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Springer Series in Pharmaceutical Statistics
Jozef Nauta
Statistics in
Clinical and
Observational
Vaccine Studies
Second Edition
Series Editors
Thomas Permutt, Walnut Creek, CA, USA
José Pinheiro, Raritan, NJ, USA
Frank Bretz, Basel, Switzerland
Peter Müller, Austin, TX, USA
Recent advances in statistics have led to new concepts and solutions in different areas
of pharmaceutical research and development. “Springer Series in Pharmaceutical
Statistics” focuses on developments in pharmaceutical statistics and their practical
applications in the industry. The main target groups are researchers in the
pharmaceutical industry, regulatory agencies and members of the academic
community working in the field of pharmaceutical statistics. In order to encourage
exchanges between experts in the pharma industry working on the same problems
from different perspectives, an additional goal of the series is to provide reference
material for non-statisticians. The volumes will include the results of recent research
conducted by the authors and adhere to high scholarly standards. Volumes focusing
on software implementation (e.g. in SAS or R) are especially welcome. The book
series covers different aspects of pharmaceutical research, such as drug discovery,
development and production.
More information about this series at http://www.springer.com/series/15122

Jozef Nauta
Statistics in Clinical
and Observational Vaccine
Studies
Second Edition
123
Jozef Nauta
Amsterdam, The Netherlands
ISSN 2366-8695 ISSN 2366-8709 (electronic)

ISBN 978-3-030-37692-5 ISBN 978-3-030-37693-2 (eBook)
https://doi.org/10.1007/978-3-030-37693-2
The output/code/data analysis for this book was generated using SAS software. Copyright ©SAS 2012
SAS Institute Inc. SAS and all other SAS Institute Inc. product or service names are registered
trademarks or trademarks of SAS Institute Inc., Cary, NC, USA.
For copies of the SAS codes, please write an e-mail to jozef.nauta@gmail.com.
1st edition: © Springer-Verlag Berlin Heidelberg 2011

2nd edition: © Springer Nature Switzerland AG 2020
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part
of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
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The use of general descriptive names, registered names, trademarks, service marks, etc. in this
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The publisher, the authors and the editors are safe to assume that the advice and information in this
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authors or the editors give a warranty, expressed or implied, with respect to the material contained
herein or for any errors or omissions that may have been made. The publisher remains neutral with regard
to jurisdictional claims in published maps and institutional affiliations.
This Springer imprint is published by the registered company Springer Nature Switzerland AG
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
It was about the beginning of September,
1664, that I, among the rest of my
neighbours, heard in ordinary discourse that
the plague was returned again in Holland; for
it had been very violent there, and particularly
at Amsterdam and Rotterdam, in the year
1663, whither, they say, it was brought
(some said from Italy, others from the Levant)
among some goods which were brought home
by their Turkey fleet; others said it was
brought from Candia; others, from Cyprus.
It mattered not from whence it came; but all
agreed it was come into Holland again.
Daniel Defoe
A Journal of the Plague Year (1722)
Preface
In the ten years between the publication of the first edition of this book and that of
this second edition, the world witnessed two major virus outbreaks. The first was
the West African Ebola outbreak, the most widest outbreak of Ebola virus disease
in history. At the time of the outbreak, no vaccine was available. A large vaccine
efficacy study with an experimental Ebola vaccine involving 11,841 people was
conducted in Guinea during 2015 [1]. The vaccine was highly protective. Among
the 5,837 participants who received the vaccine, no Ebola cases occurred. In
comparison, among the 6,004 participants who had not received the vaccine 23
cases occurred. The second outbreak was that of the Zika virus in South America,
around the time of the 2016 Olympic Summer Games in Brazil. The United States
National Institute of Allergy and Infectious Diseases is developing multiple vaccine
candidates to prevent Zika virus infection. Vaccine research and development
continues to play a major role in greatly reducing disease, disability and death
worldwide.
This book is intended for statisticians working in clinical vaccine development
in the pharmaceutical industry, at universities, at national vaccines institutes, etc.
Statisticians already involved in clinical or observational vaccine studies may find
some interesting new ideas in it, while colleagues who are new to vaccine devel-
opment or vaccine epidemiology will be able to familiarize themselves quickly with
the statistical methodology.
A good knowledge of statistics is assumed. The reader should be familiar with
hypothesis testing, point and confidence interval estimation, likelihood methods,
bootstrapping, etc. Nonetheless, the scope of the book is practical rather than
theoretical. Many real-life examples are given, and SAS codes are provided,
making application of the methods straightforward.
The book is divided into five parts. Part I comprises two chapters that should be
read in tandem, and which will provide the reader with the necessary background
knowledge of the fundamentals of vaccination and the working of the immune
system. Part II is dedicated to the analysis of immunogenicity data. New to this
second edition are the four chapters in Part III on vaccine field studies, i.e. vaccine
efficacy and vaccine effectiveness studies. The first chapter, Chap. 7, serves as an
vii
viii Preface
introduction to vaccine field studies. In Chap. 8, the analysis of vaccine efficacy data
and the assumptions underlying the different analyses are discussed. In Chap. 9,
observational vaccine studies are explored. (Hence the change of the title of the
book.) The meta-analysis of vaccine effectiveness studies is the topic of Chap. 10.
Part IV addresses correlates of protection, immunological assays that predict pro-
tection against infection. In Part V, the analysis of vaccine safety data is discussed.
Also new are Appendices E–I. In Appendix E, a proof of the ‘exponential
formula’ is presented, the formula that links the occurrence measures risk of
infection and force of infection. In Appendix F, it is shown that although a force of
infection function and a hazard function are conceptually different, they take the
same functional form and that in this sense they are synonyms. In Appendix G, it is
explained how a confidence interval for the difference of two vaccine effectiveness
estimates can be obtained by means of bootstrapping. Appendix H contains a SAS
code for the creation of the data of the examples of Chap. 8. In Appendix I, some
more SAS codes are presented, including a code for Barnard’s exact test for rate
ratios and a code for a bootstrap approach to compare two risk estimates based on
the popular Nelson–Aalen estimator.
Several changes were made to the existing chapters. Chapter 11 on correlates of
protection has been thoroughly revised. Several examples were rewritten. Last but
not least, the notation and the terminology has been improved.
April 2018 Jozef Nauta

Museo Galileo, Florence, Italy
Acknowledgement
I would like to acknowledge my colleague and good friend Dr. Walter Beyer of the
Department of Virology, Erasmus Medical Centre, Rotterdam, the Netherlands, for
his generous advice on Chaps. 1, 2 and 10, and the many inspiring discussions we
had while working on our joint publications.
Jozef Nauta
ix
Contents
Part I The Interplay Between Microorganisms and the Immune

System
1 Basic Concepts of Vaccine Immunology . . . . . . . . . . . . . . . . . . . . . 3
1.1 Vaccination and Preventing Infectious Diseases . . . . . . . . . . . . 3
1.2 Microorganisms: Bacteria, Yeasts, Protozoa and Viruses . . . . . . 4
1.3 The Immune System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.2 Microbial Clearance . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.3 Active and Passive Protection from Infectious
Diseases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.4 Antigenic Variation . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Vaccines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4.1 Viral and Bacterial Vaccines Currently in Use . . . . . . . 9
1.4.2 Routes of Administration . . . . . . . . . . . . . . . . . . . . . . 11
1.4.3 Leaky Vaccines Versus All-or-Nothing Vaccines . . . . . 12
1.4.4 Malaria Vaccines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4.5 Experimental Prophylactic and Therapeutic
Vaccines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..... 13
2 Humoral and Cellular Immunity . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Humoral Immunity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.1 Antibody Titres and Antibody Concentrations . . . . . . . 16
2.1.2 Two Assays for Humoral Immunity . . . . . . . . . . . . . . . 16
2.2 Cellular Immunity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Part II Analysis of Immunogenicity Data

3 Standard Statistical Methods for Immunogenicity Data . . . . . . . . . 23
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Geometric Mean Titres and Concentrations . . . . . . . . . . . . . . . 24
xi
xii Contents
3.2.1 Single Vaccine Group . . . . . . . . . . . . . . . . . . . . . .... 27

3.2.2 Two Vaccine Groups . . . . . . . . . . . . . . . . . . . . . .... 27
3.3 Geometric Mean Fold Increase . . . . . . . . . . . . . . . . . . . . .... 28
3.3.1 Analysis of a Single Geometric Mean Fold
Increase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... 29
3.3.2 Analysis of Two Geometric Mean Fold Increases . .... 29
3.3.3 A Misconception About Fold Increases
and Baseline Imbalance . . . . . . . . . . . . . . . . . . . . . . . 31
3.4 Two Seroresponse Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4.1 Seroprotection Rate . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4.2 Seroconversion Rate . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5 Analysis of Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5.1 Analysis of a Single Rate . . . . . . . . . . . . . . . . . . . . . . 34
3.5.2 Comparing Two Rates . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5.3 Barnard’s Exact Test for Comparing Two Rates . . . . . . 41
3.6 Multiplicity in Immunogenicity Trials and the
Intersection-Union Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.7 The Reverse Cumulative Distribution Plot . . . . . . . . . . . . . . . . 44
3.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.9 Sample Size Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.9.1 Comparing Two Geometric Mean . . . . . . . . . . . . . . . . 46
3.9.2 Comparing Two Rates . . . . . . . . . . . . . . . . . . . . . . . . 47
3.9.3 Sample Size Estimation for Trials with Multiple
Co-primary Endpoints . . . . . . . . . . . . . . . . . . . . . .... 48
4 Antibody Titres and Two Types of Bias . . . . . . . . . . . . . . ....... 51
4.1 Standard Antibody Titres Versus Mid-Value Titres . . . ....... 51
4.2 Censored Antibody Titres and Maximum Likelihood
Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....... 53
4.2.1 ML Estimation for Censored Normal Data . . . ....... 54
4.2.2 ML Estimation for Censored Antibody Titres . ....... 56
5 Adjusting for Imbalance in Pre-Vaccination State . . . . . . . . . . . . . 61
5.1 Imbalance in Pre-Vaccination State . . . . . . . . . . . . . . . . . . . . . 61
5.2 Adjusting for Baseline Imbalance . . . . . . . . . . . . . . . . . . . . . . 63
5.3 Analysis of Covariance for Antibody Values . . . . . . . . . . . . . . 63
5.3.1 A Solution to the Problem of Heteroscedasticity . . . . . 64
5.3.2 Fitting the Variance Model for Heteroscedasticity . . . . 65
5.3.3 ANCOVA for Comparative Clinical
Vaccine Trials . . . . . . . . . . . . . . . . . . . . . . . . . . .... 66
6 Vaccine Equivalence and Non-inferiority Trials . . . . . . . . . . . . . . . 71
6.1 Equivalence and Non-inferiority . . . . . . . . . . . . . . . . . . . . . . . 71
6.2 Equivalence and Non-inferiority Testing . . . . . . . . . . . . . . . . . . 72
Contents xiii
6.2.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.2.2 Normal Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.2.3 The Confidence Interval Approach . . . . . . . . . . . . . . . 75
6.3 Geometric Mean Response as Outcome . . . . . . . . . . . . . . . . . . 75
6.4 Seroresponse Rate as Outcome . . . . . . . . . . . . . . . . . . . . . . . . 77
6.5 Vaccine Lot Consistency Trials . . . . . . . . . . . . . . . . . . . . . . . . 79
6.5.1 The Confidence Interval Method . . . . . . . . . . . . . . . . . 79
6.5.2 The Wiens–Iglewicz Test . . . . . . . . . . . . . . . . . . . . . . 80
6.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.7.1 Comparing Two Geometric Mean Responses . . . . . . . . 84
6.7.2 Comparing Two Seroresponse Rates . . . . . . . . . . . . . . 86
6.7.3 Lot Consistency Trials . . . . . . . . . . . . . . . . . . . . . . . . 87
Part III Vaccine Field Studies

7 Vaccine Field Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.1 Protective Vaccine Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.2 Vaccine Efficacy and Vaccine Effectiveness Studies . . . . . . . . . 93
7.3 Definition of Vaccine Efficacy and Vaccine Effectiveness . . . . . 94
7.4 Source Populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.4.1 Cohorts Versus Dynamic Populations . . . . . . . . . . . . . 95
7.4.2 Cohorts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.4.3 Dynamic Populations . . . . . . . . . . . . . . . . . . . . . . . . . 96
7.5 Surveillance Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.6 Risk of Infection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.7 Person-Time at Risk and Population-Time at Risk . . . . . . . . . . 98
7.8 Infection Occurrence Measures . . . . . . . . . . . . . . . . . . . . . . . . 98
7.8.1 Attack Rate and Force of Infection . . . . . . . . . . . . . . . 98
7.8.2 Link Between the Risk of Infection
and the Force of Infection . . . . . . . . . . . . . . . . . ..... 99
7.8.3 Recapitulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.8.4 When the Relative Risk of Infection Cannot
be Estimated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.9 Four Simulated Cohort Studies . . . . . . . . . . . . . . . . . . . . . . . . 102
7.10 Impact of the Diagnostic Test on the Vaccine Efficacy
or Effectiveness Estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.11 Specific and Non-specific Endpoints . . . . . . . . . . . . . . . . . . . . 107
8 Vaccine Efficacy Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8.1 Comparing Attack Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8.2 Comparing Person-Time Data . . . . . . . . . . . . . . . . . . . . . . . . . 115
8.2.1 An Exact Conditional Test . . . . . . . . . . . . . . . . . . . . . 115
8.2.2 Poisson Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
xiv Contents
8.2.3 Cox Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

8.2.4 Comparing Two Nelson–Aalen Risk of Infection
Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8.3 Recurrent Infections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
8.3.1 Average Number of Episodes Experienced
by a Subject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
8.4.1 Studies Comparing Two Attack Rates . . . . . . . . . . . . . 126
8.4.2 Studies Comparing Two Infection Incidence Rates . . . . 126
8.4.3 Studies Comparing Two Forces of Infection . . . . . . . . 127
9 Vaccine Effectiveness Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
9.1 Confounding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
9.1.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
9.1.2 Eliminating Confounding . . . . . . . . . . . . . . . . . . . . . . 131
9.1.3 Some Known or Potential Confounders . . . . . . . . . . . . 132
9.1.4 Confounding Versus Effect Modification . . . . . . . . . . . 133
9.2 Case-Referent Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
9.2.1 Key Idea of Case-Referent Designs . . . . . . . . . . . . . . . 133
9.2.2 Major Case-Referent Designs . . . . . . . . . . . . . . . . . . . 135
9.2.3 The Test-Negative Design . . . . . . . . . . . . . . . . . . . . . . 137
9.3 The Odds Ratio and Its Prominent Role in Case-Referent
Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
9.4 Crude Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
9.4.1 Crude Vaccine Effectiveness . . . . . . . . . . . . . . . . . . . . 139
9.4.2 Cohort Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
9.4.3 Case-Control Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
9.4.4 Case-Cohort Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
9.5 Adjusted Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
9.5.1 Stratification to Adjust for Confounding . . . . . . . . . . . 143
9.5.2 Stratification to Adjust for Confounding
by Calendar Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
9.5.3 Regression to Adjust for Confounding . . . . . . . . . . . . . 146
9.5.4 Representation of Confounder Data . . . . . . . . . . . . . . . 148
9.6 Selecting Confounders in the Regression Model . . . . . . . . . . . . 148
9.7 Propensity Score Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
10 Meta-Analysis of Vaccine Effectiveness Studies . . . . . . . . . . . . . . . . 151
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
10.2 Non-comparative Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
10.3 Comparative Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
10.4 Meta-Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Contents xv
Part IV Correlates of Protection

