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Chapter 3.2 160 Figure 3. Dutch PBC Study. Evolution of cross-validated P 1,i (τ ) (probability of being classifi ed in Group 1) from random effect prediction based on mixed models with K = 1 (upper panel) and K = 2 (lower panel) for Group 0, patients who were alive without liver transplantation at time T = 10 years (left panel) and for Group 1, patients who encountered either liver related death or liver transplantation by time T = 10 years (right panel). discrimination procedure the values of P1,i(τ) would be zero for all τ for subjects from Group 0 (left panel of Figure 3) while conversely the values of P1,i(τ) would be one for all τ for subjects from Group 1 (right panel of Figure 3). It is seen that with K = 2 the values of P1,i(τ) in Group 0 remain close to zero for most subjects which is not always the case when the model with K = 1 was used. In Group 1, the values of P1,i(τ) go to one for most subjects, however, the difference between K = 1 and K = 2 is practically negligible.
Discriminant analysis using a MLMM with a normal mixture 161 Further, we explored the properties of the discrimination procedures based on Pg,i(τ) from different models (K =1, 2) and different discrimination approaches (marginal, conditional, random effects) in the following way. For each subject, each model and discrimination approach, the evolution � � P1,i(τ) :τ ≤ ti,ni was approximated from computed values of P1,i(ti,1),...,P1,i(ti,n∗) as piecewise linear (as shown in i Figure 3). The values of P1,i(t), for t =0, 1,...,60 months, from patients whose last visit happened at time t or later were subsequently used to draw receiver operating curves (ROC) and to compute related areas under the ROC (AUC). Figure 4 clearly shows the superiority of the random effects prediction in this case and also a visible improvement when a two component normal mixture is used for the random effects distribution compared to a single component normal distribution. More insight is given in Figure 5 which shows ROCs for t =0, 6, 12, 18, 24, 36 months and in Table 3 which provides the sensitivity values for specificity values equal to 0.99, 0.95 and 0.90. They show that with the random effects prediction, it is possible to predict already at t = 18 months the patient’s status at T = 120 months with a rather high specificity and sensitivity (e.g. with K = 2, specificity of 0.90 and sensitivity of 0.733 is obtained at t = 18 months). Furthermore, we examined how the multivariate mixed model (1) based on R =3 markers improves the prediction of the patient’s status at T = 10 years compared to separate mixed models for each marker. Hence, we separately fitted the three mixed models to each of the considered markers. In each model, K = 2 mixture components were used to model the distribution of the random effects. Figure 6 Figure 4. Dutch PBC Study. Evolution of the area under the ROC curve over time for different types of prediction methods based on mixed models with K = 1 and K = 2 mixture components. Solid line: K=2, dashed line: K=1.
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Statistical Models of Treatment Eff
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ISBN: 978-90-8559-069-9 © Bettina
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PROMOTIECOMMISSIE Promotor: Prof.dr
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CONTENTS Chapter 1. Introduction 11
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Cha pter 1 Introduction
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Chapter 1 14 Epidemiology Worldwide
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Chapter 1 16 Prediction models with
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Chapter 1 18 standard method fails
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Chapter 1 20 The extended non-linea
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Chapter 1 22 References 1. Blumberg
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Cha pter 2 Prediction of response t
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Chapter 2.1 28 ABSTRACT The aim of
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Chapter 2.1 30 been hepatitis B sur
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Chapter 2.1 32 HBV DNA decline The
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Chapter 2.1 34 Figure 2 continued.
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Chapter 2.1 36 Figure 4. Estimated
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Chapter 2.1 38 DNA was observed in
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Chapter 2.1 40 15. Kao JH. Role of
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Chapter 2.2 44 ABSTRACT Background:
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Chapter 2.2 46 low baseline HBV DNA
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Chapter 2.2 48 patient subgroups wa
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Chapter 2.2 50 p=0.002). Previous I
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Chapter 2.2 52 Application of the m
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Chapter 2.2 54 PEG-IFN, the proport
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Chapter 2.2 56 References 1. Lavanc
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Chapter 2.2 58 26. Bonino F, Lau GK
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Chap ter 2.3 Prediction of the resp
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INTRODUCTION Dynamic prediction of
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Statistical analysis Dynamic predic
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Dynamic prediction of response to P
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References Dynamic prediction of re
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Cha pter 2.4 Dynamic prediction of
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INTRODUCTION Dynamic prediction of
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For the indirect approach we rewrit
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logit pi,j = logit Pr(Ri =1|visit =
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Dynamic prediction of response usin
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Table 1. Results of different stopp
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Chapter 2.5 106 ABSTRACT Peginterfe
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Chapter 2.5 108 and placebo daily.
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Page 114 and 115: Chapter 2.5 112 Mean HBV DNA declin
Page 116 and 117: Chapter 2.5 114 peginterferon and n
Page 118 and 119: Chapter 2.5 116 hepatocellular carc
Page 120 and 121: Chapter 2.5 118 13. Werle-Lapostoll
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Page 127 and 128: Chap ter 3.1 Long-term clinical out
Page 129 and 130: INTRODUCTION Glycyrrhizin for IFN-n
Page 131 and 132: Statistics Glycyrrhizin for IFN-non
Page 133 and 134: Glycyrrhizin for IFN-non responders
Page 135 and 136: Table 2. Time dependent Cox regress
Page 143 and 144: Cha pter 3.2 Discriminant analysis
Page 145 and 146: Introduction Discriminant analysis
Page 147 and 148: Discriminant analysis using a MLMM
Page 149 and 150: Estimation Discriminant analysis us
Page 153 and 154: where wi,k(y i, θ) = (k =1,...,K).
Page 161: Discriminant analysis using a MLMM
Page 171 and 172: Appendix Discriminant analysis usin
Page 175: Cha pter 4 Statistical models of ea
Page 178 and 179: Chapter 4.1 176 ABSTRACT Nucleoside
Page 180 and 181: Chapter 4.1 178 at day 1 at t =0 an
Page 182 and 183: Chapter 4.1 180 Table 1. Baseline c
Page 184 and 185: Chapter 4.1 182 Figure 1.
Page 186 and 187: Chapter 4.1 184 Figure 1. Viral dec
Page 188 and 189: Chapter 4.1 186 suppression in seru
Page 190 and 191: Chapter 4.1 188 13. Seifer M, Hamat
Page 193 and 194: Cha pter 4.2 Viral dynamics during
Page 195 and 196: INTRODUCTION Viral dynamics during
Page 197 and 198: Viral dynamics during tenofovir the
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Page 211 and 212: Chap ter 4.3 Modelling of early vir
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INTRODUCTION HBV viral kinetics dur
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HBV viral kinetics during PEG-IFN 2
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SUMMARY AND CONCLUSION Summary and
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Summary and conclusion 233 The mode
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Summary and conclusion 235 The infe
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Summary and conclusion 237 Early st
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SAMENVATTING EN CONCLUSIE Samenvatt
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Samenvatting en conclusie 243 Er we
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Samenvatting en conclusie 245 Data
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Samenvatting en conclusie 247 Behan
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Dan kwoord
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Dankwoord 254 Lieve Marion en Margr
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BIBLI OGRAPHY Bibliography 257 1. K
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Bibliography 259 Interferon-ribavir
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Bibliography 261 Long term clinical
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Bibliography 263 Flares in chronic
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Bibliography 265 Genetic characteri
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Bibliography 267 106. Reijnders JG,
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