Preface
Authors
Glossary of Notation
Section I Basic Concepts
1. Introduction
1.1 Randomised Trials
1.1.1 Randomising Clusters
1.1.2 Some Case Studies
1.1.3 Overview of Book
2. Variability between Clusters
2.1 Introduction
2.2 The Implications of Between-Cluster Variability: Some Examples
2.3 Measures of Between-Cluster Variability
2.3.1 Introduction
2.3.1.1 Binary Outcomes and Proportions
2.3.1.2 Event Data and Person-Years Rates
2.3.1.3 Quantitative Outcomes and Means
2.3.2 Coefficient of Variation,
k
2.3.3 Intracluster Correlation Coefficient, ρ
2.3.3.1 Quantitative Outcomes
2.3.3.2 Binary Outcomes
2.3.3.3 Estimation of ρ
2.3.4 Relationship between
k and ρ
2.4 The Design Effect
2.4.1 Binary Outcomes
2.4.2 Quantitative Outcomes
2.5 Sources of Within-Cluster Correlation
2.5.1 Clustering of Population Characteristics
2.5.2 Variations in Response to Intervention
2.5.3 Correlation due to Interaction between Individuals
3. Choosing Whether to Randomise by Cluster
3.1 Introduction
3.2 Rationale for Cluster Randomisation
3.2.1 Type of Intervention
3.2.2 Logistical Convenience and Acceptability
3.2.3 Contamination
3.3 Using Cluster Randomisation to Capture Indirect Effects of Intervention
3.3.1 Introduction
3.3.2 Effects of an Intervention on Infectiousness
3.3.3 Mass Effects of Intervention
3.3.4 Direct, Indirect, Total and Overall Effects
3.4 Disadvantages and Limitations of Cluster Randomisation
3.4.1 Efficiency
3.4.2 Selection Bias
3.4.3 Imbalances between Study Arms
3.4.4 Generalisability
Section II Design Issues
4. Choice of Clusters
4.1 Introduction
4.2 Types of Cluster
4.2.1 Geographical Clusters
4.2.1.1 Communities
4.2.1.2 Administrative Units
4.2.1.3 Arbitrary Geographical Zones
4.2.2 Institutional Clusters
4.2.2.1 Schools
4.2.2.2 Health Units
4.2.2.3 Workplaces
4.2.3 Smaller Clusters
4.2.3.1 Households and Other Small Groups
4.2.3.2 Network-Defined Clusters
4.2.3.3 Individuals as Clusters
4.3 Size of Clusters
4.3.1 Introduction
4.3.2 Statistical Considerations
4.3.3. Logistical Issues
4.3.4 Contamination
4.3.4.1 Contacts between Intervention and Control Clusters
4.3.4.2 Contacts between Intervention Clusters and the Wider Population
4.3.4.3 Contacts between Control Clusters and the Wider Population
4.3.4.4 Effects of Cluster Size on Contamination
4.3.5 Transmission Zones of Infectious Diseases
4.4 Strategies to Reduce Contamination
4.4.1 Separation of Clusters
4.4.2 Buffer Zones
4.4.3 The Fried Egg Design
4.4.4 Assessment of Contamination
4.5 Levels of Randomisation, Intervention, Data Collection and Inference
5. Matching and Stratification
5.1 Introduction
5.2 Rationale for Matching
5.2.1 Avoiding Imbalance between Treatment Arms
5.2.2 Improving Study Power and Precision
5.3 Disadvantages of Matching
5.3.1 Loss of Degrees of Freedom
5.3.2 Drop-Out of Clusters
5.3.3 Limitations in Statistical Inference for Matched Trials
5.3.3.1 Adjustment for Covariates
5.3.3.2 Testing for Variation in Intervention Effect
5.3.3.3 Estimation of Intracluster Correlation Coefficient and Coefficient of Variation
5.4 Stratification as an Alternative to Matching
5.5 Choice of Matching Variables
5.5.1 Estimating the Matching Correlation
5.5.2 Matching on Baseline Values of Endpoint of Interest
5.5.3 Matching on Surrogate Variables
5.5.4 Matching on Multiple Variables
5.5.5 Matching on Location
5.6 Formal Algorithms for Forming Matched Pairs and Strata
5.7 Choosing Whether to Match or Stratify
5.7.1 Introduction
5.7.2 Trials with a Small Number of Clusters
5.7.3 Trials with a Larger Number of Clusters