11 Immune Correlates of Protection . . . . . . . . . . . . . . . . . . . . . . . . . . 163
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
11.2 Terminology for Correlates of Protection . . . . . . . . . . . . . . . . . 164
11.3 The Protection Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
11.4 Estimating the Protection Curve . . . . . . . . . . . . . . . . . . . . . . . . 165
11.4.1 Estimating the Protection Curve from Challenge
Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
11.4.2 Estimating a Protection Curve from Vaccine
Efficacy Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
11.4.3 Predicting Vaccine Efficacy . . . . . . . . . . . . . . . . . . . . . 170
11.5 Threshold of Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
11.6 Correlates of Protection and Time . . . . . . . . . . . . . . . . . . . . . . 172
11.7 Generalizability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Part V Analysis of Vaccine Safety Data

12 Vaccine Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
12.1 Ensuring Vaccine Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
12.2 Vaccine Safety Surveillance . . . . . . . . . . . . . . . . . . . . . . . . . . 178
12.3 Safety Data and the Problem of Multiplicity . . . . . . . . . . . . . . . 180
12.4 Vaccine Reactogenicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Appendix A: SAS and Floating-Point Format

for Calculated Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Appendix B: Closed-Form Solutions for the Constrained ML
~ 0 and R
Estimators R ~ 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Appendix C: Proof of Inequality (3.17) . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

Appendix D: A Generalized Worst-Case Sensitivity Analysis
for a Single Seroresponse Rate for Which
the Confidence Interval Must Fall Above
a Pre-specified Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Appendix E: Formula Linking Risk of Infection
and Force of Infection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Appendix F: Force of Infection Versus Hazard,
Two Sides of the Same Coin . . . . . . . . . . . . . . . . . . . . . . . . . 207
Appendix G: Confidence Interval for the Difference of the Medians
of Two Lognormal Distributions . . . . . . . . . . . . . . . . . . . . . 209
xvi Contents
Appendix H: SAS Code to Generate the Data Set COHORTS . . . . . . . . 211

Appendix I: Some More SAS Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
About the Author
Jozef Nauta is a principal statistician, with more than 25 years of experience in the
pharmaceutical industry, and with special interest in the development of influenza
vaccines. During his career, he has published numerous journal articles on statistics
and vaccines. He currently participates in DRIVE (Development of Robust and
Innovative Vaccine Effectiveness), a public–private partnership that advances
European cooperation in influenza vaccine effectiveness studies, and funded by,
amongst others, IMI (Innovative Medicines Initiative). He lives in Amsterdam, The
Netherlands, together with his wife and son.
xvii
Acronyms
AAP American Academy of Pediatrics

AIDS Acquired immune deficiency syndrome
ANCOVA Analysis of covariance
AOM Acute otitis media
ARI Acute respiratory illness
BCG Bacillus Calmette–Guérin
CBER Center for Biologics Evaluation and Research
CDC Centers for Disease Control and Prevention
CF Cystic fibrosis
CGD Chronic granulomatous disease
CL Confidence limit
CLRS Constrained likelihood ratio statistic
CMI Cell-mediated immunity
CoP Correlate of protection
CTL Cytotoxic T lymphocyte
DAG Directed acyclic graph
DNA Deoxyribonucleic acid
DTP Diphtheria, tetanus, pertussis
EIA Enzyme immunoassay
ELISA Enzyme-linked immunosorbent assay
ELISPOT Enzyme-linked immunospot
EMA European Medicines Agency
EPPT Events-per-person-time
FDA United States Food and Drug Administration
FDR False discovery rate
FWER Family-wise error rate
GBS Guillain Barré syndrome
GM Geometric mean
GP Glycoprotein-based; General practitioner
HA Haemagglutinin
xix
xx Acronyms
HAI Haemagglutination inhibition

HI Haemagglutination inhibition
Hib Haemophilus influenzae type b
HIV Human immunodeficiency virus
HPV Human papillomavirus
ICH International Conference on Harmonisation of Technical
Requirements for Registration of Pharmaceuticals for Human Use
IFN-c Interferon-gamma
i.i.d. Independent and identically distributed
IL Interleukin
ILI Influenza-like illness
IM Immune marker
IU Intersection-union
LL Log-likelihood
LRS Likelihood ratio statistic
mCoP Mechanistic correlate of protection
MedDRA Medical Dictionary for Regulatory Activities
ML Maximum likelihood
MMR Measles, mumps, rubella
MMRV Measles, mumps, rubella, varicella
nCoP Non-mechanistic correlate of protection
NRA National Registration Authority (Australia)
NIH National Institutes of Health
NK Natural killer
NMPA National Medical Products Administration (China)
OPSR Organization for Pharmaceutical Safety and Research (Japan)
PCR Polymerase chain reaction
PBMC Peripheral blood mononuclear cells
RCD Reverse cumulative distribution
RNA Ribonucleic acid
SBA Serum bactericidal assay
SD Standard deviation
SIDS Sudden infant death syndrome
SPC Spot-forming cell
TH1 T helper 1
TH2 T helper 2
TND Test-negative design
TOST Two one-sided tests
UTI Urinary tract infection
V Varicella
VAERS Vaccine Adverse Event Reporting System
VLP Virus-like particles
Notation and Terminology
In this book, population parameters and parameters of distributions are notated by

Greek symbols, estimators and estimates of parameters by (combinations of) italic
capitals. Random variables are notated as bold capitals.
l Mean of a normal (Gaussian) distribution

r Standard deviation of a normal distribution
D ð¼ l1 l0 Þ Difference of two normal means
el Median of a log-normal distribution
h ð¼ el1 =el0 Þ Ratio of the medians of two log-normal distributions
bi Coefficient of a regression model
p Risk
D ð¼ p1 p0 Þ Risk difference
h ð¼ p1 =p0 Þ Relative risk
k Force of infection
k ðt Þ Force of infection function
K ðt Þ Cumulative force of infection function
/ ð¼ k1 =k0 Þ Relative force of infection
0 ð ¼ 1 hÞ Vaccine efficacy; vaccine effectiveness
0/ ð¼ 1 /Þ Vaccine efficacy (approximation); vaccine effectiveness
(approximation)
GMC Geometric mean concentration, estimator/estimate (est.) of the
median concentration
GMFR Geometric mean fold ratio, est. of the ratio of two median fold
increases
GMR Geometric mean ratio, est. of the ratio of two median titres
GMT Geometric mean titre, est. of a median titre
GSD Geometric standard deviation, antilog of the sample standard
deviation of a set of log-transformed immunogenicity values
Bi Estimate of a regression coefficient
R Rate, est. of a risk
xxi
xxii Notation and Terminology
RD Rate difference, est. of a risk difference

RR Rate ratio, est. of a relative risk
RRE Relative risk estimate in a meta-analysis of vaccine effectiveness
estimates
IR Incidence rate, est. of homogeneous force of infection
IRR Incidence rate ratio, est. of a relative force of infection
OR Odds ratio, est. of a relative risk of infection or a relative force of
infection
HR Hazard rate, est. of a hazard ratio
VE Est. of the vaccine efficacy or the vaccine effectiveness
SDð::Þ Sample standard deviation
SE ð::Þ Standard error of an estimator, either asymptotic or exact
LCL Lower confidence limit
UCL Upper confidence limit
M Equivalence/non-inferiority margin
For estimators and estimates, the same notation is used. An estimator is a function,
for example:
c1 =T1
IRR ¼ :
c0 =T0
When the function is applied, an estimate of a parameter is obtained, for example:
IRR ¼ 0:328:
Occasionally, estimators and estimates are notated by a ‘hooded’ parameter: l ^, ^

h,
etc.
The term rate is usually reserved for estimators of the form number of cases per
unit of time. In this book, the term is used in what may be called the proportion
sense, for estimators of the form proportion of cases that occurred in a fixed group
of individuals. The justification is that in clinical vaccine trials, there are a number
of standard concepts that, although proportions, are called rates: seroprotection rate,
seroconversion rate and attack rate. For estimators of the form cases per unit of
time, the term incidence rate is used.
Part I
The Interplay Between Microorganisms
and the Immune System
Chapter 1
Basic Concepts of Vaccine Immunology
Abstract The first two chapters of this book are intended to provide the reader
with the necessary background knowledge of the fundamentals of vaccination. This
chapter opens with an overview of the major infectious microorganisms. Next, the
working of the immune system is explained, how it can ward off microorganisms it has
encountered before. The primary defence mechanism of microorganisms—antigenic
variation—is examined. An overview of the several types of vaccines for viruses
and bacteria, from the first-generation live attenuated vaccines to third-generation
vaccines such as recombinant vector vaccines, DNA vaccines and virus-like particles
vaccines is given.
1.1 Vaccination and Preventing Infectious Diseases
Vaccines take advantage of the body’s ability to learn how to ward off microorgan-
isms. The immune system can recognize and fight of quickly infectious organisms
it has encountered before. As an example, consider chickenpox. Chickenpox is a
highly contagious infectious disease caused by the varicella-zoster virus. First, there
are papules, pink or red bumps. These bumps turn into vesicles, fluid-filled blisters.
Finally, the vesicles crust over and scab. Clinical symptoms are fever, abdominal pain
or loss of appetite, headache, malaise and dry cough. The disease is so contagious
that most people get it during their childhood, but those infected are the rest of their
life immune to it. Vaccines contain killed or inactivated (parts of) microorganisms.
These provoke the immune system in a way that closely mimics the natural immune
response to the microorganisms. Vaccination is a less risky way to become immune,
because, due to the killing or inactivation of the microorganisms, it does not cause
the disease.
Vaccination, together with hygiene, is considered to be the most effective method
of preventing infectious diseases. When not prevented, some infectious diseases
have proven to be mass killers. Plague, caused by the bacterium Yersinia pestis, has
been one of the deadliest pandemics in history. The total number of plague deaths
worldwide has been estimated at 75 million people, and the disease is thought to
have killed almost half of Europe’s population. The pandemic arrived in Europe in
© Springer Nature Switzerland AG 2020 3
J. Nauta, Statistics in Clinical and Observational Vaccine Studies,
Springer Series in Pharmaceutical Statistics,
https://doi.org/10.1007/978-3-030-37693-2_1
4 1 Basic Concepts of Vaccine Immunology
the fourteenth century, and it would cast its shadow on the continent for five centuries,
with one of the last big outbreaks occurring in Moscow in 1771. (The reader who
wants to learn how it was to be trapped in a plague-stricken community should read
Giovanni Boccaccio’s Il Decameron (1353), Daniel Defoe’s A Journal of the Plague
Year (1722) or Albert Camus’ La Peste (1947).)
The global death toll from the Spanish influenza pandemic (1918–1920), caused
by an influenza virus, is assumed to have been 50 to 100 million people, more than
the combined total casualties of World Wars I and II.
Malaria is a potentially deadly tropical disease transmitted by a female mosquito
when it feeds on blood for her eggs. In Africa, an estimated 2,000 children a day
die from the disease, leading in 2006 to a total number of deaths from the disease
of almost one million. The Bill and Melinda Gates Foundation is funding efforts to
reduce malaria deaths, by developing more effective vaccines. The long-term goal
of the foundation is to eradicate the disease.
1.2 Microorganisms: Bacteria, Yeasts, Protozoa and

