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Chapter 2.4 84 a. b. c. Figure 1.The distribution of a marker at a. visit 1 and b. visit 2 by response and the bivariate distribution of the marker c. overall and d. by response. For the subject highlighted by * the marker lies as an outlier at visit 1 but not at visit 2, and stays an outlier in the bivariate distribution in c. as well as in d. logit pi,j = logit Pr(Ri =1| visit = j, y i,j,pi,0) = αj + βjy i,j + PIi,0, where PIi,0 = logitpi,0 the baseline log odds of response is used as offset. This results in j =1,...,m (the number of follow-up visits) logistic regression models with each an update of the baseline prediction. Alternatively we suggest to combine these models in a GEE manner: a pooled logistic regression analysis treating each visit as an observation and in the analysis correct for the fact that a patient is present with more visits. This idea is borrowed from Hernan and Robins, 12 who used it in their set up of the Marginal Structural Mean Model. With the inclusion of the visit time as an explanatory variable and an interaction term with the markers to estimate changes in effect of the markers over time the full GEE model, with an independent working correlation matrix, is written: d.
logit pi,j = logit Pr(Ri =1|visit = j, y i,j,pi,0) Dynamic prediction of response using longitudinal profi les 85 = α + βT ti,j + βY y i,j + βY,Ty i,jti,j + PIi,0 where αj = α + βT ti,j and βj = βY y i,j + βY,Ty i,jti,j. If the effect of the markers does not change significantly over time the interaction terms may be dropped and the model simplifies to: logit pi,j = logit Pr(Ri =1|visit = j, y i,j + pi,0) = α + βY y i,j + βT ti,j + PIi,0 Here time ti,j is entered as a linear term, alternatively a smooth function of time can be used. The model can further be defined to include baseline covariates Xi, the history of markers Yi,k or include interactions over time with baseline covariates. Also changes of effect of baseline variables over time and even changes of effect of markers by baseline variables as well as covariates measured during the visits could be studied. In case of irregular time intervals between visits it is advisable to extend the model with the distance between visits to study this effect on the outcome. The model results in a set of new updated predictions depending on visit j and measurement Yi,j. The patterns of the makers as predictors Above the observed values of the markers were included directly as predictors of Ri = 1. Instead the behavior of the markers over time, for example the increase or decrease over time or some other summary measures, may be better predictors of the clinical outcome. Maruyama et al. 8 applied this idea to data on smoking cessation. We shall adapt their method in a dynamic way. Suppose the markers are observed until time T then the model is fitted in two steps. First a multivariate linear mixed model is fitted to the markers Y i =(Yi,1,...,Y i,m) observed in the interval [0, T], i.e. ti,m
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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
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 and 84: INTRODUCTION Dynamic prediction of
Page 85: For the indirect approach we rewrit
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
Page 135 and 136: 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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