conditions

Fig 1 Kaplan-Meier curve for survival. The Annals of Thoracic Surgery 2012 93, 1765-1772DOI: (10.1016/j.athoracsur.2012.02.049) Copyright © 2012 The Society of Thoracic Surgeons Terms and Conditions

Fig 2 Kaplan-Meier curve for reoperation. The Annals of Thoracic Surgery 2012 93, 1765-1772DOI: (10.1016/j.athoracsur.2012.02.049) Copyright © 2012 The Society of Thoracic Surgeons Terms and Conditions

Fig 3 Graphical representation of mixed-effects models. The solid line shows the fixed-effects, which describe the average evolution in time of the aortic gradient; the dashed-lines show the random-effects (patient specific), which describe the evolution in time for each patient. (sqrt = square root.) The Annals of Thoracic Surgery 2012 93, 1765-1772DOI: (10.1016/j.athoracsur.2012.02.049) Copyright © 2012 The Society of Thoracic Surgeons Terms and Conditions

Fig 4 Fitted longitudinal profiles for 4 patients in the study. The solid line is based on the mixed-effects model analyses for aortic gradient and the dashed line is based on the regression model analyses for aortic gradient. (sqrt = square root.) The Annals of Thoracic Surgery 2012 93, 1765-1772DOI: (10.1016/j.athoracsur.2012.02.049) Copyright © 2012 The Society of Thoracic Surgeons Terms and Conditions

Fig 5 Graphical representation of joint models. (A) Contains the hazard function for an event. In (B), the dashed line describes a time-dependent covariate as used in the time-dependent Cox model, and the solid line the mixed-effects model reconstruction of the covariate path. The Annals of Thoracic Surgery 2012 93, 1765-1772DOI: (10.1016/j.athoracsur.2012.02.049) Copyright © 2012 The Society of Thoracic Surgeons Terms and Conditions

Fig 6 Effect plot based on the mixed-effects model analyses. The 47-year-old male patients without Marfan syndrome, median allograft diameter (23 mm), and donor age (59 years), and good left ventricular function are presented. (sqrt =square root.) The Annals of Thoracic Surgery 2012 93, 1765-1772DOI: (10.1016/j.athoracsur.2012.02.049) Copyright © 2012 The Society of Thoracic Surgeons Terms and Conditions

Fig 7 (A) Marginal probabilities from the mixed-effects continuation ratio model for aortic regurgitation. Profiles represent male patients who underwent subcoronary implantation at a median age of 47 years. (B) Marginal probabilities from the mixed-effects continuation ratio model for aortic regurgitation. Profiles represent male patients who underwent root replacement at a median age of 47 years. The Annals of Thoracic Surgery 2012 93, 1765-1772DOI: (10.1016/j.athoracsur.2012.02.049) Copyright © 2012 The Society of Thoracic Surgeons Terms and Conditions