Viruses
Microorganisms (also microbes) are live forms that cannot be seen by the unaided
eye, but only by using a light or an electron microscope. The Dutch scientist Anton
van Leeuwenhoek (1632–1723) was the first to look at microorganisms through
his microscope. Microorganisms that cause disease in a host organism are called
pathogens. If a microorganism forms a symbiotic relationship with a host organism
of a different species and benefits at the expense of that host, it is called a parasite.
Bacteria are unicellular organisms surrounded by a cell wall and typically 1–5 µm
in length. They have different shapes such as rods, spheres and spirals, and reproduce
asexually by simple cell division. The biological branch concerned with the study of
bacteria is called bacteriology. Examples of serious bacterial diseases are diphtheria,
tetanus, pertussis, cholera, pneumococcal disease, tuberculosis, leprosy and syphilis.
Yeasts are unicellular organisms typically larger than bacteria and measuring
around 5 µm. Most reproduce asexually, but some also show sexual reproduction
under certain conditions. Yeasts are studied within the branch of mycology. Diseases
caused by yeasts are, among others, thrush and cryptococcosis.
Protozoa are unicellular organisms, more complex and larger than bacteria and
yeasts, typically between 10 and 50 µm in diameter. They usually are hermaphroditic
and can reproduce both sexually and asexually. Protozoa are responsible for wide-
spread tropical diseases such as malaria, amoebiasis, sleeping sickness and leishma-
niasis. The biological branch of parasitology includes the study of protozoa and
of certain multicellular organisms such as Schistosoma and helminths (parasitic
worms).
In contrast with bacteria, yeasts and protozoa, which are cellular live forms, viruses
are too small to form cells (typically 0.05–0.20 µm in diameter). In the environment,
1.2 Microorganisms: Bacteria, Yeasts, Protozoa and Viruses 5
they show no metabolism. For replication, a virus needs to intrude a host cell and take
over the cell metabolism to produce and release new virus particles. Viruses con-
tain either DNA or RNA as genetic material. DNA viruses include herpes-, adeno-,
papova-, hepadna- and poxviruses. RNA viruses include rhino-, polio-, influenza-
and rhabdoviruses. Some RNA viruses have an enzyme called reverse transcriptase
that allows their viral RNA to be copied as a DNA version (retroviruses). Well-known
viral diseases are herpes, hepatitis B and smallpox (DNA viruses), common cold,
poliomyelitis, hepatitis A, influenza, rabies (RNA viruses) and human immunodefi-
ciency virus (HIV) (RNA retroviruses). The study of viruses is called virology.
1.3 The Immune System
1.3.1 Basics
The immune system can distinguish between non-foreign and foreign (also self and
non-self) molecules and structures. With this ability, it seeks to protect the organism
from invading pathogens—by detecting and killing them. The immune system has
two essential components, the innate (inborn) or non-specific and the adaptive or
specific immune system.
The innate immune system provides an immediate, albeit non-specific, response
to invading pathogens. It is triggered by cells and molecules that recognize certain
molecular structures of microorganisms, and it tries to inhibit or control their repli-
cation and spread. In vertebrates, one of the first responses of the innate immunity
to infection is inflammation, initiated by infected and injured cells that, in response,
release certain molecules (histamine, prostaglandins and others). These molecules
sensitize pain receptors, widen local blood vessels and attract certain white blood
cells (neutrophils) circulating in the bloodstream and capable to kill pathogens
by ingestion (phagocytosis) as a front-line defence. Neutrophils can release even
more signalling molecules such as chemokines and cytokines (among many oth-
ers: interferon-γ ) to recruit other immune cells, including macrophages and natural
killer cells. Macrophages reside in tissue and also ingest and destroy pathogens.
Natural killer (NK) cells can detect infected cells (and some tumour cells) and
destroy them by a mechanism which is known as apoptosis, cell death characterized
by protein and DNA degradation and disintegration of the cell. The innate immune
system responds to microorganisms in a general way during the early phase of the
infection, and it does not confer long-lasting immunity. In vertebrates, the innate
immune system actives the adaptive immune system in case pathogens successfully
evade this first line of defence.
The adaptive immune system has the remarkable ability to improve the recognition
of a pathogen, to tailor a response specific to the actual structure of that pathogen,
and to memorize that response as preparation for future challenges with the same
or a closely similar pathogen. The adaptive immune system activates bone marrow-
derived (B cells) and thymus-derived cells (T cells), leading to humoral and cellular
immunity, respectively (see also Chap. 2). In general, B cells make antibodies that
attack the pathogens directly, while T cells attack body cells that have been infected
by microorganisms or have become cancerous. When activated, B cells secrete anti-
bodies in response to antigens (from antibody-generating), molecules recognized as
non-self. An antigen can be a part of a microorganism, a cancerous structure or a
bacterial toxin. The antibodies that are produced are specific to that given antigen.
The major role of antibodies is either to mark the invaders for destruction (which,
in turn, is effected by other immune cells) or to inactivate (neutralize) them so that
they can no longer replicate.
Like B cells, T cells have surface receptors for antigens. T cells can specialize
to one of several functions: They may help B cells to secrete antibodies (T helper
cells), attract and activate macrophages, or destroy infected cells directly (cytotoxic
T cells, also T killer cells). This improved response is retained after the pathogen has
been killed (immunological memory). It allows the immune system to react faster
the next time the pathogen invades the body. This ability is maintained by memory
cells which remember specific features of the pathogen encountered and can mount
a strong response if that pathogen is detected again.
In vertebrates, the immune system is a complex of organs, tissues and cells con-
nected by two separate circulatory systems, the bloodstream and the lymphatic system
that transports a watery clear fluid called lymph.
In the red bone marrow, a tissue found in the hollow interior of bones, mul-
tipotent stem cells differentiate to either red blood cells (erythrocytes), or platelets
(thrombocytes), or white blood cells (leukocytes). The latter class is immunologically
relevant; leukocytes maturate to either granulocytes (cells with certain granules in
their cytoplasm and a multi-lobed nucleus, for example, the neutrophils mentioned
previously) or mononuclear leukocytes, including macrophages and lymphocytes.
Natural killer cells, B cells and T cells belong to the lymphocytes. T cell progeni-
tors migrate to the thymus gland, located in the upper chest, where they mature to
functional T cells. In the spleen, an organ located in the left abdomen, immune cells
are stored and antibody-coated microorganisms circulating in the bloodstream are
removed. Finally, the lymph nodes store, proliferate and distribute lymphocytes via
the lymphatic vessels.
1.3.2 Microbial Clearance
Virus clearance or elimination of a virus infection involves killing of infected cells

by NK cells and cytotoxic T cells, blocking of cell entry or cell-to-cell transmission
by neutralizing antibodies, and phagocytosis by macrophages.
The major process of bacterial clearance is phagocytosis. Pathogenic bacteria
have three means of defence against it. The first defence is the cell capsule, a layer
outside the cell wall that protects bacteria from contact with macrophages and other
phagocytes (cells that protect the body by ingesting harmful foreign particles and
1.3 The Immune System 7
dead or dying cells). The second defence is the cell wall, which acts as a barrier
to microbicidal activity. The third defence is the secretion of exotoxins, poisonous
substances that damage phagocytes and local tissues and, once circulating in the
bloodstream, remote organs. Frequently, exotoxins (and not the bacteria themselves)
are the cause of serious morbidity of an infected organism. Most cell capsules and
exotoxins are antigenic, meaning that antibodies can block their effects.
Protozoan clearance is exceptionally difficult. Immunity is usually limited to keep-
ing the parasite density down. Malaria clearance, for example, involves phagocytosis
of parasitized red blood cells by macrophages and antibodies. During the brief liver
stage of the malaria parasites, immunity can be induced by cytotoxic T cells.
1.3.3 Active and Passive Protection from Infectious Diseases
The immune system can quickly recognize and fight off infectious organisms it
has encountered before. Measles is a highly contagious infectious childhood dis-
ease caused by the measles virus and transmitted via the respiratory route. Infected
children become immune to it for the rest of their life. This is called naturally
acquired active immunity. Because newborn infants are immunologically naive (no
prior exposure to microorganisms), they would be particularly vulnerable to infec-
tion. Fortunately, during pregnancy, antibodies are passively transferred across the
placenta from mother to foetus (maternal immunity). This type of immunity is called
naturally acquired passive immunity. Depending on the half-life time of these pas-
sively transferred antibodies, maternal immunity is usually short-term, lasting from
a few days up to several months.
1.3.4 Antigenic Variation
While measles does usually not infect an individual twice in lifetime due to natu-
rally acquired active immunity, some other pathogens try to trick the immunological
memory by various mechanisms. One is an adaptation process called antigenic vari-
ation: small alterations of the molecular composition of antigens of the surface of
microorganisms to become immunologically distinct from the original strain. (A
strain is a subset of a species differing from other members of the same species
by some minor but identifiable change.) Antigenic variation can occur either due to
gene mutation, gene recombination or gene switching. Antigenic variation can occur
very slowly or very rapidly. For example, the poliovirus, the measles virus and the
yellow fever virus have not changed significantly since vaccines against them were
first developed, and these vaccines therefore offer lifelong protection. Examples for
rapidly evolving viruses are HIV and the influenza virus. Rapid antigenic variation
is an important cause of vaccine failure.
A serotype is a variant of a microorganism in which the antigenic variations are

to such a degree that it is no longer detected by antibodies directed to other members
of that microorganism. For example, of the bacterium Pseudomonas aeruginosa,
more than sixteen serotypes are known, of the hepatitis B virus four major serotypes
have been identified, and of the rhinovirus, cause of the common cold, there are so
many serotypes (more than 100) that many people suffer from common cold several
times every winter—each time caused by a member of a different serotype. In case
of influenza, antigenic variation is called antigenic drift, which is the process of
mutations in the virus surface proteins haemagglutinin and neuraminidase. This drift
is so rapid that the composition of influenza vaccines must be changed almost every
year. Antigenic drift should not be confused with antigenic shift, the process at which
two different strains of an influenza virus combine to form a new antigenic subtype,
for which the immune system of the host population is naive and which makes it
extremely dangerous because it can lead to pandemic outbreaks.
1.4 Vaccines
The word vaccination (Latin: vacca–cow) was first used by the British physician
Edward Jenner (1749–1823) who searched for a prevention of smallpox, a widespread
disease localized in small blood vessels of the skin, mouth and throat, causing a macu-
lopapular rash and fluid-filled blisters and often resulting in disfigurement, blindness
and death. In 1798, Jenner published his An Inquiry into the Causes and Effects of
the Variolae Vaccinae, a Disease Discovered in Some of the Western Counties of
England, Particularly Gloucestershire, and Known by the Name of the Cow-Pox.
He reported how he, two years earlier, had taken the fluid from a cowpox pustule
on a dairymaid’s hand and inoculated an eight-year-old boy. Six weeks later, he
exposed the boy to smallpox, but the boy did not develop any symptoms of small-
pox disease. Today, the virological background of Jenner’s successful intervention is
understood: smallpox virus, the cause of smallpox, and cowpox virus, the cause of a
mild veterinary disease with only innocent symptoms in men, are quite similar DNA
viruses belonging to the same viral genus orthopoxvirus. Unintendedly, dairymaids
were often exposed to and infected by cowpox virus during milking. Consequently,
they developed immunity which also protected against the smallpox virus (cross-
protection). Previously, this type of immunity was called naturally acquired active
immunity. By intended inoculation with cowpox virus, Jenner had the eight-year-old
boy actually achieve artificially acquired active immunity—the aim of any vaccina-
tion. The year 1996 marked the two hundredth anniversary of Jenner’s experiment.
After large-scale vaccination campaigns throughout the nineteenth and twentieth cen-
tury using vaccinia virus, another member of the same viral genus, the World Health
Organization in 1979 certified the eradication of smallpox. To this day, smallpox is
the only human infectious disease that has been completely eradicated.
Among the pioneers of vaccinology were the French chemist Louis Pasteur
(1822–1895), who developed a vaccine for rabies, and the German Heinrich
1.4 Vaccines 9
Hermann Robert Koch (1843–1910), who isolated Bacillus anthracis, Vibrio