6. Randomisation Procedures
6.1 Introduction
6.2 Restricted Randomisation
6.2.1 Basic Principles
6.2.2 Using Restricted Randomisation to Achieve Overall Balance
6.2.3 Balance Criteria
6.2.4 Validity of Restricted Randomisation
6.2.5 Restricted Randomisation with More than Two Treatment Arms
6.2.6 Alternative Methods for Achieving Balance
6.3 Some Practical Aspects of Randomisation
6.3.1 Concealment of Allocation
6.3.2 Public Randomisation
7. Sample Size
7.1 Introduction
7.2 Sample Size for Unmatched Trials
7.2.1 Event Rates
7.2.2 Proportions
7.2.3 Means
7.2.3.1 Arbitrary Scales and/or Scales with Negative Values
7.2.4 Sample Size Calculations Based on Intracluster Correlation Coefficient
7.2.5 Variable Sample Size per Cluster
7.3 Sample Size for Matched and Stratified Trials
7.3.1 Matched Trials
7.3.1.1 Event Rates
7.3.1.2 Proportions
7.3.1.3 Means
7.3.2 Stratified Trials
7.4 Estimating the Between-Cluster Coefficient of Variation
7.4.1 Unmatched Trials
7.4.1.1 Event Rates
7.4.1.2 Proportions
7.4.1.3 Means
7.4.2 Matched and Stratified Trials
7.4.2.1 Event Rates
7.4.2.2 Proportions and Means
7.4.3 Alternative Approach to Estimating Between-Cluster Variation
7.5 Choice of Sample Size in Each Cluster
7.6 Further Issues in Sample Size Calculation
7.6.1 Trials with More than Two Treatment Arms
7.6.2 Trials with Treatment Arms of Unequal Size
7.6.3 Equivalence Trials
7.6.4 Power and Precision
7.6.5 Assumptions about Intervention Effects
7.6.6 Accounting for Baseline Covariates
7.6.7 Sample Size for Examining Interaction
8. Alternative Study Designs
8.1 Introduction
8.2 Design Choices for Treatment Arms
8.2.1 Trials with Several Treatment Arms
8.2.2 Factorial Trials
8.2.2.1 Independent Effects
8.2.2.2 Non-Independent Effects
8.2.3 Crossover Design
8.2.4 Stepped Wedge Design
8.2.4.1 Introduction
8.2.4.2 Efficiency
8.2.4.3 Design Variants
8.2.4.4 Interpretation Difficulties
8.2.5 Parallel Designs with Multiple Baselines
8.3 Design Choices for Impact Evaluation
8.3.1 Introduction
8.3.2 Repeated Cross-Sectional Samples
8.3.3 Cohort Follow-Up
Section III Analytical Methods
9. Basic Principles of Analysis
9.1 Introduction
9.2 Experimental and Observational Units
9.3 Parameters of Interest
9.3.1 Event Rates
9.3.2 Proportions
9.3.2.1 Cluster-Specific Odds Ratio
9.3.2.2 Population-Average Odds Ratio
9.3.3 Means
9.3.4 More Complex Parameters
9.4 Approaches to Analysis
9.4.1 Cluster-Level Analysis
9.4.2 Individual-Level Analysis
9.5 Baseline Analysis
10. Analysis Based on Cluster-Level Summaries
10.1 Introduction
10.2 Point Estimates of Intervention Effects
10.2.1 Point Estimates Based on Cluster Summaries
10.2.2 Point Estimates Based on Individual Values
10.2.3 Using the Logarithmic Transformation
10.2.4 Case Studies
10.3 Statistical Inference Based on the
t Distribution
10.3.1 Unpaired
t-Test
10.3.2 Confidence Intervals Based on Cluster Summaries
10.3.2.1 Rate Difference
10.3.2.2 Rate Ratio
10.3.3 Case Studies
10.3.4 Using the Logarithmic Transformation
10.3.5 The Weighted
t-Test
10.4 Statistical Inference Based on a Quasi-Likelihood Approach
10.5 Adjusting for Covariates
10.5.1 Stage 1: Obtaining Covariate-Adjusted Residuals
10.5.1.1 Event Rates
10.5.1.2 Proportions
10.5.1.3 Means
10.5.2 Stage 2: Using the Covariate-Adjusted Residuals
10.5.2.1 Ratio Measures of Effect
10.5.2.2 Difference Measures of Effect
10.5.3 Case Study
10.6 Analysis of Ordinal Outcomes
10.6.1 Introduction
10.6.2 Cluster Summaries Approach to the Ordinal Logit Model
10.6.3 Adjusting the Ordinal Logit Model for Covariates
10.6.4 Case Study
