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Chapter 3.2 152 For each g =0,...,G−1, model (25) is estimated using subjects from the respective prognostic group in the training dataset. That is, samples θ g,(1) ,...,θ g,(M) are obtained from the posterior distribution p � θ g � � y g � . Furthermore, each prognostic group is assigned prevalences π0,...,πG−1, � G−1 g=0 πg = 1 which play the role of prior pertinence probabilities for the discrimination procedure. Let Y new =(Y ′ new,1,...,Y ′ new,R) ′ be the history of relevant markers for a new sub- ject. Without loss of generality, we assume that Y new contains only the history up to time τ
Discriminant analysis using a MLMM with a normal mixture 153 profiles and fitted mixed model leading to marginal, conditional and random effects prediction. Marginal prediction For marginal prediction, the predictive density fg,new is equal to the marginal density of Y new where the term marginal reflects the fact that the random effects are integrated out. That is, for our model f marg g,new = f marg (y new; θ g ) ≡ p � � y � g new θ � = K� k=1 w g k pk � � y � g new θ � , (28) � � where pk y � g new θ � � is the density of N Xg newαg + Zg new(sg + Sgμk), V g � new,k V g new,k = ZgnewSg D g kSg′ Zg new ′ +Σ g new. Conditional prediction with For conditional prediction, the predictive density fg,new is equal to the conditional density of Y new given the estimated values of individual random effects. That is, for our model f cond g,new = f cond (y new; θ g ) ≡ p � � y � new bnew = � b g new, θ g� (29) � which is a density of N Xg newαg + Zg new � b g new, Σ g � new . As explained in Section ’Estimates of individual values of random effects’, a suitable estimate of the individual random effects, denoted by � b g new, is the mean of the conditional distribution p(bnew | y new, θ g ) which is computed using an expression analogous to (22), with y i, bi, θ replaced by y new, bnew, θ g , respectively. Random effects prediction Random effects prediction is based on the distribution of the individual random effects. The predictive density fg,new is then equal to the density of bnew evaluated at the estimated value of the random effect, i.e., at � b g new. Hence, in our case, f rand g,new = f rand (y new; θ g ) ≡ p � g � b� � g new θ � = K� k=1 � g � where pk �b � g new θ � is the density of N � sg + Sgμ g k , SgD g kSg′� . w g k pk � g � �b � g new θ � , (30)
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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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Page 108 and 109: Chapter 2.5 106 ABSTRACT Peginterfe
Page 110 and 111: Chapter 2.5 108 and placebo daily.
Page 112 and 113: Chapter 2.5 110 for patients with a
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: where wi,k(y i, θ) = (k =1,...,K).
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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Viral dynamics during tenofovir the
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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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