cholerae and Mycobacterium tuberculosis, a discovery for which he in 1905 was
awarded the Nobel Prize in Physiology or Medicine. Koch also developed criteria to
establish, or refute, the causative relationship between a given microorganism and
a given disease (Koch’s postulates). This was, and is, essential for vaccine devel-
opment. First, one has to prove that a given microorganism is really the cause of
a given clinical disease, and then one can include that microorganism in a vaccine
to protect people from that disease. The causative relationship between a microbe
and a disease is not always self-evident. In the first decades of the twentieth century,
it was widely believed that the cause of influenza was the bacterium Haemophilus
influenzae, because it was often isolated during influenza epidemics. Only when
in the 1930s influenza viruses were discovered and proven, by Koch’s postulates,
to be the real cause of influenza, the way was opened to develop effective vaccines
against that disease. A vaccine-containing H. influenzae would not at all protect from
influenza.
Most vaccines contain attenuated (weakened) or inactivated microorganisms. Ide-
ally, they provoke the adaptive immune system in a way that closely mimics the
immune response to the natural pathogenic microorganisms. Vaccination is a less
risky way to become immune, because, due to the attenuation or inactivation of the
microorganisms, a vaccine does not cause the disease associated with the natural
microorganism. Yet, naive B and T cells are activated as if an infection had occurred,
leading to long-lived memory cells, which come into action after eventual exposure
with the natural microorganism.
1.4.1 Viral and Bacterial Vaccines Currently in Use
Live attenuated vaccines contain living viruses or bacteria of which the genetic mate-
rial has been altered so they cannot cause disease. The classical way of attenuation
is achieved by growing the microorganisms over and over again under special lab-
oratory conditions. This passaging process deteriorates the disease-causing ability
of the microorganisms. The weakened viruses and bacteria still can infect the host,
and thus stimulate an immune response, but they can rarely cause disease. However,
in certain immune-compromised patients, even attenuated microorganisms may be
dangerous so that manifest immune-suppression can be a contra-indication for live
vaccines.
An example of a live attenuated vaccine is the RIX4414 human rotavirus vaccine.
Rotavirus infection is the leading cause of potentially fatal dehydrating diarrhoea in
children. The parent strain RIX4414 was isolated from a stool of a 15-month-old child
with rotavirus diarrhoea and attenuated by tissue culture passaging. Other examples
of diseases for which vaccines are produced from live attenuated microorganisms
are the viral diseases measles, rubella and mumps, polio, yellow fever and influenza
(an intranasal vaccine), and the bacterial diseases pertussis (whooping cough) and
tuberculosis. In general, live attenuated vaccines are considered to be very immuno-
genic. To maintain their potency, they require special storage such as refrigerating
and maintaining a cold chain. There is always a remote possibility that the attenuated
bacteria or viruses mutate and become virulent (infectious).
In contrast, inactivated vaccines contain microorganisms whose DNA or RNA was
first inactivated, so that they are ‘dead’ and cannot replicate and cause an infection
anymore. Therefore, these vaccines are also safe in immune-compromised patients.
Inactivation is usually achieved with heat or chemicals, such as formaldehyde or
formalin, or radiation. There are several types of inactivated vaccines.
Whole inactivated vaccines are composed of entire viruses or bacteria. They are
generally quite immunogenic. However, they are often also quite reactogenic (pro-
ducing adverse events), which means that vaccinees may frequently suffer from local
vaccine reactions at the site of vaccination (redness, itching, pain) or even from sys-
temic vaccine reactions such as headache and fever. Fortunately, these reactions are
usually benign, mild and transitory, and only last from hours to a few days. Whole
vaccines have been developed for prophylaxis of, amongst others, pertussis (bacte-
rial), cholera (bacterial) and influenza (viral).
Component vaccines do not contain whole microorganisms but preferably only
those parts which have proven to stimulate the immune response most. The advan-
tage of this approach is that other parts of the microorganism in question, which
do not contribute to a relevant immune response but may cause unwanted vac-
cine reactions, can be removed (vaccine purification). Thus, component vaccines
are usually less reactogenic than whole vaccines. Simple component vaccines are
the split vaccines, which result after the treatment with membrane-dissolving liq-
uids like such as ether. More sophisticated, subunit vaccines are produced using
biological or genetic techniques. They essentially consist of a limited number of
defined molecules, which can be found on the surface of microorganisms. Their
vaccine reactogenicity is thereby further decreased. A disadvantage can be that iso-
lated antigens may not stimulate the immune system as well as whole microorgan-
isms. To overcome this problem, virus-like particles (VLP) vaccines and liposomal
vaccines have been developed. Virus-like particles are particles that spontaneously
assemble from viral surface proteins in the absence of other viral components. They
mimic the structure of authentic spherical virus particles and they are believed to be
more readily recognized by the immune system. In liposomal vaccines, the immuno-
genic subunits are incorporated into small vesicles sized as viruses (0.1–0.2 µm)
and made of amphiphilic chemical compounds such as phospholipids (main compo-
nents of biological membranes). Examples of component vaccines are Haemophilus
influenzae type b (Hib) vaccines, hepatitis A and B vaccines, pneumococcal vac-
cines, and, again, influenza vaccines. The current generation of HPV vaccines are
virus-like particles vaccines.
Another approach to increase the immunogenicity of inactivated vaccines is the
use of adjuvants. These are agents that, by different mechanisms, augment the
immune response against antigens. A potent adjuvant which has been used for over
50 years is aluminium hydroxide. In recent years, several new adjuvants have been
developed: MF59 (an oil-in-water emulsion), MPL (a chemically modified derivative
of lipopolysaccharide) and CpG 7909 (a synthetic nucleotide). Adjuvanted vaccines
1.4 Vaccines 11
tend to more enhanced reactogenicity, i.e. they lead to higher incidences of local and
systemic reactions. Some known adjuvants are therefore not suitable for human use
(possibly still for veterinary use), for example, Freund’s complete adjuvant (heat-
killed Mycobacterium tuberculosis emulsified in mineral oil). This adjuvant is very
effective to enhance both humoral and cellular immunity, but has been found to
produce skin ulceration, necrosis and muscle lesion when administered as intramus-
cular injection. Other potential safety concerns of adjuvanted vaccines are immune-
mediated adverse events (for example, anaphylaxis or arthritis) or chemical toxicity.
The immune system of infants and young children has difficulties to recognize
those bacteria which have outer coats that disguise antigens. A notorious example
is the bacterium Streptococcus pneumoniae. Conjugate vaccines may overcome this
problem. While an adjuvanted vaccine consists of a physical mixture of vaccine
and adjuvant, in a conjugate vaccine the microbial antigens are chemically bound
to certain proteins or toxins (the carrier proteins), with the effect that recognition
by the juvenile immune system is increased. This technique is used for Hib and
pneumococcal vaccines.
Certain bacteria produce exotoxins capable of causing disease. Diphtheria is a
bacterial disease, first described by Hippocrates (ca. 460–377 b.c.). Epidemics of
diphtheria swept Europe in the seventeenth century and the American colonies in
the eighteenth century. The causative bacterium is Corynebacterium diphtheriae,
which produces diphtheria toxin. This toxin can be deprived of its toxic properties by
inactivation with heat or chemicals, but it still carries its immunogenic properties; it is
then called a toxoid and can be used for diphtheria toxoid vaccine. Another example
is the tetanus vaccine containing the toxoid of the bacterium Clostridium tetani.
Diphtheria and tetanus toxoid vaccines are often given to infants in combination
with a vaccine for pertussis. This combination is known as DTP vaccine.
DTP vaccine is an example of a combination vaccine, which intends to prevent a
number of different diseases, or one disease caused by different strains or different
serotypes of the same species, such as the seasonal influenza vaccines which cur-
rently contain antigens of three or four virus (sub)types: one or two B-strains, an A-
H1N1 strain and an A-H3N2 strain. Pneumococcal vaccines are currently available as
7-valent to even 23-valent vaccines. In contrast, a monovalent vaccine is intended to
prevent one specific disease only caused by one defined microorganism, for example
the hepatitis B vaccine.
1.4.2 Routes of Administration
Licensed vaccines differ with respect to the route of administration. This is not
only a question of comfort for the vaccinee but also depends on the exact types
and location of immune cells to which the vaccine is offered to achieve the opti-
mal prophylactic effect. Injectable vaccines are usually given subcutaneously (into
the fat layer between skin and muscle) or intramuscularly (directly into a muscle).
Preferred vaccination sites are the deltoid region of the arm in adults and elderly,
and the thigh in newborns and infants. Some vaccines—hepatitis B vaccines, for
example—can also be administered intramuscularly in the buttock. An alternative
to subcutaneous/intramuscular injection is intradermal vaccination, directly into the
dermis. Intradermal vaccination is successfully used for rabies and hepatitis B. In
case of influenza, it reduces the dose needed to be given. This route could thus
increase the number of available doses of vaccine, which can be relevant in case of
an influenza pandemic. Vaccination by injection is often felt to be uncomfortable
by vaccinees, it usually needs some formal medical training to administer it, and it
carries the risk of needle prick accidents with contaminated blood.
An alternative is administration by the oral route, since the 1950s used for the live
attenuated polio vaccine: some droplets of vaccine-containing liquid on a lump of
sugar to be swallowed. This route builds up a strong local immunity in the intestines,
the site of poliovirus entry. Obvious advantages are the increased ease and acceptance
of vaccination and the absence of the risk of blood contamination.
The third option is intranasal vaccine administration, preferably used for respi-
ratory pathogens. Intranasal vaccines are dropped or sprayed into the cavity of the
nose. Advantages are, again, the ease of administration (in particular for childhood
vaccines), the direct reach of the respiratory compartment, and hence induction of
local protective immunity at the primary site of pathogen entry.
1.4.3 Leaky Vaccines Versus All-or-Nothing Vaccines
Leaky vaccines (also partial vaccines) are vaccines that reduce but do not eliminate a
vaccinated person’s risk of infection upon exposure to the pathogen, meaning that the
protection against infection is incomplete. In contrast, all-or-nothing vaccines reduce
infection rates to zero for some fraction of subjects while the remaining fraction is
fully susceptible. The subjects who after vaccination are no longer at risk for the
disease are said to be completely protected. Leaky vaccines protect subjects with
fewer exposures at a higher rate than subjects with more exposures. Examples of
leaky vaccines are influenza vaccines and pertussis vaccines. Examples of vaccines
that are assumed to function as all-or-nothing vaccines are measles vaccines and
rubella vaccines.
1.4.4 Malaria Vaccines
Malaria is an example of a protozoan disease. The most serious forms of the dis-
ease are caused by the parasites Plasmodium falciparum and Plasmodium vivax.
The parasites are transmitted by the female Anopheles mosquito. Sporozoites (from
sporos, seed) of the parasites are injected in the bitten person. In the liver, sporo-
zoites develop into blood-stage parasites which then reach red blood cells. There are
three types of malaria vaccines in development: pre-erythrocytic vaccines, blood-
stage vaccines and transmission-blocking vaccines. Pre-erythrocytic vaccines target
1.4 Vaccines 13
the sporozoites and the liver life forms. If fully effective, they would prevent blood-
stage infection. In practice, they will be only partially effective, but they may reduce
the parasite density (density of malaria parasites in the peripheral blood) in the initial
blood-stage of the disease. Blood-stage vaccines try to inhibit parasite replication by
binding to the antigens on the surface of infected red blood cells. These vaccines also
may reduce parasite density to a level that prevents development of clinical disease.
Transmission-blocking vaccines try to prevent transmission of the parasite to humans
rather than preventing infection. This is attempted by trying to induce antibodies that
act against the sexual stages of the parasite, to prevent it from becoming sexually
mature.
1.4.5 Experimental Prophylactic and Therapeutic Vaccines
Some recent developments in vaccine research, still in an experimental stage in animal

models, are recombinant vector vaccines and DNA vaccines. Recombinant vector
vaccines are vaccines created by recombinant DNA technology. The pathogen’s
DNA is inserted into a suitable virus or bacterium that transports the DNA into
healthy body cells where the foreign DNA is read. Consequently, foreign proteins
are synthesized and released, which act as antigens stimulating an immune response.
Similarly, DNA vaccines are made of plasmids, circular pieces of bacterial DNA
with incorporated genetic information to produce an antigen of a pathogen. When
the vaccine DNA is brought into suitable body cells, the antigen is expressed, and
the immune system can respond to it. The advantage of DNA vaccines is that no
outer source of protein antigen is needed. Serious safety concerns will have to be
addressed before these experimental approaches can be tested in man.
The vaccines discussed so far were all prophylactic vaccines, intended to prevent
infection. A fairly recent development is the emergence of therapeutic vaccines, not
given with the intention to prevent but to treat. The targeted diseases need not to be
infectious. Therapeutic tumour vaccines, for example, are aimed at tumour forms that
the immune system cannot destroy. The hope is to stimulate the immune system in
such a way that the enhanced immune response is able to kill the tumour cells. Thera-
peutic tumour vaccines are being developed for acute myelogenous leukaemia, breast
cancer, chronic myeloid leukaemia, colorectal cancer, oesophageal cancer, head and
neck cancer, liver and lung cancers, melanoma, non-Hodgkin lymphoma and ovar-
ian, pancreatic and prostate cancers. Other examples of therapeutic vaccines being
developed are addiction vaccines for cocaine and nicotine abuse. Nicotine is made
of small molecules that are able to pass the blood–brain barrier, a filter to protect
the brain from dangerous substances. One vaccine in development has the effect that
the subject develops antibodies to nicotine, so that when they smoke, the antibodies
attach to the nicotine and make the resulting molecule too big to pass the blood–brain
barrier, so that smoking stops being pleasurable. Another nicotine vaccine in devel-
opment leads to the production of antibodies that block the receptor that is involved in
smoking addiction. Therapeutic vaccines are also being tested for hyperlipidaemia,
hypertension, multiple sclerosis, rheumatoid arthritis and Parkinson’s disease.
Chapter 2
Humoral and Cellular Immunity
Abstract This chapter offers a clear account of humoral immunity, the component
of the immune system involving antibodies that circulate in the humor, and cellular
immunity, the component that provides immunity by action of cells. Antibody titres
and antibody concentrations are looked at, and two standard assays for humoral
immunity, the haemagglutination inhibition test and ELISA, are introduced. Standard
assays for cellular immunity are briefly looked at including the ELISPOT assay.
2.1 Humoral Immunity
When the adaptive immune system is activated by the innate immune system, the
humoral immune response (also antibody-mediated immune response) triggers spe-
cific B cells to develop into plasma cells. These plasma cells then secrete large
amounts of antibodies. Antibodies circulate in the lymph and the bloodstreams.
(Hence the name, humoral immunity. Humoral comes from the Greek chymos, a key
concept in ancient Greek medicine. In this view, people were made out of four fluids:
blood, black bile, yellow bile and mucus (phlegm). Being healthy meant that the four
humors were balanced. Having too much of a humor meant unbalance resulting in
illness.) The more general term for antibody is immunoglobulin, a group of proteins.
There are five different antibody classes: IgG, IgM, IgA, IgE and IgD. The first three,
IgG, IgM and IgA, are involved in defence against viruses, bacteria and toxins. IgE
is involved in allergies and defence against parasites. IgD has no apparent role in
defence. The primary humoral immune response is usually weak and transient, and
has a major IgM component. The secondary humoral response is stronger and more
sustained and has a major IgG component.
Antibodies attack the invading pathogens. Different antibodies can have different
functions. One function is to bind to the antigens and mark the pathogens for destruc-
tion by phagocytes, which are cells that phagocytose (ingest) harmful microorganism
and dead or dying cells. Some antibodies, when bound to antigens, activate the com-
plement, serum proteins able to destroy pathogens or to induce the destruction of
pathogens. These antibodies are called complement-mediated antibodies. Neutraliz-
ing antibodies are antibodies that bind to antigens so that the antigen can no longer
https://doi.org/10.1007/978-3-030-37693-2_2
16 2 Humoral and Cellular Immunity
recognize host cells, and infection of the cells is inhibited. For example, in case of
a virus, neutralizing antibodies bind to viral antigens and prevent the virus from
attachment to host cell receptors.
It is good practice to state the antigen against which the antibody was produced:
anti-HA antibody, anti-tetanus antibody, anti-HPV antibody, etc.
2.1.1 Antibody Titres and Antibody Concentrations
Antibody levels in serum samples are measured either as antibody titres or as antibody
concentrations. An antibody titre is a measure of the antibody amount in a serum
sample, expressed as the reciprocal of the highest dilution of the sample that still
gives (or still does not give) a certain assay read-out. To determine the antibody titre,
a serum sample is serially (stepwise) diluted. The dilution factor is the final volume
divided by the initial volume of the solution being diluted. Usually, the dilution factor
at each step is constant. Often used dilution factors are 2, 5 and 10. In this book, the
starting dilution will be denoted by 1:D. A starting dilution of 1:8 and a dilution
factor of 2 will result in the following twofold serial dilutions: 1:8, 1:16, 1:32, 1:64,
1:128, and so on. To each dilution, a standard amount of antigen is added. An assay
(test) is performed which gives a specified read-out either when antibodies against
the antigen are detected or, depending on the test, when no antibodies are detected.
The higher the amount of antibody in the serum sample, the higher the dilutions
at which the assay read-out occurs (or no longer occurs). Assume that the assay
read-out occurs for the dilutions 1:8, 1:16 and 1:32, but not for the dilutions 1:64,
1:128, etc. The antibody titre is the reciprocal of the highest dilution at which the
read-out did occur, 32 in the example. If the assay read-out does not occur at the
starting dilution—indicating a very low number of antibodies, below the detection
limit of the assay—then often the antibody titre for the sample is set to D/2, half of
the starting dilution. By definition, antibody titres are dimensionless.
Antibody concentrations measure the amount of antibody-specific protein per
millilitre serum, expressed either as micrograms of protein per millilitre (µg/ml) or
as units per millilitre (U/ml). (A unit is an arbitrary amount of a substance agreed
upon by scientists.) The measurement of antibody concentrations is usually done on
a single serum sample rather than on a range of serum dilutions.
2.1.2 Two Assays for Humoral Immunity
To give the reader an idea of how antibody levels in serum samples are determined,
below two standard assays for humoral immunity are discussed, the haemagglutina-
tion inhibition test involving serum dilutions, and the enzyme-linked immunosorbent
assay involving a single serum.
2.1 Humoral Immunity 17
Some viruses—influenza, measles and rubella, amongst others—carry on their

surface a protein called haemagglutinin (HA). When mixed with erythrocytes (red
blood cells) in an appropriate ratio, it causes the blood cells clump together (agglu-
tinate). This is called haemagglutination. Anti-HA antibodies can inhibit (prevent)
this reaction. This effect is the basis for the haemagglutination inhibition (HI, also
HAI) assay, an assay to determine antibody titres against viral haemagglutinin. First,
serial dilutions of the antibody-containing serum are allowed to react with a constant
amount of antigen (virus). In the starting dilution and the lower dilutions, the amount
of antibody is larger than the amount of antigen, which means that all virus particles
are bound by antibody. At a certain dilution, the antibody amount becomes smaller
than the antigen amount, which means that free, unbound virus remains. This free
antigen is then detected by the second part of the test: to all dilutions, a defined
amount of erythrocytes is added. In the lower dilutions, where all antigen is bound
by antibody, the erythrocytes freely sink to the lowest point of the test tube or well
and form a red spot there (no haemagglutination). In higher dilutions, where there
is so less antibody that free virus remains, this virus binds to erythrocytes, which
then form a wide layer in the test tube (haemagglutination). The reciprocal of the
last dilution where haemagglutination is still inhibited (i.e. where haemagglutination
does not occur) is the antibody titre.
The enzyme-linked immunosorbent assay (ELISA), also called enzyme immunoas-
say (EIA), is another assay to detect the presence of antibodies in a serum sample.
Many variants of the test exist, and here only the basic principle will be explained. In
simple terms, a defined amount of antigen is bound to a solid-phase surface, usually
the plastic of the wells of a microtitre plate. Then a serum sample with an unknown
amount of antigen-specific antibody is added and allowed to react. If antibody is
present, it will bind to the fixed antigen. Consequently, the serum (with unbound anti-
body, if any) is washed away, while the fixed antigen–antibody complexes remain on
the solid-phase surface. They are detected by adding a solution of antibodies against
human immunoglobulin, prepared in animals and chemically linked to an enzyme.
The fixed complexes consist of three components: the test antigen, the antibody of
unknown amount from the serum specimen and the enzyme-labelled secondary test
antibody against the serum antibody. A substrate to the enzyme is added, which is
split by the enzyme, if present. One of the released splitting products can give a
detectable signal, a certain colour, for example. Only if the three-component com-
plex is present (i.e. if there has been antibody in the serum specimen), this signal
will occur. The strength of the signal is a measure of the amount of serum antibody.
The first-generation ELISA uses chromogenic substrates, which release colour
molecules after enzymatic reaction. By a spectrophotometer, the intensity of the
colour in the solution (or the amount of light absorbed by the solution) can be
determined (optical density). The antibody concentration is determined by comparing
the optical density of the serum sample with an optical density curve constructed with
the help of a standard sample.
In a fluorescence ELISA, which has a higher sensitivity than a colour-releasing
ELISA, the signal is given by fluorescent molecules, whose amount can be measured
by a spectrofluorometer.
18 2 Humoral and Cellular Immunity
2.2 Cellular Immunity
Cellular immunity (also cell-mediated immunity (CMI)) is an adaptive immune

