Preface |
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xvii | |
Authors |
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xix | |
Glossary of Notation |
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xxi | |
Part A: Basic Concepts |
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1.1.1 Randomising Clusters |
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2 Variability between Clusters |
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2.2 The Implications of Between-cluster Variability: Some Examples |
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2.3 Measures of Between-cluster Variability |
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2.3.1.1 Binary Outcomes and Proportions |
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2.3.1.2 Event Data and Person-years Rates |
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2.3.1.3 Quantitative Outcomes and Means |
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2.3.2 Coefficient of Variation, k |
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2.3.3 Intracluster Correlation Coefficient, ρ |
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2.3.3.1 Quantitative Outcomes |
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2.3.4 Relationship between k and ρ |
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2.4.2 Quantitative Outcomes |
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2.5 Sources of Within-cluster Correlation |
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2.5.1 Clustering of Population Characteristics |
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2.5.2 Variations in Response to Intervention |
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2.5.3 Correlation Due to Interaction between Individuals |
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3 Choosing Whether to Randomise by Cluster |
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3.2 Rationale for Cluster Randomisation |
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3.2.1 Type of Intervention |
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3.2.2 Logistical Convenience and Acceptability |
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3.3 Using Cluster Randomisation to Capture Indirect Effects of Intervention |
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3.3.2 Effects of an Intervention on Infectiousness |
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3.3.3 Mass Effects of Intervention |
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3.3.4 Direct, Indirect, Total and Overall Effects |
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3.4 Disadvantages and Limitations of Cluster Randomisation |
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3.4.3 Imbalances between Study Arms |
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Part B: Design Issues |
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4.2.1 Geographical Clusters |
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4.2.1.2 Administrative Units |
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4.2.1.3 Arbitrary Geographical Zones |
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4.2.2 Institutional Clusters |
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4.2.3.1 Households and Other Small Groups |
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4.2.3.2 Individuals as Clusters |
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4.3.2 Statistical Considerations |
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4.3.4.1 Contacts between Intervention and Control Clusters |
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4.3.4.2 Contacts between Intervention Clusters and the Wider Population |
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4.3.4.3 Contacts between Control Clusters and the Wider Population |
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4.3.4.4 Effects of Cluster Size on Contamination |
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4.3.5 Transmission Zones of Infectious Diseases |
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4.4 Strategies to Reduce Contamination |
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4.4.1 Separation of Clusters |
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4.4.3 The Fried Egg Design |
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4.5 Levels of Randomisation, Intervention, Data Collection and Inference |
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5 Matching and Stratification |
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5.2 Rationale for Matching |
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5.2.1 Avoiding Imbalance between Treatment Arms |
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5.2.2 Improving Study Power and Precision |
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5.3 Disadvantages of Matching |
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5.3.1 Loss of Degrees of Freedom |
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5.3.2 Drop-out of Clusters |
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5.3.3 Limitations in Statistical Inference for Matched Trials |
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5.3.3.1 Adjustment for Covariates |
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5.3.3.2 Testing for Variation in Intervention Effect |
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5.3.3.3 Estimation of Intracluster Correlation Coefficient and Coefficient of Variation |
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5.4 Stratification as an Alternative to Matching |
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5.5 Choice of Matching Variables |
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5.5.1 Estimating the Matching Correlation |
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5.5.2 Matching on Baseline Values of Endpoint of Interest |
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5.5.3 Matching on Surrogate Variables |
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5.5.4 Matching on Multiple Variables |
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5.5.5 Matching on Location |
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5.6 Choosing Whether to Match or Stratify |
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5.6.2 Trials with a Small Number of Clusters |
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5.6.3 Trials with a Larger Number of Clusters |
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6 Randomisation Procedures |
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6.2 Restricted Randomisation |
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6.2.2 Using Restricted Randomisation to Achieve Overall Balance |
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6.2.4 Validity of Restricted Randomisation |
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6.2.5 Restricted Randomisation with More than Two Treatment Arms |
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6.3 Some Practical Aspects of Randomisation |
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6.3.1 Concealment of Allocation |
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6.3.2 Public Randomisation |
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7.2 Sample Size for Unmatched Trials |
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7.2.4 Variable Sample Size per Cluster |
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7.2.5 Sample Size Calculations Based on Intracluster Correlation Coefficient |
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7.3 Sample Size for Matched and Stratified Trials |
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7.4 Estimating the Between-cluster Coefficient of Variation |
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7.4.2 Matched and Stratified Trials |
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7.4.2.2 Proportions and Means |
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7.5 Choice of Sample Size in each Cluster |
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7.6 Further Issues in Sample Size Calculation |
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7.6.1 Trials with More than Two Treatment Arms |
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7.6.2 Trials with Treatment Arms of Unequal Size |
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7.6.4 Power and Precision |
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7.6.5 Assumptions about Intervention Effects |
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8 Alternative Study Designs |
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8.2 Design Choices for Treatment Arms |
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8.2.1 Trials with Several Treatment Arms |
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8.2.2.1 Independent Effects |
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8.2.2.2 Non-independent Effects |
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8.2.4 Stepped Wedge Design |
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8.3 Design Choices for Impact Evaluation |
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8.3.2 Repeated Cross-sectional Samples |
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Part C: Analytical Methods |
