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Chapter 2.4 82 prediction is necessary. For the indirect approach (2) two steps are needed: first the longitudinal profiles of the markers are modeled separately for each outcome group using a multivariate linear mixed effect model, whereafter the posterior probability of each response category over time is calculated. This approach was proposed by Brant 9 and further extended by Morrell et al. 10 Below the general concept of the approaches is introduced and the two methods are presented. These are illustrated with data from the HBV9901-study on chronic hepatitis B patients. The performance of the methods are compared and different treatment strategies and stopping rules are designed. Finally the methods are discussed in view of their computational effort, predictive performance and their clinical applicability. DYNAMIC PREDICTION MODELS Let us first introduce some notation: Denote by Y i,j = (Y1,i,j,...,Yr,i,j) a random vector of l continuous markers obtained at visit j for subject i and let y i,j = (y1,i,j,...,yr,i,j) be the corresponding observed values; i =1,...,Nand j =1,...,m, m = maximum number of visits over all subjects. Define by Yi,k = {y i,j, j ≤ k} the history of the observed markers until visit k. The observed visit time for the jth visit for the ith subject is given by ti,j. Let Ri be the binary outcome variable for subject i, in this paper consider Ri as the response to therapy (0=no response/ 1=response). For individual i define with pi,j,0≤ pi,j ≤ 1, the probability of Ri =1 at ti,j. Especially let p0 be the overall baseline probability of response, Ri =1. Our interest is to estimate pi,j based on the longitudinal history of the observed markers Yi,j . For the covariates measured at baseline (visit 0), let Xi be the corresponding design matrix for subject i. Cross sectional prediction Consider the most simple situation of only one visit and one binary covariate Y (0 or 1) measured per subject. The direct approach to analyse the prediction of response, R =1givenY = y is with a logistic regression model logit Pr(R =1| Y = y) =α + βy.
For the indirect approach we rewrite Pr(R =1| Y = y) as Pr(R =1| Y = y) = Dynamic prediction of response using longitudinal profi les 83 pSE pSE+(1− p)(1− SP) using Bayes’ theorem. Here p = Pr(R = 1) is the overall fraction of responders (the ’prior probability’) and Pr(Y =1| R = 1) is the behavior of Y in the group of responders, i.e. the sensitivity (SE) of Y and Pr(Y =1| R =0)isthe behavior of Y in the group of non-responders, corresponding to 1-specificity (1- SP). Bayes’ theorem then states that the left hand side is the ’posterior probability’ of response given Y = y. In this simple situation the direct and the indirect methods are similar and α = log ((1 − SE)/SP ) + log (p/(1 − p)) and β = log (SE · SP/((1 − SE)(1 − SP))). Suppose Y is continuous, then the indirect approach is written Pr(R =1| Y = y) = p f1(y) p f1(y)+(1− p) f0(y) where f1(y) represents the probability density function of Y at the point y in the presence of response (R=1), and f0(y) the probability density function of Y at y in the absence of response (R=0), illustrated in Figure 1a. The direct method and the indirect method are the same when Y is normal distributed in both populations of responders and non-responders with mean μ1 and μ0, respectively, and common variance σ2 . In this case α = − μ2 1−μ2 0 2σ2 and β = μ1−μ0 σ2 . Both methods are easily generalized to handle a multivariate normal vector Y of covariates with common covariance matrix for the responders and non-responders. For the indirect approach the requirement of a common covariance matrix for responders and non-responders is ignored in the longitudinal prediction. In the following the two approaches are extended to handle repeated measurements of Y over time. Longitudinal prediction with the direct approach The observed makers as predictors Suppose a baseline prediction at t=0 exist and at visit j the markers Y i,j are observed. A simple update of the baseline prediction model is to extend the prediction at t=0, pi,0 with the new information observed at visit j, as suggested by Steyerberg(chapter 20), 11 i.e.
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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
Page 34 and 35: Chapter 2.1 32 HBV DNA decline The
Page 36 and 37: Chapter 2.1 34 Figure 2 continued.
Page 38 and 39: 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: INTRODUCTION Dynamic prediction of
Page 87 and 88: logit pi,j = logit Pr(Ri =1|visit =
Page 89 and 90: Dynamic prediction of response usin
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
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Table 2. Time dependent Cox regress
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Glycyrrhizin for IFN-non responders
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Glycyrrhizin for IFN-non responders
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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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