response that is primarily mediated by thymus-derived small lymphocytes, which
are known as T cells. Here, two types of T cells are considered: T helper cells and
T killer cells. T helper cells are particularly important because they maximize the
capabilities of the immune system. They do not destroy infected cells or pathogens,
but they activate and direct other immune cells to do so, which explains their name:
T helper cells. The major roles of T helper cells are to stimulate B cells to secrete
antibodies, to activate phagocytes, to activate T killer cells and to enhance the activity
of natural killer (NK) cells. Another term for T helper cells is CD4+ T cells (CD4
positive T cells), because they express the surface protein CD4. T helper cells are
subdivided on the basis of the cytokines they secrete after encountering a pathogen.
T Helper 1 cells (TH1 cells) secrete many different types of cytokines, the prin-
cipal being interferon-γ (IFN-γ ), interleukin-2 (IL-2) and interleukin-12 (IL-12).
IFN-γ has many effects including activation of macrophages to deal with intra-
cellular bacteria and parasites. IL-2 stimulates the maturation of killer T cells and
enhances the cytotoxicity of NK cells. IL-12 induces the secretion of INF-γ . The
principal cytokines secreted by T helper 2 cells (TH2 cells) are interleukin-4 (IL-4)
and interleukin-5 (IL-5) for helping B cells. An infection with the human immun-
odeficiency virus (HIV) demonstrates the importance of helper T cells. The virus
infects CD4+ T cells. During an HIV infection, the number of CD4+ T cells drops,
leading to the disease known as the acquired immune deficiency syndrome (AIDS).
The major function of T killer cells is cytotoxicity to recognize and destroy cells
infected by viruses, but they also play a role in the defence against intracellular
bacteria and certain types of cancers. Intracellular pathogens are usually not detected
by macrophages and antibodies, and clearance of infection depends upon elimination
of infected cells by cytotoxic lymphocytes. T killer cells are specific, in the sense
that they recognize specific antigens. Alternative terms for T killer cells are CD8+
T cells (CD8 positive T cells), cytotoxic T cells and CTLs (cytotoxic T lymphocytes).
CD8+ T cells secrete INF-γ and the inflammatory cytokine tumour necrosis factor
(TNF).
Most assays for cellular immunity are based on cytokine secretion, as marker
of T cell response. A wide variety of assays exists, but the most used one is the
enzyme-linked immunospot (ELISPOT) assay, which was originally developed as a
method to determine the number of B cells secreting antibodies. Later the method
was adapted to determine the number of T cells secreting cytokines. ELISPOT assays
are performed in microtitre plates coated with the relevant antigen. Peripheral blood
mononuclear cells (PBMCs) are added to it and then incubated. (PBMCs are white
blood cells such as lymphocytes and monocytes.) When the cells are secreting the
specific cytokine, discrete coloured spots are formed, which can be counted. One
of the most popular of this type of assays to evaluate cellular immune responses
2.2 Cellular Immunity 19
is the INF-γ ELISPOT assay, an assay for CTL activity. Results are expressed as
spot-forming cells (SPCs) per million peripheral blood mononuclear cells (SPC/106
PMBC). Other types of the assay are the IL-2 ELISPOT assay, the IL-4 ELISPOT
assay, etc.
The FluoroSpot assay is a modification of the ELISPOT assay and is based
on using multiple fluorescent anticytokines, which makes it possible to spot two
cytokines in the same assay.
Other assays that can quantitate the number of antigen-specific T cells are the
intracellular cytokine assay and the tetramer assay.
Flow cytometry uses the principles of light scattering and emission of fluo-
rochrome molecules to count cells. Cells are labelled with a fluorochrome, a flu-
orescent dye used to stain biological specimens. A solution with cells is injected
into the flow cytometer, and the cells are then forced into a stream of single cells
by means of hydrodynamic focusing. When the cells intercept light from a source,
usually a laser, they scatter light and fluorochromes are realized. Energy is released
as a photon of light with specific spectral properties unique to the fluorochrome. By
using different colours of fluorescent labelling, a single assay can quantify different
types of cells.
Part II
Analysis of Immunogenicity Data
Chapter 3
Standard Statistical Methods
for Immunogenicity Data
Abstract In this chapter, the four standard statistics to summarize humoral and cel-
lular immunogenicity data—the geometric mean response, the geometric mean fold
increase, the seroprotection rate and the seroconversion rate—are introduced. For
each of these summary statistics, the standard statistical analysis is covered in great
detail, both for single vaccine and comparative vaccine trials. A persistent miscon-
ception about the geometric mean fold increase and baseline imbalance is ironed
out. The analysis of rates (i.e. proportions) receives extensive treatment, because
binary immunogenicity and safety endpoints are very common in clinical vaccine
research. A simple but very effective bias correction for the rate ratio is brought
to the attention of the reader. Superior performing alternatives to the conventional
methods for comparing two rates are given a prominent place. It is explained how
exact confidence intervals for a risk difference or a relative risk can be obtained. The
reverse cumulative distribution plot, an intuitively pleasing and useful graphic tool to
display immune response profiles, is exemplified. Statistical tests that can be applied
to compare reverse cumulative distribution curves are presented.
3.1 Introduction
There is an ancient proverb, popularized by Spanish novelist Cervantes in his Don

Quixote (1605), that says that the proof of the pudding is in the eating. Putting it
figuratively, ideas and theories should be judged by testing them. For vaccines, the
test is the vaccine efficacy study. A group of infection-free subjects are randomized
to be vaccinated with either the investigational vaccine or a placebo vaccine. The
subjects are then followed-up, to monitor how many cases of the infectious disease
occur in each of the two arms of the trial. If in the investigational arm the number of
cases is significantly lower than in the placebo arm, this is considered to be proof that
the investigational vaccine protects from infection. Vaccine efficacy studies, however,
have a notorious reputation among vaccine researchers. They are extremely if not
prohibitively costly, as they usually require large sample sizes and a lengthy follow-
up. If during the follow-up period the attack rate of the infection and thus the number
of cases is low, the period has to be extended, meaning even higher costs. Many
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24 3 Standard Statistical Methods for Immunogenicity Data
vaccine efficacy studies have been negative as a result of imperfect case finding.
Placebo-controlled vaccine efficacy studies in elderly are considered unethical if for
the infectious disease a vaccine is available.
A popular alternative to vaccine efficacy studies are vaccine immunogenicity tri-
als. In such trials, the primary endpoint is a humoral or a cellular immunity mea-
surement which is known to correlate with protection against infection (Chap. 11.)
Vaccine immunogenicity trials are usually much smaller and require often only a
short follow-up, which makes them less costly than vaccine efficacy studies. Regis-
tration authorities such as the United States Food and Drug Administration (FDA),
the European Medicines Agency (EMA), Japan’s Organization for Pharmaceutical
Safety and Research (OPSR), China’s National Medical Products Administration
(NMPA) and the National Registration Authority (NRA) of Australia all accept the
results of vaccine immunogenicity trials in support of licensure of new vaccines.
In early vaccine development, they may be used to explore dose formulation. They
may be used to expand the use of a vaccine by extending the age eligible for the
vaccine. This was done to extend the lower age range of an HPV vaccine down to
age 9 from 11. Also, when a vaccine is updated, by adding serotypes to an existing
vaccine, immunogenicity studies can play an important role. In paediatric studies
where children are expected to take a several vaccines, immunogenicity assays are
often used to check that the new vaccine doesn’t impact immunogenicity of already
recommended vaccines. Finally, in assessing the long-term effect of a vaccine, some
kind of immunogenicity assay is used.
Until recently vaccine immunogenicity trials typically focused on the humoral
immune response, i.e. on serum antibody levels. Today, many papers on vaccine
immunogenicity report also on cellular immunity. Nevertheless, cellular immunity
in vaccine trials is still largely in the investigational phase.
There are four standard statistics to summarize humoral and cellular immunity
data: the geometric mean response, the geometric mean fold increase, the seropro-
tection rate and the seroconversion rate. Two of these statistics, the geometric mean
response and the seroprotection rate, quantify absolute immunogenicity values, while
the other two, the geometric mean fold increase and the seroconversion rate, quan-
tify intra-individual changes in values. In the next sections, the statistical analysis
of these four summary statistics is discussed, both for single vaccine groups and for
two vaccine groups.
3.2 Geometric Mean Titres and Concentrations
Distributions of post-vaccination humoral and cellular immunogenicity values tend

to be skewed to the right. Log-transformed immunogenicity values, on the other hand,
usually are approximately normally distributed. Thus, standard statistical methods
requiring normal data can be applied to the log-transformed values. Antilogs of point
and interval estimates can be used for inference about parameters of the distribution
underlying the untransformed values.
3.2 Geometric Mean Titres and Concentrations 25
The standard statistics to summarize immunogenicity values is the geometric mean

titre (GMT) if the observations are titres, or the geometric mean concentration (GMC)
if the observations are concentrations. Let v1 , . . . , vn be a group of n immunogenicity
values. (Throughout this book, groups of observations are assumed to be independent
and identically distributed (i.i.d.).) The geometric mean is defined as
GM = (v1 × · · · × vn )1/n .
An equivalent expression is
n

GM = exp log vi /n .
i=1
The geometric mean response is thus on the same scale as the immunogenicity
measurements.
The transformation of the immunogenicity values need not to be loge , it can be
any logarithmic transformation, log2 , log10 , etc. Care should be taken that when
calculating the geometric mean response the correct base is used. Thus, if log10 is
used, the geometric mean should be calculated as
n
log10 vi /n
GM = 10 i=1 .
If antibody titres ti are reciprocals of twofold serial dilutions with 1:D as the
lowest tested dilution, then a convenient log transformation is
ui = log2 [ti /(D/2)]. (3.1)
The ui ’s are then the dilution steps: 1, 2, 3, etc. The geometric mean should be
calculated as n
GM = (D/2)2 i=1 ui /n .
Transformation (3.1) will be referred to as the standard log transformation for anti-
body titres.
Example 3.1 Rubella (German measles) is a disease caused by the rubella virus. In
adults, the disease itself is not serious, but infection of a pregnant woman by rubella
can cause miscarriage, stillbirth or damage to the foetus during the first three months
of pregnancy. A haemagglutination inhibition (HI) test for rubella is often performed
routinely on pregnant women. The presence of a detectable HI titre indicates previous
infection and immunity to reinfection. If no antibodies can be detected, the woman
is considered susceptible and is followed accordingly. Assume that in the HI test the
lowest dilution is 1:8. Then the HI titres can take on the values 8, 16, 32, etc. The
standard log-transformed values are log2 (8/4) = 1, log2 (16/4) = 2, log2 (32/4) =
3, etc. The geometric mean of the five titres 8, 8, 16, 32, 64 is
GMT = 4 × 2(1+1+2+3+4)/5 = 18.379.
With the standard log transformation, differences between log-transformed values

are easy to interpret: a difference of 1 means a difference of one dilution, a difference
of 2 means a difference of two dilutions, etc.
A statistic often reported with the geometric mean response is the geometric standard
deviation (GSD), which is the antilog of the sample standard deviation of the log
transformed immunogenicity values. The statistic allows easy calculation of confi-
dence limits for the geometric mean of the distribution underlying the immunogenic-
ity values (the underlying geometric mean for short). Let SD be the sample standard
deviation of the log transformed immunogenicity values, then the geometric standard
deviation is
GSD = exp(SD).
The lower and upper limit of the two-sided 100(1−α)% confidence interval for the
underlying geometric mean eμ are
√
LCLeμ = GMT /GSDtn−1;1−α/2 / n
(3.2)
and √
UCLeμ = GMT × GSDtn−1;1−α/2 / n , (3.3)
where tn−1;1−α/2 is the 100(1−α/2)th percentile of Student’s t-distribution with

(n − 1) degrees of freedom.
Example 3.1 (continued) The sample standard deviation SD of the five log-
transformed HI titres is 0.904. Thus, the geometric standard deviation is
GSD = exp(0.904) = 2.469.
Percentiles of Student’s t-distribution can be obtained with the SAS function TINV.
The lower 95% confidence limit for the underlying geometric mean is
√
LCLeμ = 18.379/2.4692.776/ 5
= 5.98
and the upper 95% confidence limit is

√
UCLeμ = 18.379 × 2.4692.776/ 5
= 56.4,
where 2.776 = TINV(0.975,4).