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9 Basic Principles of Analysis |
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9.2 Experimental and Observational Units |
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9.3 Parameters of Interest |
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9.3.2.1 Cluster-specific Odds Ratio |
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9.3.2.2 Population-average Odds Ratio |
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9.3.4 More Complex Parameters |
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9.4 Approaches to Analysis |
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9.4.1 Cluster-level Analysis |
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9.4.2 Individual-level Analysis |
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10 Analysis Based on Cluster-level Summaries |
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10.2 Point Estimates of Intervention Effects |
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10.2.1 Point Estimates Based on Cluster Summaries |
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10.2.2 Point Estimates Based on Individual Values |
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10.2.3 Using the Logarithmic Transformation |
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10.3 Statistical Inference Based on the t Distribution |
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10.3.2 Confidence Intervals Based on Cluster Summaries |
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10.3.4 Using the Logarithmic Transformation |
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10.3.5 The Weighted t-test |
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10.4 Statistical Inference Based on a Quasi-likelihood Approach |
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10.5 Adjusting for Covariates |
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10.5.1 Stage 1: Obtaining Covariate-adjusted Residuals |
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10.5.2 Stage 2: Using the Covariate-adjusted Residuals |
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10.5.2.1 Ratio Measures of Effect |
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10.5.2.2 Difference Measures of Effect |
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10.6 Nonparametric Methods |
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10.7 Analysing for Effect Modification |
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11 Regression Analysis Based on Individual-level Data |
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11.2 Random Effects Models |
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11.2.1 Poisson and Cox Regressions with Random Effects |
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11.2.1.1 Poisson Regression with Random Effects |
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11.2.1.2 Cox Regression with Random Effects |
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11.2.2 Mixed Effects Linear Regression |
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11.2.3 Logistic Regression with Random Effects |
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11.3 Generalised Estimating Equations |
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11.3.1 GEE Models for Binary Data |
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11.3.2 GEE for Other Types of Outcome |
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11.4 Choice of Analytical Method |
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11.4.1 Small Numbers of Clusters |
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11.4.2 Larger Numbers of Clusters |
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11.5 Analysing for Effect Moditication |
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11.6 More Complex Analyses |
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11.6.1 Controlling for Baseline Values |
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11.6.2 Repeated Measures during Follow-up |
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12 Analysis of Trials with More Complex Designs |
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12.2 Analysis of Pair-matched Trials |
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12.2.2 Analysis Based on Cluster-level Summaries |
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12.2.3 Adjusting for Covariates |
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12.2.4 Regression Analysis Based on Individual-level Data |
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12.3 Analysis of Stratified Trials |
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12.3.2 Analysis Based on Cluster-level Summaries |
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12.3.3 Regression Analysis Based on Individual-level Data |
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12.4 Analysis of Other Study Designs |
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12.4.1 Trials with More than Two Treatment Arms |
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12.4.3 Stepped Wedge Trials |
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Part D: Miscellaneous Topics |
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13 Ethical Considerations |
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13.3 Ethical Issues in Group Allocation |
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13.4 Informed Consent in Cluster Randomised Trials |
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13.4.1 Consent for Randomisation |
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13.4.1.1 Political Authorities |
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13.4.1.3 Community Representatives |
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13.4.1.4 Medical Practitioners |
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13.4.2 Consent for Participation |
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13.5 Other Ethical Issues |
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13.5.1 Scientific Validity |
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13.5.2 Phased Intervention Designs |
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14.2 Data Monitoring Committees |
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14.2.1 Review of DMC Responsibilities |
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14.2.2 When Are DMCs Necessary for CRTs? |
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14.2.2.1 Likelihood of Adverse Events |
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14.2.2.2 Seriousness or Severity of Outcome Measures |
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14.2.2.3 Timing of Data Collection |
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14.2.3 Monitoring for Adverse Events |
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14.2.4 Monitoring for Efficacy |
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14.2.5 Monitoring Adequacy of Sample Size |
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14.2.6 Assessing Comparability of Treatment Arms |
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14.2.7 Approving the Analytical Plan |
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14.2.8 Presentation of Data to the DMC |
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14.3.2 Timing of Interim Analyses |
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14.3.4 Disadvantages of Premature Stopping |
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15 Reporting and Interpretation |
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15.2 Reporting of Cluster Randomised Trials |
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15.2.1.1 Extended CONSORT Statement |
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15.2.1.2 Publication Bias |
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15.2.2 Reporting of Methods |
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15.2.2.1 Rationale for Cluster Randomisation |
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15.2.2.2 Description of Clusters and Interventions |
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15.2.2.4 Matching, Stratification and Randomisation |
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15.2.2.5 Blinding and Allocation Concealment |
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15.2.2.6 Definition of Primary Endpoints |
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15.2.2.7 Statistical Methods |
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15.2.3 Reporting of Results |
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15.2.3.2 Baseline Comparisons |
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15.2.3.3 Analysis of Endpoints |
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15.2.3.4 Subgroup Analyses |
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15.2.3.6 Estimates of Between-cluster Variability |
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15.3 Interpretation and Generalisability |
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15.3.3 Systematic Reviews |
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References |
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Index |
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