Design and Analysis of Vaccine Studies (eBook)

Preface 6
Contents 9
1 Introduction and Examples 17
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
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
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
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
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
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
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 outbreak in Burundi 155
7.2.4 Model selection in low-dose challenge studies 156
7.3 Estimating Waning Efficacy 157
7.3.1 Waning efficacy in the cholera vaccine trial 158
7.3.2 Nonparametric estimation of time-varying vaccine effects 159
7.3.3 Other approaches to estimate waning 162
7.4 Summary Strategy for Estimating Protective Effects 163
7.4.1 Interpretation of measures 164
Problems 165
8 Further Evaluation of Protective Effects 166
8.1 Case-Control Studies 166
8.1.1 Choosing controls to estimate VES,IR (VES,) 168
8.1.2 Choosing controls with leaky and all-or-none models 170
8.1.3 Choosing controls from the nondiseased population 171
8.1.4 Estimating VES using the screening method 172
8.2 Validation Sets for Outcomes 172
8.2.1 Influenza vaccine field study in central Texas 173
8.2.2 Analysis using surveillance samples 174
8.3 Sensitivity Analysis for Selection Bias 176
8.3.1 Sensitivity analysis in the vaccine study 177
8.3.1.1 Vaccine Efficacy 177
8.3.1.2 Identification of Px[Y(z)=1] 178
8.3.2 Frequentist sensitivity analysis 178
8.3.3 Bayesian inference 180
8.3.3.1 Informative priors 181
8.4 Validation Sets with Time-to-Event Data 183
8.4.1 Time-to-event analysis 184
8.5 Assessing Differential Protection Against Variants 187
Problems 188
9 Vaccine Effects on Post-Infection Outcomes 189
9.1 Scientific Questions of Interest 189
9.1.1 Different measures of VEP 189
9.1.2 Vaccine effects on dichotomous post-infection outcomes 191
9.1.2.1 Relation of VEP, VES, and VESP 192
9.1.3 Statistical validity and VEP 193
9.2 Effect of Vaccination on Disease Severity 193
9.2.1 Global score of disease severity 194
9.2.2 VEP for severity of pertussis disease 195
9.2.3 Rotavirus vaccine in Finland 196
9.3 Causal Effects on Post-Infection Outcomes 197
9.3.1 Post-infection selection bias 197
9.3.2 Defining causal estimands for post-infection outcomes 199
9.4 Causal Effects for Binary Post-Infection Outcomes 204
9.4.1 Parameterization 205
9.4.2 Estimation 206
9.4.3 Applications 208
9.4.3.1 Rotavirus candidate vaccine 208
9.4.3.2 Pertussis vaccine 209
9.4.4 Selection bias models 209
9.4.4.1 No selection bias 210
9.4.4.2 Upper and lower bounds 210
9.4.4.3 Sensitivity analysis for selection bias 211
9.4.4.4 Log odds ratio of infection 211
9.4.4.5 Conditioning on 1 as the sensitivity analysis parameter 212
9.4.4.6 Complete data model 212
9.4.4.7 Statistical variability 213
9.4.4.8 Applications, continued 213
9.4.4.9 Rotavirus candidate vaccine 213
9.4.4.10 Pertussis vaccine 214
Problems 214
10 Household-Based Studies 216
10.1 Concepts of Household Studies 216
10.2 Pertussis Vaccination 218
10.2.1 History 218
10.2.2 Michigan, USA 219
10.2.3 Niakhar, Senegal 220
10.2.4 England 222
10.2.5 Sweden 225
10.3 Influenza 225
10.3.1 Seattle USA 226
10.3.2 Tecumseh, USA 227
10.3.3 Cleveland, USA 228
10.3.4 Influenza Epigrippe, France 229
10.3.5 Influenza antivirals 230
10.4 Measles Vaccination 231
10.4.1 Niakhar, Senegal 232
10.5 Pneumococcal Carriage Studies 233
10.5.1 Finland 234
10.5.2 France 235
10.5.3 United Kingdom 235
10.5.4 Bangladesh 236
10.6 Design Considerations 237
10.6.1 Transmission units and contacts 237
10.6.2 Ascertainment 238
10.6.3 Case definition 240
10.6.4 Data structure 240
10.6.5 Assignment mechanism 240
10.7 Related Designs 242
10.7.1 Case-contact design 242
10.7.2 Cluster designs 242
10.7.3 Susceptibles exposed to infective contacts 243
10.7.4 Augmented vaccine studies 243
10.7.5 Mini-community designs 244
Problems 245
11 Analysis of Households in Communities 246
11.1 Overview 246
11.1.0.1 Discrete-time model 247
11.1.0.2 Continuous-time model 247
11.1.0.3 Vaccine effects and other covariates 247
11.1.0.4 Estimation 248
11.2 Final-Value Data 249
11.2.1 Discrete-time model 249
11.2.1.1 Final-size distribution 250
11.2.1.2 Likelihood Estimation 251
11.2.1.3 Analysis of data from an Asian influenza epidemic 252
11.2.1.4 Extension to covariates 253
11.2.1.5 Using Markov chain Monte Carlo methods 254
11.2.2 Generalized stochastic model 254
11.2.3 Other final-value analyses 255
11.3 Time-of-Onset Data 256
11.3.1 Likelihood approach 256
11.3.1.1 Notation and escape probabilities 257
11.3.2 Bayesian latent variable approach 258
11.3.3 Other time-of-onset analyses 259
11.4 Longitudinal Data 260