3.2 Geometric Mean Titres and Concentrations 27
3.2.1 Single Vaccine Group
If the ui = log vi are normally distributed with mean μ and variance σ 2 , then the
arithmetic mean of the ui is a point estimate of μ, and
n

GMT = exp ui /n
i=1
a point estimate of eμ , the underlying geometric mean. The distribution of the ui is

known as the log-normal distribution.
Because the ui are normally distributed, confidence intervals for μ can be based on
the one-sample t-test. Antilogs of the limits of the t-test based 100(1−α)% confidence
interval for μ constitute 100(1−α)% confidence limits for the parameter eμ . These
confidence limits are identical to those in (3.2) and (3.3). A nice property of the
log-normal distribution is that eμ is not only its geometric mean but also its median.
Example 3.2 The following data are six Th1-type IFN-γ values: 3.51, 9.24, 13.7,
35.2, 47.4 and 57.5 IU/L. The natural logarithms are 1.256, 2.224, 2.617, 3.561,
3.859 and 4.052, with arithmetic mean 2.928 and standard error 0.444. Hence,
GMC = exp(2.928) = 18.7.
With t0.975,5 = 2.571, it follows that the two-sided 95% confidence limits for μ are
2.928 − 2.571(0.444) = 1.786
and
2.928 + 2.571(0.444) = 4.070.
Thus, the lower and upper 95% confidence limits for the geometric mean eμ of the
distribution underlying the IFN-γ values are e1.786 = 5.97 and e4.070 = 58.6.
By definition, confidence intervals for geometric mean responses are non-
symmetrical.
3.2.2 Two Vaccine Groups
If there are two vaccine groups, statistical inference is based on the two-sample t-test,
applied to the log-transformed immunogenicity values. Point and interval estimates
for the difference Δ = μ1 − μ0 are transformed back to point and interval estimates
for the ratio θ = eμ1 /eμ0 .
The standard statistic to compare two groups of immunogenicity values is the
geometric mean ratio (GMR):
GMR = GM1 /GM0 ,
where GM1 and GM0 are the geometric mean response of investigational and the
control vaccine group, respectively. Let AM1 and AM0 denote the arithmetic means
of the log-transformed values of the two groups, then the following equality holds:
GMR = exp(AM1 − AM0 ).
Thus, the P-value from the two-sample t-test to test the null hypothesis H0 : = 0
can be used to test the null hypothesis H0 : θ = 1.
Example 3.2 (continued) Assume that the six Th1-type IFN-γ values are to be com-
pared with a second group of six values, and that the arithmetic mean and standard
error of the log-transformed values are 2.754 and 0.512, respectively. Thus,
GMC0 = exp(2.754) = 15.7,
and the geometric mean ratio is
GMR = exp(2.928 − 2.754) = exp(0.174)

= 1.19 = 18.7/15.7.
The estimated standard error of the difference is 0.678. Lower and upper 95% con-
fidence limits for the underlying geometric mean ratio are obtained as
exp[1.19 − 2.228(0.677)] = 0.727
and
exp[1.19 + 2.228(0.677)] = 14.855,
where 2.228 = TINV(0.975,10).
3.3 Geometric Mean Fold Increase
For some infectious diseases, pre-vaccination immunogenicity levels are not zero.
An example is influenza. Recipients of influenza vaccines have usually been exposed
to various influenza viruses during lifetime, by natural infections or previous vacci-
nations (exceptions are very young children). In that case, post-vaccination immuno-
genicity levels do not only express the immune responses to the vaccination but also
the pre-vaccination levels. In that case, an alternative to the geometric mean titre or
concentration is the geometric mean fold increase (also mean fold increase, geometric
mean fold rise).
3.3 Geometric Mean Fold Increase 29
If vpre is a subject’s pre-vaccination (baseline) immunogenicity value and vpost the

post-vaccination value, then the fold increase is
f = vpost /vpre .
Fold increases express intra-individual relative increases in immunogenicity values.

Just like immunogenicity values, log-transformed fold increases tend to be normally
distributed, and for the statistical analysis of fold increases, the methods described
above for the analysis of immunogenicity values can be used.
3.3.1 Analysis of a Single Geometric Mean Fold Increase
The standard statistic to summarize a group of n fold increases f1 , . . . , fn is the

