| Preface | 6 |
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| Contents | 9 |
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| 1 Introduction and Examples | 17 |
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| 1.1 The Need of Vaccine Studies Framework | 17 |
| 1.2 Scope and Outline of the Book | 23 |
| 1.3 Concepts in Infectious Disease Research | 26 |
| 1.3.1 Transmission | 26 |
| 1.3.2 Time line of infection | 27 |
| 1.3.3 Basic reproductive number, R0 and generation interval, Tg | 29 |
| 1.4 Causal Inference and Vaccine Effects | 31 |
| Problems | 33 |
| 2 Overview of Vaccine Effects and Study Designs | 35 |
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| 2.1 Introduction | 35 |
| 2.2 Vaccine Effects of Interest | 35 |
| 2.3 Vaccine Efficacy for Susceptibility, VES (VESP) | 37 |
| 2.3.1 VES conditional on knowledge of exposure to infection | 38 |
| 2.3.2 VES not conditional on knowledge of exposure to infection | 40 |
| 2.4 Hierarchy of VES Measures | 42 |
| 2.5 Vaccine Efficacy for Infectiousness, VEI | 43 |
| 2.5.1 Estimating multiple levels of parameters | 45 |
| 2.6 Vaccine Efficacy for Progression or Pathogenesis, VEP | 45 |
| 2.7 Contact Rates and Exposure Efficacy | 47 |
| 2.8 Indirect, Total, and Overall Effectiveness | 47 |
| 2.8.1 Hypothetical example | 49 |
| 2.8.2 Influenza example | 51 |
| 2.9 Counting Process Models for Hierarchy of Parameters | 51 |
| 2.9.1 Contact, infection, susceptibility, and infectiousness processes | 52 |
| 2.9.1.1 Overview | 52 |
| 2.9.1.2 Notation and definitions | 52 |
| 2.9.1.3 Intensities for contact processes | 53 |
| 2.9.1.4 Intensities for infection processes | 54 |
| 2.9.2 Information levels and types of statistical analyses | 54 |
| 2.9.2.1 Level I | 55 |
| 2.9.2.2 Level II | 56 |
| 2.9.2.3 Level III | 57 |
| 2.9.2.4 Level IV | 57 |
| 2.9.3 Homogeneous mixing | 59 |
| Problems | 59 |
| 3 Immunology and Early Phase Trials | 62 |
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| 3.1 Immunology and Infection | 63 |
| 3.1.1 Innate and adaptive immune systems | 63 |
| 3.1.2 Immune response to infection | 64 |
| 3.1.3 Antibodies and epitopes | 65 |
| 3.2 Vaccines | 66 |
| 3.2.1 Smallpox | 66 |
| 3.2.2 Early development | 67 |
| 3.2.3 Recent developments and beyond | 69 |
| 3.2.4 Adjuvants | 70 |
| 3.3 Vaccine Safety | 70 |
| 3.4 Immune Assays | 71 |
| 3.4.1 Antibody assays | 71 |
| 3.4.2 T-cell assays | 72 |
| 3.5 Herd Immunity | 73 |
| 3.6 Early Phase Vaccine Studies | 75 |
| 3.7 Human Challenge Studies | 76 |
| Problems | 76 |
| 4 Binomial and Stochastic Transmission Models | 78 |
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| 4.1 Overview | 78 |
| 4.2 Contact Processes and Mixing Structures | 79 |
| 4.2.1 Random mixing | 79 |
| 4.2.2 Transmission units within populations | 80 |
| 4.2.3 Mutually exclusive subpopulations | 81 |
| 4.2.4 Population dynamics | 82 |
| 4.3 Probability of Discrete Infection Events | 82 |
| 4.3.1 Probability of infection in discrete time or contacts | 82 |
| 4.3.2 Other transmission models | 84 |
| 4.3.3 Probability of infection in continuous time | 85 |
| 4.3.4 Contacts with persons of unknown infection status | 85 |
| 4.4 Chain Binomial Models | 86 |
| 4.4.1 The Reed–Frost model | 88 |
| 4.4.1.1 History | 90 |
| 4.4.2 The Greenwood model | 91 |
| 4.4.3 Stochastic realizations of the Reed–Frost model | 91 |
| 4.5 Stochastic Simulation Models | 93 |
| 4.5.1 Endemic cholera and vaccination | 94 |
| 4.5.2 Use in study design | 98 |
| Problems | 98 |
| 5 R0 and Deterministic Models | 100 |
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| 5.1 Basic Reproductive Number | 100 |
| 5.1.1 R0 and public health | 102 |
| 5.2 Vaccination and R0 | 102 |
| 5.2.1 The critical vaccination fraction and R0 | 103 |
| 5.2.2 R with VES and VEI | 105 |
| 5.2.3 R0 and influenza vaccination | 106 |
| 5.3 Other Aspects of R0 | 109 |
| 5.3.1 Evolution and R0 | 110 |
| 5.3.2 Estimating R0 in real-time | 111 |
| 5.3.3 Caveats | 111 |
| 5.4 Deterministic Transmission Models | 111 |
| 5.4.1 Simple deterministic SIR model | 112 |
| 5.4.2 Dynamics of an epidemic | 113 |
| 5.4.3 Other simple models | 114 |
| 5.4.4 Within host dynamics | 115 |
| 5.5 Modeling Vaccination Programs | 116 |
| Problems | 117 |
| 6 Evaluating Protective Effects of Vaccination | 118 |
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| 6.1 Overview | 118 |
| 6.2 Estimating VES | 119 |
| 6.2.1 Absolute versus relative efficacy | 120 |
| 6.2.2 Types of studies | 121 |
| 6.2.2.1 Randomized versus observational cohort studies | 122 |
| 6.2.3 Estimation and inference | 123 |
| 6.3 Design Considerations | 126 |
| 6.3.1 Vaccines and vaccination schedule | 126 |
| 6.3.2 Study population | 127 |
| 6.3.2.1 Recruitment and vaccination | 127 |
| 6.3.3 Case definition | 127 |
| 6.3.4 Ascertainment of cases | 127 |
| 6.3.4.1 Safety and Immunogenicity | 127 |
| 6.3.5 Sample size calculations | 128 |
| 6.4 Examples of Randomized Trials | 129 |
| 6.4.1 Relative efficacy of pertussis vaccines in Senegal | 129 |
| 6.4.2 Absolute efficacy of pertussis vaccine in Sweden | 131 |
| 6.4.3 Absolute efficacy of live attenuated influenza vaccine in children | 134 |
| 6.4.4 Live attenuated influenza vaccine in adults without biological confirmation | 135 |
| 6.4.5 Relative efficacy of live and killed influenza vaccine in young children | 137 |
| 6.4.6 Oral cholera vaccines in Bangladesh | 138 |
| 6.4.7 Pneumococcal conjugate vaccine in California | 140 |
| 6.5 Report of a Study | 141 |
| 6.6 Reduction in Burden of Illness | 142 |
| Problems | 144 |
| 7 Modes of Action and Time-Varying VES | 145 |
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| 7.1 Mode of Action and Choice of Measures | 145 |
| 7.1.1 Leaky and all-or-none modes of action | 146 |
| 7.1.2 Implications for choice of efficacy measures | 147 |
| 7.1.3 Attack rates versus transmission probabilities | 149 |
| 7.1.3.1 Example | 150 |
| 7.2 Frailty Mixture Models for VES, | 151 |
| 7.2.1 Mixing models | 151 |
| 7.2.2 Frailty model | 153 |
| 7.2.2.1 Statistical inference | 154 |
| 7.2.3 Measles out
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