11.4.1 Bayesian latent variable approach 261
11.4.2 Markov transition model 264
Problems 266
12 Analysis of Independent Households 268
12.1 Introduction 268
12.2 Conventional SAR Analysis 268
12.2.1 Vaccine efficacy from conventional SAR 270
12.3 SAR Analysis Taking Correlation into Account 271
12.3.1 Notation 272
12.3.2 Vaccine efficacy based on the logistic model 273
12.3.2.1 The marginal model 273
12.3.2.2 The random-effects model 274
12.3.3 Pertussis vacccine efficacy 276
12.3.4 Varying case definition and cutoff 277
12.4 Estimating Influenza Antiviral Efficacies 278
12.5 Mini-Community Design for Indirect Effects 278
12.5.1 Pertussis 279
Problems 279
13 Assessing Indirect, Total, and Overall Effects 282
13.1 Study Designs for Dependent Happenings 282
13.1.1 Definitions and study designs 283
13.2 Observational Studies 285
13.2.1 Pre- and post-vaccination comparisons 285
13.2.2 Pertussis 286
13.2.2.1 Pertussis in Niakhar, Senegal 286
13.2.2.2 Pertussis in England and Wales 288
13.2.3 Pneumococcal vaccine in Alaska 289
13.2.4 Meningococcal vaccine in the United Kingdom 291
13.2.5 Cholera vaccine in Bangladesh 291
13.2.6 Drawbacks of nonrandomized evaluation 293
13.3 Group-Randomized Studies 294
13.3.1 Scientific or public health question of interest 295
13.3.2 Choice of group-level randomization unit 296
13.3.3 Sources of transmission 297
13.3.4 Designs and randomization schemes 297
13.3.5 Other design considerations 299
13.3.5.1 Study population, vaccines, and vaccination strategy 299
13.3.5.2 Case ascertainment and clinical endpoints 300
13.4 Parallel and Stepped Wedge Designs 302
13.4.1 Parallel designs 302
13.4.2 Parallel pneumoccocal vaccine study 302
13.4.3 Stepped wedge designs 303
13.4.4 The Gambia Hepatitis Intervention Study 304
13.5 Covariate-Constrained Randomization 306
13.5.1 Parallel design 306
13.5.1.1 Hypothetical dengue vaccine study 307
13.5.1.2 Hypothetical influenza vaccine study 308
13.5.2 Stepped wedge design 309
13.6 Power and Number of Communities 309
13.6.1 Sample size for parallel design 311
13.6.2 Coefficient of variation 312
13.6.3 Sample size for stepped wedge design 313
13.7 Analysis 314
13.7.1 Pneumococcal vaccine study 314
13.7.2 Other approaches 316
13.8 Causal Inference for Indirect, Total, and Overall Effects 317
13.8.1 General approach 317
13.8.2 Formalization 319
13.8.2.1 Treatment Assignment Mechanisms 319
13.8.2.2 Average potential outcomes 320
13.8.2.3 Causal estimands 320
13.8.2.4 Estimation and inference 321
Problems 322
14 Randomization and Baseline Transmission 324
14.1 Interpreting Efficacy Estimates 324
14.1.1 Malaria vaccine trials 325
14.2 Biologic Versus Outcome Efficacy 326
14.2.1 Principles of validity in vaccine studies 328
14.3 Randomization and Baseline Transmission 330
14.3.1 Stochastic risk model 331
14.3.1.1 Individual measures 331
14.3.1.2 Special role of exposure to infection 332
14.3.1.3 Population measures 332
14.3.2 Randomization and comparability of treatment groups 334
14.3.2.1 Limits of comparability with one homogeneous exposure to infection 335
14.3.2.2 Comparability-based confounding: Homogeneous effect two or more exposures to infection
14.3.2.3 Collapsibility with balance of unmeasured covariates 337
14.3.2.4 Collapsibility-based confounding 337
14.3.2.5 Heterogeneity of effect: Effect modification 338
14.3.3 Examples 338
14.3.3.1 C is post-vaccination challenge homogeneous VE
14.3.3.2 C is related to heterogeneous VE effect modification
14.3.3.3 C related to infection history: Pre-vaccination heterogeneity, heterogeneity of effect, boosting 342
14.3.3.4 C related to infection history: prevaccination heterogeneity, heterogeneity of effect, no boosting 343
14.3.3.5 Varying the proportion with covariate C, boosting or no boosting 344
14.3.3.6 Effect in naive susceptibles and boosting 345
14.3.3.7 Varying susceptibility, vaccine response and exposure to infection 346
14.3.4 Interpretation 346
15 Surrogates of Protection 348
15.1 Replacing Clinical Outcomes 348
15.1.1 Biological versus statistical issues 349
15.1.2 Exposure to infection 350
15.1.3 Statistical versus principal surrogates 351
15.2 Thresholds for Protection 352
15.3 Regression Models for Correlates 354
15.3.1 Regression models separating level of exposure 355
15.3.2 Household exposure as natural challenge 357
15.4 Framework for Confidence in a Biomarker 359
15.4.1 Correlates of risk 359
15.4.2 Surrogates of protection 360
15.5 Evaluating Principal Surrogate Endpoints 362
15.5.1 Set-up 362
15.5.2 Defining surrogates of protection 363
15.5.3 Causal effect predictiveness surface 364
15.5.4 Estimating the CEP surface 365
15.5.5 Augmented designs to assess immune response 366
15.6 Carriage as an Endpoint 366
Problems 367
Solutions 369
References 371
Index 390