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Chapter 2.4 92 a. b. c. Figure 3. Behavior and prediction of tree typical subjects: a. subject with a response at week 78, b. subject without response at week 78 and c. a subject without response at week 78, but with a sudden dip in HBV DNA at week 12. In the left panel the observed individual behavior of HBV DNA and ALT the fi rst 32 weeks is given. In the right panel the estimated dynamic prediction of response at each new visit with the different methods Applying the logistic regression method of the patterns of the markers the following results were obtained. A simple linear mixed model without baseline covariates with random intercepts and random slopes was first designed to estimate the subject specific patterns of the load during the first 32 weeks:
Dynamic prediction of response using longitudinal profi les 93 Y i,j = β1 + β2ti,j + b1,i + b2,iti,j + ɛi,j where (b1,i,b2,i) ′ are i.i.d. normally distributed random effects with covariance matrix D. Further, ɛi,j are i.i.d. normally distributed error terms with zero mean and variance σ 2 and β1 and β2 are the fixed effects. For each subject i the model was first fitted omitting data after visit 3 (week 8) of subject i. (Omitting also visit 3 brings us back to a simple logistic regression model with extension of one observation, which therefore is not considered here.) The logistic regression of response, R = 1, was subsequently fitted including the PI as an offset, similar to the previous method, and then adding the random effects as predictors: logit (pi,3) =logit (Ri =1|ˆb1,i, ˆb2,i, offset = PIi,0) = γ0 + γ1 ˆb1,i + γ2 ˆb2,i + PIi,0 With the covariance matrix of the estimated random intercept and random slope the prediction of response was afterwards adjusted as described in section 2.2. Subsequently, the next visits of subject i were added one at a time to the total data and the models (first the linear mixed model and then the logistic regression) were refitted. We extended the linear mixed model with baseline covariates and repeated the process described above. As could be expected this did not change the predictions since the logistic regression also includes these variables via the PI’s. Next we designed a bivariate linear mixed model of the load and the ALT. At all visits the random intercept and random slope of ALT were never significant (p’s>0.85) and even the c-statistics declined reflecting overfitting. We therefore chose to present the simple model above. The results are displayed in figure 3 for three typical subjects and in figure 4 the overall plots of the prediction of response separate for subject with and without an observed response. The prediction of response looks very similar to the previous approach for subject a and b while for subject c the estimates are more smooth and without sudden jumps. This observation is also seen in figure 4.
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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
Page 46 and 47: Chapter 2.2 44 ABSTRACT Background:
Page 48 and 49: Chapter 2.2 46 low baseline HBV DNA
Page 50 and 51: Chapter 2.2 48 patient subgroups wa
Page 52 and 53: Chapter 2.2 50 p=0.002). Previous I
Page 54 and 55: Chapter 2.2 52 Application of the m
Page 56 and 57: Chapter 2.2 54 PEG-IFN, the proport
Page 58 and 59: Chapter 2.2 56 References 1. Lavanc
Page 60 and 61: Chapter 2.2 58 26. Bonino F, Lau GK
Page 63 and 64: Chap ter 2.3 Prediction of the resp
Page 65 and 66: INTRODUCTION Dynamic prediction of
Page 67 and 68: Statistical analysis Dynamic predic
Page 69 and 70: Dynamic prediction of response to P
Page 77 and 78: References Dynamic prediction of re
Page 81 and 82: Cha pter 2.4 Dynamic prediction of
Page 83 and 84: INTRODUCTION Dynamic prediction of
Page 85 and 86: For the indirect approach we rewrit
Page 87 and 88: logit pi,j = logit Pr(Ri =1|visit =
Page 89 and 90: Dynamic prediction of response usin
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Page 101 and 102: 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
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Introduction Discriminant analysis
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Discriminant analysis using a MLMM
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Estimation Discriminant analysis us
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where wi,k(y i, θ) = (k =1,...,K).
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Appendix Discriminant analysis usin
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Cha pter 4 Statistical models of ea
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Chapter 4.1 176 ABSTRACT Nucleoside
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Chapter 4.1 178 at day 1 at t =0 an
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Chapter 4.1 180 Table 1. Baseline c
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Chapter 4.1 182 Figure 1.
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Chapter 4.1 184 Figure 1. Viral dec
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Chapter 4.1 186 suppression in seru
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Chapter 4.1 188 13. Seifer M, Hamat
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Cha pter 4.2 Viral dynamics during
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INTRODUCTION Viral dynamics during
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Viral dynamics during tenofovir the
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log HBV DNA (copies/mL) 10.0 9.0 8.
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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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