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Chapter 2.4 88 Finally in the random approach the distribution of the individual random effects br,new ∼ N(0, Dr ) is used to compute the posterior probabilities. The density func- tion fr (y r,new) is equal to the density of br,new evaluated at the estimated value of the random effect ˆbr,new, r =0, 1, at each stage of the prediction process. For each of the three approaches the prediction process proceeds sequentially one observation at a time for the new subject. First the markers of the first visit are considered and the Xr,new and the Zr,new design matrices are constructed for each outcome non-responder and responder, r = 0, 1. The marginal means and the EBs are calculated for each outcome and finally depending on the approach the considered and the prediction process continues: the Xr,new and the Zr,new design matrices are constructed for each outcome group, the marginal means and then the posterior probabilities are calculated etc. The prediction process is completed for all observations, sequentially extending with the markers of the next visit. The influence of three approaches on the posterior probabilities depends on how well the mixed linear model describes the markers. If the patterns of the markers of the new subject follow the patterns of the population mean well of either the response or non-response group the random effects are either close to zero or far away from zero. If close to zero this indicates that the data is more likely to come from this particular group. If far away from zero this indicates that the subject is unlikely to come from this group. For the marginal and the conditional approach this results in posterior probabilities close to one or zero. The random effect approach depends only on the distribution of the random effects and this maybe explains the more moderate posterior probabilities (see application). The impact of a subject with patterns of the markers which do not follow the mean pattern of neither the response nor the non-response group may be illustrated with the following simple example. Consider the case where Y is observed at two visits: (Y1, Y2), figure 1. In figure 1.a and 1.b the density of the observations Y1 and Y2 are given by response yes or no. In figure 1.c the density of (Y1, Y2) is plotted and in 1.d by response yes or no. In the specific case where Y1 is an outlier of the distribution, but at visit 2 at the center of the distribution in the multivariate normal distribution the case remains an outlier. The influence on the marginal and the conditional approach is enormous once a prediction in the wrong direction is made and it is difficult to get back on track. In the application an example of this situation is given. Summarizing the indirect method of Morrell and Brant, 10 three approaches are considered each giving a new posterior prediction of response depending on the longitudinal profile of the observed markers. In the following all three approaches are applied.
Dynamic prediction of response using longitudinal profi les 89 CLINICAL DATA ON HEPATITIS B PATIENTS The data reported here are from the international HBV9901-trial on chronic hepatitis B, HBeAg positive patients, Janssen et al. 1 Two-hundred and sixty-six patients were randomized to receive either peg-interferon mono-therapy for 52 weeks or PEG- IFN in combination with lamivudine. The final overall response, defined as HBeAg negativity 24 weeks after treatment, was achieved in 36%, there was no significant difference between treatment arms (36% vs 35%, p=0.91). During treatment the two markers: the viral load (HBV DNA (copies/ml)) and the disease activity (ALT (U/ml)) were measured every 4th week until the end of follow-up (week 76). Since the HBV DNA decline under lamivudine showed a total different pattern in comparison with PEG-IFN monotherapy, with in general a steep decline during therapy followed by a relapse post-treatment, only the subset of patients with peg-interferon monotherapy (n=136) will be studied here. Furthermore patients with other HBV genotypes than A, B, C, and D (n=11) are excluded. For this study response to therapy, R = 1 is defined as loss of HBeAg at end of follow-up, week 78 and R = 0 otherwise. The time unit is weeks with Y1,i,j the load, i.e. log 10 value of the viral load (HBV DNA) and Y2,i,j the log e value of the ALT. Our main clinical interest is to estimate pi,j in the first time-interval from week 4 to week 32 to identify a possible stopping rule as early as possible in the treatment schedule. In a previous study13,14 we described in detail baseline factors influencing the response rate and developed a prediction model which provides a subject specific prediction of response. The baseline factors associated with response were: HBVgenotype, age, gender, load = baseline HBV DNA (copies/ml, log10), ALT (loge) and previous treatment with IFN. The effect of the baseline covariates is summarized by the prognostic index PIi,0 of subject i. In general define for the explanatory baseline variables: HBV-genotype, binary variables genoi,G, where G = A, B, C or D (genotype A is set as the reference) , agei (in years), sexi (0 is male, 1 is female), PrRx (0 for not treated before, and 1 for previous treated) and baseline ALT0 and load0. RESULTS The observed evolution and variability of the two markers: HBV DNA and the ALT in the group of non-responders and responders are shown in figure 2. For the responders an early decline of the load is observed while the non-responders show
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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
Page 40 and 41: Chapter 2.1 38 DNA was observed in
Page 42: 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: 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
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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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