geometric mean fold increase (gMFI)
n

gMFI = exp log fi /n .
i=1
It is easy to show that

gMFI = GMpost /GMpre .
Thus, the geometric mean fold increase is identical to the geometric mean of the
post-vaccination values divided by the geometric mean of the pre-vaccination values.
Note, though, that this equation only holds if for all n subjects both the pre- and the
post-vaccination value is non-missing.
Example 3.3 Consider an influenza trial in which pre- and post-vaccination anti-HA
antibody levels are measured by means of the HI test. Let (5,40), (5,80), (10,160),
(10,320), (20,80) and (20,640) be the pre- and post-vaccination antibody titres of the
first six subjects enrolled. GMTpre = 10.0 and GMTpost = 142.5. The fold increases
are 8, 16, 16, 32, 4 and 32. The geometric mean of these sixfold increases is gMFI =
14.25. The same value is obtained if GMTpost is divided by GMTpre . The geometric
standard deviation of the fold increases is GSD = 2.249. Forms. (3.2) and (3.3) can
be used to obtain a confidence interval for the geometric mean of the distribution
underlying the fold increases.
3.3.2 Analysis of Two Geometric Mean Fold Increases
To compare two groups of fold increases, the two-sample t-test can be applied to the
log-transformed fold increases.
In case of two groups of fold increases, the following equation holds
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Further, on 27th December 1784 he stated to Wyvill his intention to
bring forward a Reform Bill as early as possible in the next session,
and that he would “exert his whole power and credit as a man, and as
a minister, honestly and boldly, to carry such a meliorated system of
representation as may place the constitution on a footing of permanent
264
security.” This at least was the version of his words which Wyvill at
once circulated to Reform Committees throughout the country. With a
belated access of prudence, he added a postscript, urging that it must
in no case be published; but some foolish friend or wise opponent
bruited it abroad, with the result that members of the House now
contrasted his eagerness for Reform with his inability to secure any
mention of it in the King’s Speech. He might declare that the subject
was the nearest to his heart, and that nothing but its complexity
prevented him sketching an outline of his proposal; but members drew
their own conclusions. North made a skilful use of Wyvill’s letter, but
elicited from Pitt no definite disclaimer of the words quoted from it.
Indeed Pitt afterwards assured Wyvill that those words well expressed
265
his thoughts.
Pitt judged that it would be best to proceed circumspectly in the
matter of Reform, perhaps because he wished the affair of Wyvill’s
letter to blow over, or because he had obstacles to face in his Cabinet.
Owing to these or other causes he decided to give precedence to his
resolutions for according greater freedom of trade to Ireland, which will
be dealt with in another chapter; and not until 18 April 1785 did he
bring before Parliament the subject of parliamentary Reform. The
delay was unfortunate, for the trading classes were by this time ruffled
by proposals which promised to bring in the products of Irish cheap
labour.
Meanwhile Pitt drew up a draft scheme of Reform and sent it to
Wyvill for his perusal. He proposed to set aside a sum of somewhat
more than £1,000,000 in order to indemnify electors in nomination
boroughs, provided that two-thirds of their total number should agree
to forego their right of sending members to Parliament. In that case the
borough should be disfranchised, the electors receiving compensation
by a Parliamentary Committee after due examination of their claims.
The seats thus vacated were to be added to counties or to districts of
the larger counties. Pitt also hinted at the enfranchisement of certain
suburban areas of London, and suggested that notoriously corrupt
boroughs (such as Shoreham and Cricklade) should be disfranchised
without compensation, their electoral powers being transferred to
counties. He further proposed to widen the county franchise by
admitting copyholders of 40 shillings a year and leaseholders whose
266
leases had a certain term yet to run.
These suggestions strike us as strangely cramped, except in the
matter of copyholds, which were dealt with more generously than in
Earl Grey’s Bill of 1831. The proposals for disfranchising the pocket
boroughs resemble a political auction, Pitt dangling a million before the
potwallers of Gatton, Grampound, Castle Rising, etc., as the sole
means of endowing the great counties with political power, and of
enabling Manchester, Birmingham, Leeds, and Sheffield to find
articulate utterance. Wyvill in 1797 noted that these towns formed a
part of Pitt’s scheme of enfranchisement; but the Prime Minister does
not seem in 1785 to have ventured distinctly to formulate so
revolutionary a proposal. In the draft of a preamble to his Bill he
suggested the advisability of enlarging the electorate in the case of
several towns such as Edinburgh, Glasgow, and Winchester, where
the Corporation or the Guild Merchant alone returned the members of
Parliament.
These draft proposals reveal the caution, not to say nervousness,
with which Pitt approached this great subject; and the same
characteristics appear in the speech of 18th April 1785 in which he
introduced his measure. While lacking glow and enthusiasm, it was
instinct with moderation and persuasiveness. He started with the
assumption that the House of Commons ought to be “an Assembly
freely elected, between whom and the mass of the people there was
the closest union and most perfect sympathy”; but he proceeded to
allay the fears of those who, like Burke, saw in any change a death-
blow to the constitution, by disclaiming “vague and unlimited notions.”
He desired, he said, “a sober and practicable scheme which should
have for its basis the original principle of representation.” He then
showed how that principle had been warped by time and Court
intrigues. Sometimes method was discoverable, and he cited a case
that occurred shortly after the Restoration when, after the
disfranchisement of 72 boroughs, 36 of them regained their rights on
petition, but the 36 others, having decreased in size, remained without
representatives. Therefore, by the discretionary powers of the Crown
to grant, or to withhold, representation, there was a clear recognition of
the principle that the chief towns, not the decayed towns, should return
members to Parliament. Who, he asked, was the truer supporter of the
constitution? He who sought to preserve the mere form of it, or he who
preferred its substance and essence to the empty shell? Coming next
to the outlines of his scheme, he declared that he would change
neither the proportion of Scottish to English members, as settled by the
Act of Union of 1707, nor the numbers of the House. All that he aimed
at for the present was to disenfranchise 36 decayed boroughs and to
assign their 72 members to the counties which most needed a larger
representation, as also to London and Westminster.
Moderation such as this implies timidity. Moreover this was not all.
As we have seen, Pitt did not intend to carry out this reform by
compulsion; and he now declared that, recognizing as he did the
monetary value of the franchises of these decayed boroughs, he
proposed to form a fund whence they might gain compensation for this
undoubted loss. Very skilfully he introduced this novel proposal by
deprecating the “squeamish and maiden coyness” which members
affected in speaking there on a topic which they frankly discussed
outside the House. For himself he faced the fact that the right of
returning two members to Parliament had a certain monetary value,
and he therefore offered a due indemnity. Further, if in the future any
other decayed borough should wish to surrender its franchise “on an
adequate consideration,” he proposed to facilitate such a surrender,
and to allot the two seats to any district or town that seemed most to
need the franchise. Finally he desired to widen the electorate in the
counties by including copyholders, whose property was as secure as,
267
sometimes more secure than, that of the freeholders.
Such were the proposals. They were brought forward at a time
when Pitt had suffered in the opinion of the House, first by his
obstinacy in persevering with the Westminster election scrutiny, and,
secondly, by the Irish Commercial Resolutions. Members were
therefore in an unsettled state of mind, and an eye-witness describes
them as listening to the Prime Minister “with that sort of civil attention
which people give to a person who has a good claim to be heard, but
with whom the hearers are determined to disagree.” The same
witness, Daniel Pulteney, found that most of Pitt’s friends “lamented
that he would not keep clear of this absurd business—this Yorkshire
268
system of Reform.”
Despite this chilling reception, Pitt set forth his proposals “with the
attractions of a most seductive eloquence.” Such is the testimony of
Wraxall, which by itself would tend to refute the venomous assertion
that Pitt was not in earnest. The contrary is proved by his words and
deeds. At Christmastide 1784 he begged Wilberforce to return from the
south of France in order to work in the cause of Reform; and on 12th
January 1785 he wrote to the Duke of Rutland in these terms: “I really
think that I see more than ever the chance of effecting a safe and
temperate plan [of Reform], and I think its success as essential to the
credit, if not to the stability, of the present administration, as it is to the
269
good government of the country hereafter.” Further, it is certain that
those ardent reformers, Robert Smith (afterwards Lord Carrington) and
Wyvill, had no doubt of his earnestness. The latter stated in his letters
that Pitt was striving his hardest to arouse interest in the Reform of
270
Parliament.
There is also ground for thinking that the King had privately
assured him that, though he regretted his advocacy of Reform, no
word of his should influence any one against that measure. Wraxall,
who voted against Pitt, admits that his plan of Reform was highly
attractive in theory—a phrase which leaves us wondering what would
have been the practical scheme of reform after which this earth-born
271
soul was dimly groping. Even Burke, who saw mortal danger to the
body politic in the removal of the smallest rag of antiquity,
complimented the Minister on the skill with which he had sought to
make the change palateable to all parties. None the less did that fervid
Celt consider the whole plan an ignis fatuus, calculated to mislead and
bewilder. Herein Burke for once voiced the feelings of the country
gentry who thought the fate of the constitution bound up with the
maintenance of the rotten boroughs. The speeches of Duncombe and
Wilberforce in support of the measure were poor and rambling.
Dundas, an unwilling convert to Reform, had nothing better to say than
that he highly approved the principle of compensation.
The chief arguments against the measure were those of North,
Fox, and Bankes. The first declared that the country cared not a jot for
Reform. Birmingham had not petitioned for it. One of the members for
Suffolk, who sought advice from his constituents, had received no
instructions from them. The effort to get up a Reform meeting in
London had resulted in the attendance of only three hundred persons;
and the outcome of similar efforts in the provinces might be summed
up in the line from “The Rehearsal”:
What horrid sound of silence doth assail mine ear?
As for Fox, though he voted with Pitt, he did his best to defeat the
measure. He wittily explained the silence of the people by their alarm
at Pitt’s Irish Resolutions; for when on the point of emigrating from a
land on the brink of ruin, why should they trouble about its
constitution? Further, he stoutly objected to the award of any indemnity
to the owners of pocket boroughs. The same point was shrewdly
pressed by Bankes. The measure, he said, was absurd on the face of
it. For why declare against the whole principle of the traffic in such
boroughs, and yet proceed to allow liberal compensation to the
traffickers? The argument was more clever than sound, as appeared in
1834 when Parliament awarded £20,000,000 to slave-owners. The
taunt also came with an ill grace from the owner and representative of
Corfe Castle; but it cut Pitt to the quick. He immediately arose and
avowed that the remark wounded him deeply on account of his long
friendship with the speaker; the point touched was a tender one; but
the evil was such that it must be cured, and it could be cured in no
other way than the present. And so, in this mood of “Et tu, Brute,” Pitt
and his friends withdrew into the lobby, and soon learned that his third
attempt to redress the glaring ills of the representation had been
defeated by 248 votes to 174.
The blow was crushing and final as regards Parliamentary Reform
in that age. The storms of the French Revolution and the mightier
subterranean forces of the Industrial Revolution were to work upon the
old order of things before the governing classes of England were
brought to see the need of renovation; and when the change came in
1832, it was not until the nation had drawn near to the verge of civil
war. In 1785 the transition would have been peaceful and progressive.
Pitt was content to work by permissive methods, and to leave open the
decision as to which of the rising industrial towns should gain the
franchise as it was sold by the decaying boroughs. Such a mode of
advance seems to us that of a snail, and marked by a trail of slime. But
we must remember that the brains of that generation worked very
slowly on political questions; for in truth they had to do with a society
which was to ours almost as a lake is to a torrent. Further, it is
noteworthy that the offer to buy out the pocket boroughs was the chief
recommendation of Pitt’s measure to the House of Commons. Burke
praised him for thus gilding his pill; and Dundas’s chief plea for the
measure was that it did not outrage “the sacred inheritance of
property.” Alone among Pitt’s supporters Bankes reprobated these
bartering methods. The attitude of the House should be remembered,
as it bears on the question how far Pitt was justified in buying off the
opposition of the Irish borough-holders and others who suffered by the
Act of Union of 1800.
Could Pitt have taken any further steps to ensure the passing of
his Reform Bill? Mr. Lecky, followed in this by lesser historians, has
maintained the affirmative. He avers that, by making it a ministerial
measure, Pitt could have brought to bear on it all the influence of party
272
discipline. To this it may be replied that Pitt’s majority, though large,
was very independent. As will appear in the next chapter, we find him
writing that he could not then count on the support of many of his
followers from one day to another. They had floated together from the
wreckage of the Fox and North parties, and had as yet gained no
distinct cohesion, except such as arose from admiration of him.
Further, he strained this feeling too severely in the session of 1785 by
his harsh treatment of Fox over the Westminster election, and by
pressing on three unpopular measures, namely, the Irish Resolutions
(22nd February), the fortification of Portsmouth and Plymouth (14th
March), and Parliamentary Reform (18th April). Sooner or later he
suffered defeat on all these proposals. Yet it is clear that his followers
did not intend to drive him from office, but merely to teach him caution.
In this they succeeded only too well. Thereafter he acted far more
warily; and, except in the Warren Hastings’ case, and in the French
Commercial Treaty, he for some time showed little of that power of
initiative which marked the early part of the session of 1785. The fact is
to be regretted; but the need of caution is manifest when we remember
that a single irretrievable blunder would have entailed a Fox-North
Ministry with all the discords and confusion that must have come in its
train. Even zealous reformers, while regretting that Pitt did not
persevere with Reform, continued to prefer him to Fox and North. This
appears in a letter written by Major Cartwright at the close of the year
1788. On the news of the mental derangement of George III, that
veteran reformer wrote to Wilberforce: “I very much fear that the King’s
present derangement is likely to produce other derangements not for
the public benefit. I hope we are not to be sold to the Coalition faction.
Mr. Fox is, I see, arrived, and cabal, I doubt not, is labouring with
redoubled zeal under his direction to overturn the present
273
Government.” The distrust felt for Fox after his union with North
survived in full force even in 1788. Their accession to power, and the
triumph of the Prince of Wales, were looked on as the worst of all
political evils. This, I repeat, explains and justifies the determination of
Pitt to continue in office.
But other reasons must also have influenced his decision to shelve
the question of Reform at least for the present. His Cabinet was too
divided on it to warrant his risking its existence on a proposal which
had always been rejected. The marvel was that a Prime Minister
should bring it forward. Further, if we may judge from George III’s letter
of 20th March, the active though secret opposition of the King was
averted only by Pitt giving an unmistakable hint that he would resign if
274
it were used against the measure. Having secured the King’s
neutrality, Pitt could hardly go further and leave his sovereign in the
lurch by breaking up his Cabinet on a question on which he alone of
the executive Government felt strongly.
Another possible alternative was that he himself should resign. But
this again would almost certainly have involved the fall of an
Administration of which he was the keystone. It is also noteworthy that
the doctrine of ministerial responsibility, whether collective or personal,
had not then been definitely established. Cabinets and individual
Ministers resigned on points of honour, or when they held that the
Government could no longer be satisfactorily carried on. But neither of
these cases had arisen. The Government of the country obviously
could go on as well as before. True, a legislative proposal of great
importance had been rejected; but it cannot be too clearly stated that
in that century the chief work of Government was to govern, not to
pass new laws. Far on in the next century the main business of a
Cabinet came to be the proposing and carrying through of new
measures; but this idea was foreign to that more stationary age; and
probably everyone would have accused Pitt of deserting his post had
he resigned owing to his inability to carry a legislative enactment of a
very debatable character. Walpole has not been blamed because he
held to office despite his failure to carry his very important Excise Bill.
Again, why should Pitt have persevered with the cause of Reform?
Despite all the efforts of Wyvill and the Associations, only eight
petitions had been sent up to the House in favour of it. The taunts of
North as to the apathy of the country were unanswerable. No voice
was heard in protest against the rejection of the measure; and the
judgement of Wilberforce was that of practically all reformers, that,
275
after Pitt’s failure, Reform was hopeless. Wyvill himself, in a
pamphlet written amidst the excitements of 1793, admitted that Pitt’s
measure received little attention in 1785, and soon fell into oblivion—a
fact which he explained by the complete satisfaction which the nation
then felt with its new Ministry. Here we have the true explanation,
furnished by the man who had his hand on the nation’s pulse. Wyvill
saw that the practical character of the reforms already carried by Pitt
had reconciled the people even to rotten boroughs. He also stated that
the proposals of 1785 did not go far enough to satisfy many reformers,
but that they aroused the bitter hostility of the boroughmongers. There,
indeed, was the gist of the difficulty. The boroughmongers carried the
House with them; and it was impossible at that period to stir up a
national enthusiasm which would brush aside the fears of the timid and
the sophistries of the corrupt. Only under the overpowering impulse of
1832 could the House be brought to pass sentence against itself.
Because Grey and Russell carried a Reform Bill nearly half a century
later, is Pitt to be blamed for abandoning, after the third attempt, a
measure which aroused invincible opposition in Parliament, and only
the most languid interest in the nation at large?
Further, be it noted that the conduct of Fox had irretrievably
damaged the cause of Reform. His union with Lord North had split in
twain the party of progress; and we have the testimony of an ardent
young reformer, Francis Place, that that unprincipled union dealt a
death blow to the London Society for promoting Constitutional
Information, the last expiring effort of which was to publish a volume of
276
political tracts in the year 1784. Not until the year 1791 was this
useful society revived, and then owing to the impulses set in motion by
French democracy.
Finally, it is noteworthy that Pitt gave his support to a smaller
measure of Reform brought forward in the session of 1786 by Earl
Stanhope. That nobleman had persuaded Wilberforce to widen the
scope of a proposal which the member for Yorkshire had first designed
for that county alone. It provided for the registration of all freeholders
and the holding of the poll in several places at the same time. Pitt
spoke warmly for the Bill as tending to remedy the chief defects in the
county representation, and he expressed the hope that at some future
time the whole of the representation would undergo the same
improvements (15th May). Despite the opposition of Grenville and
Powys, leave was granted to bring in the measure by 98 votes to 22.
Though Stanhope emphatically declared in the Lords that the summary
rejection of a Bill affecting the Commons would be an act of
“unutterable indecency,” the Peers rejected the measure by 38 votes to
277
15.
This was the last effort made by Pitt’s friends and supporters to
improve the old system. For the present, Reform had come to an
impasse. Even practical little proposals which passed the Commons
were doomed to failure in the Lords; and it was clear that nothing short
of a convulsion would open up a passage. The events that followed
tended to discredit the cause of progress. As will appear in Chapter
XIV, the violence of the Dutch democrats threatened to wreck their
constitution, to degrade the position of the Prince of Orange, and to
make their country a footstool of the French monarchy. Pitt perforce
took the side of the Prince; and this question, together with the torpor
of the populace, served by degrees to detach the young statesman
from uncompromising reformers like Stanhope and Wyvill.
* * * * *
The defection or apathy of many of his friends in the session of
1785 was undoubtedly a severe blow to Pitt. It sounded the death-knell
of his earlier idealism, and led him on, somewhat dazed, to a time
marked by compromise and a tendency to rely upon “influence.” Daniel
Pulteney noted, when he saw him in the park on the day following the
278
rebuff, that he was in deep sorrow. That was natural in a man who
had hoped to arouse the nation to a vivid interest in good government,
and suddenly found himself headed back to the old paths. The shock
must have been the greater as he had been guided by what I have
termed his bookish outlook on life.
Pulteney, as a man of the world, pointed out to his patron, the
Duke of Rutland, this defect in the young Prime Minister: “This system
of Pitt’s, to act upon general ideas of the propriety or wisdom of a
measure, without attending enough to the means by which it can be
best and most happily introduced—I mean, knowing the general
opinion of the House at the time—must, I foresee, involve him in time
in one or other of these difficulties,” namely, the rash introduction of a
measure, or its abandonment through a sudden access of distrust.
Again he says that Pitt is very much “fettered in his conduct on great
affairs. From a very partial and confined knowledge of the world, he is
too full of caution and suspicions where there does not exist the
shadow of a pretext for them; and, from having no immediate
intercourse with the generality of the House of Commons here, he is
as ignorant of their opinions on particular questions as if he was
Minister of another country.” He then states that, when Pitt suddenly
came to see the facts of the case, he was apt to be unduly despondent
and to bring forward only those questions on which he was sure of a
majority. He concludes that this habit of “acting only on abstract
principles” would greatly embarrass him; but that he might expect long
to continue in power, because “whenever he was to quit, I think no
279
Ministry, not founded on corruption, could stand against him.”
This estimate, by a practical politician, though marked by a desire
to depreciate Pitt and exalt the Duke of Rutland, goes far towards
explaining the symptoms of change which are thereafter noticeable in
Pitt’s career. It shows us Pitt, not a superb parliamentarian dominating
men and affairs from the outset, but rather an idealist, almost a
doctrinaire, who hoped to lead his majority at his will by the inspiring
power of lofty principles, but now and again found that he had to do,
not with Humanity, but with humdrum men. We see him in the midst of
his upward gazings, disconcerted by the force of material interests,
and driven thenceforth to pay more attention to the prejudices of his
party.
First in importance among the expedients to which he was driven
after the spring of 1785 was the use of “influence.” As was shown in
the Introduction, that word, when used in a political sense, denoted the
system of rewards or coercion whereby the King and his Prime
Minister assured the triumph of their policy. Peerages, bishoprics,
judgeships, magistracies, sinecures and gaugerships, were the
dainties held out by every Ministry in order to keep their sleek following
close to heel and thin the ranks of the lean and hungry Opposition.
Peerages alone counted for much; for we find Pitt writing, during the
Fox-North Ministry of 1783, that the King’s determination not to create
a single peer during their term of office must sooner or later be fatal to
them. Government by rewards and exclusions was looked upon as the
natural order of things; but up to the session of 1785 Pitt used
“influence” sparingly. At a later date Wilberforce ventured on the very
questionable assertion that Pitt’s command over Parliament after the
General Election of 1784 was so great that he might have governed by
“principle” and have dispensed with “influence.” He expressed,
however, his admiration of him for refusing to associate with trading
politicians, a connection which, even in the hours of recreation, was
280
certain to bring defilement.
Pitt, as we have seen, never stooped to associate with jobbers, but
he seems to have decided, after the severe rebuffs of February–April
1785, to use “influence” more and more. We notice in his letters to the
Duke of Rutland and Orde several injunctions as to the management
of members in the Irish Parliament; and he sought to conciliate
waverers by other means, such as the abandonment of those clauses
of the Irish Resolutions which were most obnoxious to British traders,
and an almost lavish use of honours and places. This last expedient he
adopted unwillingly; for on 19th July 1785 he wrote to the Duke of
Rutland that circumstances compelled him to recommend a larger
addition to the British peerage than he liked, and that he was very
281
desirous not to increase it farther than was absolutely necessary.
This shows that his hand was forced either by his colleagues or by the
exigencies of the time. Possibly the promises of peerages had to be
made in order to secure the passing of the Irish Resolutions even in
their modified form. It is humiliating to reflect that this descent from a
higher to a lower level of policy thenceforth secured him a majority
which followed his lead, except on the isolated questions of the
fortification of Portsmouth and Plymouth, and of the impeachment of
Warren Hastings, the latter of which he left entirely open.
* * * * *
It will be convenient to consider here the question of the
fortification of the chief national dockyards, as it shows the
determination of the Prime Minister to secure economy and efficiency
in the public services. As we have seen, his great aim was to carry out
a work of revival in every sphere of the nation’s life. When thwarted in
one direction he did not relax his energies, but turned them into new
channels. On the rejection of the Irish Resolutions, he urged the Duke
of Rutland to seek out the most practicable means of healing the
discontent in that island. Above all he suggested an alleviation in the
matter of tithe (then the most flagrant of all material grievances), if
282
possible, with the assent of the (Protestant) Established Church.
Similarly in the cause of Free Trade, when foiled by Anglo-Irish
jealousies, he turned towards France; and, after discovering the
impossibility of carrying out his aim for the regeneration of Parliament,
he vindicated the claims of morality in the administration of India.
Finally, it is a crowning proof of the many-sidedness and practical
character of his efforts that, amidst all his strivings to reduce the
National Debt, he sought to strengthen the nation’s defences.
Despite the many distractions of the years 1785–1786, he devoted
much care and thought to the navy. Already, in 1784, he had instituted
a Parliamentary inquiry into the state of the fleet and the dockyards,
which brought to light many defects and pointed the way to remedies.
His anxiety respecting the first line of defence also led him to keep the
number of seamen at 18,000, a higher total than ever was known in
time of peace; and he allotted the large sum of £2,400,000 for the
building of warships by contract. Further, he sought to stop the
corruption which was rife in the dockyards and the naval service.
The letter which Sir Charles Middleton (afterwards Lord Barham)
wrote to him on 24th August 1786 reveals an astounding state of
affairs. From his official knowledge he declared—
The principle of our dockyards at present is a total disregard to