10.7 Nonparametric Methods
10.7.1 Introduction
10.7.2 Rank Sum Test
10.7.3 Permutation Tests
10.8 Analysing for Effect Modification
11. Regression Analysis Based on Individual-Level Data
11.1 Introduction
11.2 Random Effects Models
11.2.1 Poisson and Cox Regressions with Random Effects
11.2.1.1 Poisson Regression with Random Effects
11.2.1.2 Cox Regression with Random Effects
11.2.2 Mixed Effects Linear Regression
11.2.3 Logistic Regression with Random Effects
11.3 Generalised Estimating Equations
11.3.1 GEE Models for Binary Data
11.3.2 GEE for Other Types of Outcome
11.4 Choice of Analytical Method
11.4.1 Small Numbers of Clusters
11.4.2 Larger Numbers of Clusters
11.5 Analysing for Effect Modification
11.6 More Complex Analyses
11.6.1 Controlling for Baseline Values
11.6.2 Repeated Measures during Follow-Up
11.6.3 Repeated Episodes
12. Analysis of Trials with More Complex Designs
12.1 Introduction
12.2 Analysis of Pair-Matched Trials
12.2.1 Introduction
12.2.2 Analysis Based on Cluster-Level Summaries
12.2.3 Adjusting for Covariates
12.2.4 Regression Analysis Based on Individual-Level Data
12.3 Analysis of Stratified Trials
12.3.1 Introduction
12.3.2 Analysis Based on Cluster-Level Summaries
12.3.3 Regression Analysis Based on Individual-Level Data
12.4 Analysis of Other Study Designs
12.4.1 Trials with More than Two Treatment Arms
12.4.2 Factorial Trials
12.4.3 Stepped Wedge Trials
Section IV Miscellaneous Topics
13. Ethical Considerations
13.1 Introduction
13.2 General Principles
13.2.1 Beneficence
13.2.2 Equity
13.2.3 Autonomy
13.3 Ethical Issues in Group Allocation
13.4 Informed Consent in Cluster Randomised Trials
13.4.1 Consent for Randomisation
13.4.1.1 Political Authorities
13.4.1.2 Village Heads
13.4.1.3 Community Representatives
13.4.1.4 Medical Practitioners
13.4.2 Consent for Participation
13.5 Other Ethical Issues
13.5.1 Scientific Validity
13.5.2 Phased Intervention Designs
13.5.3 Trial Monitoring
13.5.4 Non-Participants in Clusters
13.6 Conclusion
14. Data Monitoring
14.1 Introduction
14.2 Data Monitoring Committees
14.2.1 Review of DMC Responsibilities
14.2.2 When are DMCs Necessary for CRTs?
14.2.2.1 Likelihood of Adverse Events
14.2.2.2 Seriousness or Severity of Outcome Measures
14.2.2.3 Timing of Data Collection
14.2.3 Monitoring for Adverse Events
14.2.4 Monitoring for Efficacy
14.2.5 Monitoring Adequacy of Sample Size
14.2.6 Assessing Comparability of Treatment Arms
14.2.7 Approving the Analytical Plan
14.2.8 Presentation of Data to the DMC
14.3 Interim Analyses
14.3.1 Introduction
14.3.2 Timing of Interim Analyses
14.3.3 Stopping Rules
14.3.3.1 Event Rates
14.3.3.2 Proportions
14.3.3.3 Means
14.3.4 Disadvantages of Premature Stopping
15. Reporting and Interpretation
15.1 Introduction
15.2 Reporting of Cluster Randomised Trials
15.2.1 Overview
15.2.1.1 Extended CONSORT Statement
15.2.1.2 Publication Bias
15.2.2 Reporting of Methods
15.2.2.1 Rationale for Cluster Randomisation
15.2.2.2 Description of Clusters and Interventions
15.2.2.3 Sample Size
15.2.2.4 Matching, Stratification and Randomisation
15.2.2.5 Blinding and Allocation Concealment
15.2.2.6 Definition of Primary Endpoints
15.2.2.7 Statistical Methods
15.2.3 Reporting of Results
15.2.3.1 Flow Diagram
15.2.3.2 Baseline Comparisons
15.2.3.3 Analysis of Endpoints
15.2.3.4 Data Display
15.2.3.5 Subgroup Analyses
15.2.3.6 Contamination
15.2.3.7 Estimates of Between-Cluster Variability
15.3 Interpretation and Generalisability
15.3.1 Interpretation
15.3.2 Generalisability
15.3.3 Systematic Reviews
References
Appendix
Index
