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Chapter 3.2 142 Abstract We have developed a method to longitudinally classify subjects into two or more prognostic groups using longitudinally observed values of markers related to the prognosis. We assume the availability of a training data set where the subjects’ allocation into the prognostic group is known. The proposed method proceeds in two steps as described earlier in the literature. First, multivariate linear mixed models are fitted in each prognostic group from the training data set to model the dependence of markers on time and on possibly other covariates. Secondly, fitted mixed models are used to develop a discrimination rule for future subjects. Our method improves upon existing approaches by relaxing the normality assumption of random effects in the underlying mixed models. Namely, we assume a heteroscedastic multivariate normal mixture for random effects. Inference is performed in the Bayesian framework using the Markov chain Monte Carlo methodology. Software has been written for the proposed method and it is freely available. The methodology is applied to data from the Dutch Primary Biliary Cirrhosis Study.
Introduction Discriminant analysis using a MLMM with a normal mixture 143 The Dutch Multicenter Primary Biliary Cirrhosis (PBC) Study is a prospective cohort study of patients with PBC with participation of 7 university hospitals and 39 general hospitals. Recruitment of patients started in January 1990 and follow-up data until April 2007 were available for analysis. Follow-up data were collected at approximately 3-monthly intervals in the first year and yearly intervals thereafter. In total, 375 patients were recruited with a median follow-up of 9.7 years. See Kuiper et al. 1 for details of the study. It is of clinical interest to predict the future patients’ status. In this paper, we are interested in predicting whether the patient will suffer from a serious disease progression (liver related death or liver transplantation) in the first T = 10 years after the start of treatment by ursodeoxycholic acid (UDCA, 13–15 mg/day/kg of weight). Many factors are known to be related to progression of PBC and hence could be used to establish the prognosis. Here we consider the following three markers whose longitudinal profiles are available: bilirubin, albumin, alkaline phosphatase (AP). A prognostic group (status at T = 10 years) is also known for many patients. Our aim is to use these patients as a training data set, model the dependence of these markers on time and possibly other covariates (e.g., age) and subsequently use the developed models to predict longitudinally the prognostic group of future patients. We now introduce the following notation. Let Y i,r =(Yi,r,1,...,Yi,r,ni,r )′ be a random vector of the r-th marker (r =1,...,R) observed for the i-th patient (i =1,...,N) at time points 0 ≤ ti,r,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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Dynamic prediction of response usin
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Page 110 and 111: 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
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Page 147 and 148: Discriminant analysis using a MLMM
Page 149 and 150: Estimation Discriminant analysis us
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Page 178 and 179: Chapter 4.1 176 ABSTRACT Nucleoside
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Page 182 and 183: Chapter 4.1 180 Table 1. Baseline c
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Page 186 and 187: Chapter 4.1 184 Figure 1. Viral dec
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Page 190 and 191: Chapter 4.1 188 13. Seifer M, Hamat
Page 193 and 194: 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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