public œconomy in all its branches; and it is so rooted in the
professional officers that they cannot divest themselves of it when
brought into higher stations. They have so many relatives and
dependants, too, in the dockyards, that can only be served by
countenancing and promoting improper expences, that they never
lose an opportunity of supporting them when in their power, and on
this account ought to have as small a voice as possible in creating
283
them.
In this and other letters to Pitt, Middleton expressed his belief that
much might be done to check these evils by the help of a firm and
upright Minister. Probably this appeal from a patriotic and hard-working
official sharpened the attention which Pitt bestowed on naval affairs.
We know from the notes of Sir T. Byam Martin that Pitt frequently
visited the Navy Office in order to discuss business details with the
Comptroller, and by his commanding ability left the impression that he
might have been all his life engaged on naval affairs. In particular he
used to inspect the reports of the building and repairing of the ships-of-
the-line.—“He also (wrote Martin) desired to have a periodical
statement from the Comptroller of the state of the fleet, wisely holding
that officer responsible personally to him without any regard to the
Board.” The results of this impulse given by one master mind were
speedily seen. More work was got out of the dockyards, and twenty-
four new sail-of-the-line were forthcoming from private yards in the
years 1783–1790. Thus, by the time of the Spanish war-scare in 1790,
284
ninety-three line-of-battle ships were ready for commission. The
crises of the years 1786–1788 had also been so serious that they
might speedily have led to war had not Britain’s first line of defence
been invincible.
In regard to the proposal to strengthen the defences of Portsmouth
and Plymouth, Pitt was less fortunate. The proposal really came from
the Duke of Richmond, Master of the Ordnance, who was far from
popular—a fact which perhaps influenced the votes of members.
Though Pitt and other Ministers adduced excellent reasons for not
leaving those vital points in their present weak state, he did not carry
the House of Commons with him. After an exciting debate, which
lasted till 7 a.m. of 28th February 1786, the numbers on a division
were found to be exactly equal. Then there arose a shout such as had
not been heard since the memorable vote which wrecked Lord North’s
Ministry. At once all eyes turned to the Speaker, Cornwall. He declared
that he was too exhausted to give his reasons for his vote, but he
would merely declare that the “Noes” had it. Wraxall states that the
sense of the House was against Pitt, the country gentlemen especially
285
disliking the addition of £700,000 to the next year’s expenses. One
of the arguments of the Opposition seems to us curious. It was urged
that the fortification of the two towns in question might be the
beginning of a despotic system which would undermine the liberties of
Englishmen. While treating this argument with the contempt it
deserved, Pitt declared that he bowed before the feeling of the House.
The commencement of huge works at Cherbourg later in the year must
have caused qualms even to the watch-dogs of the constitution.
Some of the more eager Whigs called out for him to resign, it being
the third time in twenty-two months that he had failed to carry an
important measure. We may, however, point out that the proposal
emanated from the Duke of Richmond; and there is the curious fact
that Courtenay during the debate of 20th March 1789 asserted that the
plan was merely the Duke’s, and had not come from the Royal
286
Engineers. He was also not contradicted. Further, it should be
noticed that though Pitt made the proposal his own, Dundas and
others of his Cabinet were known to dislike it. There is the final
consideration already dwelt on, that the custom which requires a
Ministry to resign on the rejection of any important measure, had not
yet crystallized into a rule.
This was the last severe check which Pitt sustained in Parliament
for many years. The fact that he suffered as many as three in twenty-
two months with little or no diminution of prestige shows that his
majority really trusted him and had no desire to put Fox and North in
power. That alternative was out of the question, as Fox knew, even
when he twitted his rival with being kept in office solely by the royal
favour.
Nevertheless in the years following 1785 we notice a distinct
weakening in Pitt’s progressive tendencies. Whig though he was in his
inmost convictions, he drifted slowly but surely towards the Tory
position. Fortunately for him, the folly of his rivals in the year 1784, and
again in the Regency crisis of 1788–9, enabled him to link the cause of
the King with that of the nation. But these occasions were exceptional.
It is never safe to owe a triumph to the mistakes of opponents amidst
unusual conditions. For mistakes will be made good; and in the whirl of
life circumstances will arise which range men and parties according to
elemental principles.
* * * * *
Even before the French Revolution tested the strength of Pitt’s
reforming convictions, there came a question which acted as a
touchstone. This was the proposal to repeal the Corporation and Test
Acts of the reign of Charles II. Those measures had excluded from
office in Corporations, or under Government, all who would not receive
the Sacrament according to the rites of the Church of England. By this
ban a large body of intelligent and loyal citizens were thrust out of the
pale of political and civic preferment; and though the Toleration Act and
Annual Acts of Indemnity screened them from actual persecution, their
position was yet one of hardship. Certain bodies had not scrupled to
make money out of their conscientious objections. As is well known,
the Corporation of the City of London hit upon the plan of augmenting
the building fund of their new Mansion House by passing a by-law in
1748 fining any Londoner who refused to serve when presented for
nomination as Sheriff, and then proposing rich Nonconformists for that
office. Not until 1767 did the able pronouncement of Lord Mansfield in
the Upper House secure the rejection of this odious device.
Thenceforth Nonconformists secured immunity from fines for refusing
to serve in offices that were barred by the test of the Sacrament.
Nevertheless their position was far from enviable. By the freaks of
insular logic Protestant Dissenters were allowed to vote in
parliamentary elections and even to sit in the House of Commons; but
though they had a share in the making and amending of laws, they
could hold no office in a Corporation, or any of the great London
Companies; commissions in the army, navy, and offices in other public
services were also legally closed to them. Severe penalties hung over
the head of any one who, in reliance on the annual Act of Indemnity,
ventured to infringe any of these singular enactments. Public opinion
approved this exclusiveness; and an anecdote told of that humorous
mass of intolerance, Dr. Johnson, shows that prejudice was still keen
in the circles which he frequented. He, Sir Robert Chambers, and John
Scott (the future Lord Eldon), were walking in the gardens of New Inn
Hall at Oxford, when Chambers began picking up snails and throwing
them into the next garden. Johnson sharply rebuked him for this
boorish act, until there came the soothing explanation that the
neighbour was a Dissenter.—“Oh,” said the Doctor, “if so, Chambers,
287
toss away, toss away as hard as you can.”
The choice blend of Anglicanism and culture discernible in
Chambers and Johnson, might be seen elsewhere than in the seat of
learning on the Isis. It was the rule in the rural districts, except among
the sturdy yeomen of the Eastern Counties, where the spirit that fought
at Naseby had so far survived as to render snail-throwing a pastime of
doubtful expediency. The same remark applies to London, where the
tactics of the city fathers had signally failed to suppress Dissent. Very
many churchmen were ashamed of these petty attempts at
persecution, and the progress of the Evangelical revival aroused a
feeling of uneasiness at seeing the most sacred rite of the Church
degraded into a political shibboleth. Comprehension within the bosom
of Mother Church was highly desirable; but clearly it might be too
dearly purchased by Erastian laws which enabled a lax Nonconformist
to buy his way into the Customs or Excise by presenting himself at the
altar of the nearest church along with convinced communicants.
Accordingly Nonconformists had a strong body of opinion on their
side in the session of 1787, when they asked for the repeal of those
exclusive statutes. A staunch churchman, Mr. Beaufoy, championed
their cause in a very powerful and eloquent speech, which won the
288
admiration of Wraxall. Beaufoy dwelt on the anomaly of retaining
this old-world exclusiveness, which would expose to the penalties of
the law the illustrious John Howard, if ever he returned to this country.
He showed that no danger need be apprehended for the Established
Church, especially as the Act of Supremacy would continue to exclude
from office all Roman Catholics, as well as Quakers. Further, the
loyalty of the Protestant Dissenters had been sufficiently shown in the
election of 1784, when they voted with Pitt on behalf of the
prerogatives of the Crown. He then inveighed against the continuance
of enactments which “degraded the altar into a qualification-desk for
tax-gatherers and public extortioners.” Fox followed with a strong plea
for religious toleration, quoting Locke and other writers who denounced
the imposition of religious tests in political matters. The Church of
England, said the Whig leader, was disgraced by the present state of
things; and, seeing that it represented the majority of the English
people, it could not be endangered by the proposed change.
On the other hand North, now quite blind, came into the House
leaning on his son, Colonel North, in order to oppose the motion.
Speaking with much earnestness, he declared that the Test and
Corporation Acts were the bulwarks of our Constitution. Pitt must have
felt some surprise at speaking on the same side as North; but he now
asserted that those Acts did not impose any stigma or penalty on
Nonconformists, for whom, indeed, he had a great respect. There must
be a Church Establishment, and it of necessity implied some
restrictions on those outside its pale. The constitution of Society
involved limitations of individual rights; and he averred that the laws in
question were justified by that consideration. Further, there were no
means whereby moderate Dissenters could be admitted to these
privileges while the more violent were excluded. If all were admitted,
they might overthrow the outworks of the Establishment. These
arguments carried the day by one hundred and seventy-six votes to
289
ninety-eight (28th March 1787).
Bishop Watson, of Llandaff, in his “Reminiscences,” explains Pitt’s
conduct on this occasion. He declares that the Chancellor of the
Exchequer had no strong feelings of his own on the subject, and had
therefore referred the matter to the Archbishop of Canterbury. The
Primate had assembled his colleagues at Lambeth, and by ten votes to
two they had decided to uphold the Caroline enactments. If this be
correct, Pitt’s action was weak. Certainly his speech was half-hearted,
and utterly different in tone from his orations on Reform, the Regency,
Slavery, and other topics which moved him deeply. Moreover, the
referring a matter of this kind to the bench of bishops was about as
reasonable as taking the opinion of country squires on a proposed
mitigation of the Game Laws, or of college dons on a reform of their
university. A Prime Minister abdicates his functions when he defers to
the opinions of a class respecting a proposal which will trench on its
prerogatives.
CHAPTER X
INDIA
“We hold ourselves bound to the natives of our Indian territory

by the same obligations of duty which bind us to all our other
subjects.”—(Proclamation of Queen Victoria, 1st November 1858.)
M ONTAIGNE once uttered a protest against those historians who

“chew the mouthfuls for us,” and spoil all in the process. He
coupled with it, however, another vice which is really far more serious,
namely, their habit of laying down rules for judging, and “for bending
history to their fancy.” As for the presenting history in mouthfuls, it is
probably the only way of making it digestible except for those mighty
intellects which seize facts and figures with avidity, and assimilate
them as if by magic.
Further, the modern historian may urge in defence of the topical
method that it is the only practicable way of dealing with the infinity of
topics of the last two centuries, ranging over parliamentary debates
and wars, finance and social gossip, mean intrigues and philanthropic
movements, industrial changes and empire-building, the efforts of
great men and the impersonal forces that mould and move great
nations, together with the denuding agencies that weather away the
old surface and the resistless powers that thrust up a new world. How
shall a finite intellect grasp at once all the moving details of this varied
life? The mind craves to consider at any one time only one part of the
majestic procession, just as it demands that the facts of Nature shall
be grasped under different sciences. Human life is one as Nature is
one; but the division in each case is necessitated by the increasing
width of man’s outlook. All that is essential in the sorting-out process is
that it shall honestly set forth all the important facts, and here and
there open out vistas revealing the connection with other fields of
human activity. In short, history can no longer be a detailed panorama
of life, but it can and ought to be a series of companion pictures,
informed by the personality of the artist and devoid of conscious
prejudice.
Among the diverse subjects which confront us in the many-sided
career of Pitt, none stands more apart than that of his relations to
India. Of his Herculean labours we may, perhaps, term this one the
cleansing of the Augean stables. The corruption that clung about the
Indian Government, the baffling remoteness of its duties, the singular
relations of the East India Company to the Crown, and of its own
officials to it, above all, the storms of passion which had been aroused
by the masterful dealings of Warren Hastings and the furious
invectives of Burke, presented a problem which could not be solved
save by the exercise of insight, patience, and wise forcefulness. It
would greatly overburden this narrative to recount the signal services,
albeit marred by deeds of severity and injustice, whereby Hastings
grappled with the Mahratta War and the incursion of Hyder Ali into the
Carnatic. All that need be remembered here is that Parliament had
censured some of his actions and demanded his recall, that the Court
of Directors of the Company had endorsed that demand, but that the
Court of Proprietors had annulled it. Hastings therefore remained at his
post, mainly, it would appear, from a conviction that he alone could
safeguard British supremacy.
Accordingly, on this all-important question there was division in the
executive powers at Calcutta, and in the East India Company itself;
while the insubordination of very many of the Company’s servants in
India further revealed the insufficiency of Lord North’s Regulating Act
of 1773. Fortunately, however, the finances of the Company were in
such disorder as to make it amenable to pressure from Westminster. It
owed a very large sum to the Home Government for duties on its
imports into Great Britain; and Parliament was thus the better able to
assert the supremacy of the nation.
It was high time to make good this claim. The India Bills of Fox and
of Pitt had been thrown out; and thus, despite an infinity of talk, the
whole situation remained unchanged, except that nearly every one
now agreed that it must be changed. On questions of detail opinions
differed widely. Some of the proprietors and Directors of the Company

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Statistics in Clinical and Observational

Vaccine Studies 2nd Edition Jozef

Replication and Evidence Factors in Observational

Foreign Ministries and the Information Revolution Going

Vaccine Safety Manual 2nd Edition Neil Z. Miller

Studies in Extended Metapsychology: Clinical

Handbook for Clinical Research Design Statistics and

mRNA Vaccine Toxicity Michael Palmer

Post Genomic Approaches in Drug and Vaccine Development

Questions and Answers Part 4 1st Edition Jozef Rulof

More information about this series at http://www.springer.com/series/15122

ISSN 2366-8695 ISSN 2366-8709 (electronic)

1st edition: © Springer-Verlag Berlin Heidelberg 2011

April 2018 Jozef Nauta

Part I The Interplay Between Microorganisms and the Immune

Part II Analysis of Immunogenicity Data

3.2.1 Single Vaccine Group . . . . . . . . . . . . . . . . . . . . . .... 27

6.2.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Part III Vaccine Field Studies

8.2.3 Cox Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

Part IV Correlates of Protection

Part V Analysis of Vaccine Safety Data

Appendix A: SAS and Floating-Point Format

Appendix C: Proof of Inequality (3.17) . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

Appendix H: SAS Code to Generate the Data Set COHORTS . . . . . . . . 211

AAP American Academy of Pediatrics

HAI Haemagglutination inhibition

In this book, population parameters and parameters of distributions are notated by

l Mean of a normal (Gaussian) distribution

RD Rate difference, est. of a risk difference

When the function is applied, an estimate of a parameter is obtained, for example:

Occasionally, estimators and estimates are notated by a ‘hooded’ parameter: l ^, ^

1.1 Vaccination and Preventing Infectious Diseases

1.2 Microorganisms: Bacteria, Yeasts, Protozoa and

1.3 The Immune System

1.3.2 Microbial Clearance

Virus clearance or elimination of a virus infection involves killing of infected cells

1.3.3 Active and Passive Protection from Infectious Diseases

1.3.4 Antigenic Variation

A serotype is a variant of a microorganism in which the antigenic variations are

Hermann Robert Koch (1843–1910), who isolated Bacillus anthracis, Vibrio

1.4.1 Viral and Bacterial Vaccines Currently in Use

1.4.2 Routes of Administration

1.4.3 Leaky Vaccines Versus All-or-Nothing Vaccines

1.4.4 Malaria Vaccines

1.4.5 Experimental Prophylactic and Therapeutic Vaccines

Some recent developments in vaccine research, still in an experimental stage in animal

2.1 Humoral Immunity

2.1.1 Antibody Titres and Antibody Concentrations

2.1.2 Two Assays for Humoral Immunity

Some viruses—influenza, measles and rubella, amongst others—carry on their

2.2 Cellular Immunity

Cellular immunity (also cell-mediated immunity (CMI)) is an adaptive immune

There is an ancient proverb, popularized by Spanish novelist Cervantes in his Don

3.2 Geometric Mean Titres and Concentrations

Distributions of post-vaccination humoral and cellular immunogenicity values tend

The standard statistics to summarize immunogenicity values is the geometric mean

ui = log2 [ti /(D/2)]. (3.1)

GMT = 4 × 2(1+1+2+3+4)/5 = 18.379.