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Chapter 3.2 158 Table 2. Dutch PBC Study. Posterior summary statistics for standard deviations of random effects (square roots of diagonal elements of the matrix D) and error terms (σ1 , σ2 , σ3 ) in models with K = 2. Group 0 Group 1 Posterior Median 95% HPD Interval Posterior Median 95% HPD Interval Bilirubin intercept 0.39 (0.30, 0.51) 1.24 (0.66, 2.12) time (months) 0.0050 (0.0034, 0.0071) 0.17 (0.09, 0.27) Error 0.24 (0.24, 0.25) 1.34 (1.24, 1.44) Albumin intercept 0.12 (0.10, 0.14) 0.18 (0.12, 0.28) time (months) 0.0010 (0.0009, 0.0012) 0.0045 (0.0026, 0.0071) Error 0.069 (0.067, 0.071) 0.10 (0.09, 0.10) Alkal. phosph. intercept 1.18 (1.03, 1.36) 1.82 (1.32, 2.40) time (months) 0.0070 (0.0059, 0.0084) 0.046 (0.026, 0.077) Error 0.62 (0.61, 0.64) 0.97 (0.89, 1.04) the standard deviations of the random effects given in Table 2 which are higher in Group 1 than in Group 0. Especially for bilirubin, the random effects are clearly necessary to model the between-patients variation of the longitudinal evolution. Further, we computed the posterior predictive density of the random effects in all considered models and explored in more detail the univariate and pairwise bivariate marginal densities. We conclude that in models with K = 2, neither of these densities is clearly bimodal. Nevertheless, in many cases, the two components mixture helped to capture skewness in the distribution of the random effects. As an illustration, Figure 2 shows the estimated pairwise marginal densities for two selected pairs in models with K = 1 and K = 2 in Group 1. Let 0 ≤ ti,1 < ···
Discriminant analysis using a MLMM with a normal mixture 159 Figure 2. Dutch PBC Study. Estimates of selected pairwise densities from the joint distribution of the random effects in the model in Group1 for K=1 (left panel) abd K=2 (right panel). The upper panel shows the estimated distribution of (b i,3 , b i,4 )’(random intercept and time effect in the model for albumin), the lower panel shows the estimated distribution of (b i,3 , b i,6 )’(random intercept in the model for albumin and the random time effect in the model for log(alkaline phosphatase)). used π0 =0.8, π1 =0.2 which approximately correspond to the relative sizes of the prognostic groups in the training data set. All three prediction approaches described in Section ’Discrimination procedure’ have been used for models with K =1and K = 2 mixture components. The random effects prediction with K =2showedthe best results, as will be illustrated. The evolution of the cross-validated values of P1,i(τ), i.e. probabilities at time τ that the subject i encounters serious disease progression by T = 10 years obtained from the random effects prediction is shown in Figure 3. Note that for a perfect
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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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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
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Page 159: 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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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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