Cluster Randomised Trials

326 Pages·2009·3.06 MB·English

by  Richard J. Hayes, Lawrence H. Moulton

CLUSTER
RANDOMISED
TRIALS
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CHAPMAN & HALL/CRC
Interdisciplinar y Statistics Series
Series editors: N. Keiding, B.J.T. Morgan, C.K. Wikle, P. van der Heijden
Published titles
AN INVARIANT APPROACH TO S. Lele and J. Richtsmeier
STATISTICAL ANALYSIS OF SHAPES
ASTROSTATISTICS G. Babu and E. Feigelson
BAYESIAN DISEASE MAPPING: Andrew B. Lawson
HIERARCHICAL MODELING IN SPATIAL
EPIDEMIOLOGY
BIOEQUIVALENCE AND S. Patterson and
STATISTICS IN CLINICAL B. Jones
PHARMACOLOGY
CLINICAL TRIALS IN ONCOLOGY J. Crowley, S. Green,
SECOND EDITION and J. Benedetti
CLUSTER RANDOMISED TRIALS R.J. Hayes and L.H. Moulton
CORRESPONDENCE ANALYSIS M. Greenacre
IN PRACTICE, SECOND EDITION
DESIGN AND ANALYSIS OF D.L. Fairclough
QUALITY OF LIFE STUDIES
IN CLINICAL TRIALS
DYNAMICAL SEARCH L. Pronzato, H. Wynn,
and A. Zhigljavsky
GENERALIZED LATENT VARIABLE A. Skrondal and
MODELING: MULTILEVEL, S. Rabe-Hesketh
LONGITUDINAL, AND STRUCTURAL
EQUATION MODELS
GRAPHICAL ANALYSIS OF K. Basford and J. Tukey
MULTI-RESPONSE DATA
INTRODUCTION TO M. Waterman
COMPUTATIONAL BIOLOGY:
MAPS, SEQUENCES, AND GENOMES
MARKOV CHAIN MONTE CARLO W. Gilks, S. Richardson,
IN PRACTICE and D. Spiegelhalter
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Published titles
MEASUREMENT ERROR AND P. Gustafson
MISCLASSIFICATION IN STATISTICS
AND EPIDEMIOLOGY: IMPACTS AND
BAYESIAN ADJUSTMENTS
META-ANALYSIS OF BINARY DATA D. Böhning, R. Kuhnert,
USING PROFILE LIKELIHOOD and S. Rattanasiri
STATISTICAL ANALYSIS OF GENE T. Speed
EXPRESSION MICROARRAY DATA
STATISTICAL AND COMPUTATIONAL R. Wu and M. Lin
PHARMACOGENOMICS
STATISTICS IN MUSICOLOGY J. Beran
STATISTICAL CONCEPTS J. Aitchison, J.W. Kay,
AND APPLICATIONS IN and I.J. Lauder
CLINICAL MEDICINE
STATISTICAL AND PROBABILISTIC P.J. Boland
METHODS IN ACTUARIAL SCIENCE
STATISTICAL DETECTION AND P. Rogerson and I. Yamada
SURVEILLANCE OF GEOGRAPHIC
CLUSTERS
STATISTICS FOR ENVIRONMENTAL A. Bailer and W. Piegorsch
BIOLOGY AND TOXICOLOGY
STATISTICS FOR FISSION R.F. Galbraith
TRACK ANALYSIS
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Chapman & Hall/CRC
Interdisciplinary Statistics Series
CLUSTER
RANDOMISED
TRIALS
Richard J. Hayes
Lawrence H. Moulton
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Library of Congress Cataloging-in-Publication Data
Hayes, Richard J., DSc.
Cluster randomised trials / authors, Richard J. Hayes and Lawrence H. Moulton.
p. ; cm. -- (Interdisciplinary statistics)
“A CRC title.”
Includes bibliographical references and index.
ISBN 978-1-58488-816-1 (hardcover : alk. paper)
1. Clinical trials. 2. Cluster analysis. I. Moulton, Lawrence H. II. Title. III. Series.
[DNLM: 1. Cluster Analysis. 2. Randomized Controlled Trials as Topic--methods. 3.
Data Interpretation, Statistical. WA 950 H418c 2009]
R853.C55H39 2009
615.5072’4--dc22 2008035804
Visit the Taylor & Francis Web site at
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and the CRC Press Web site at
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To our families:
Anne, Clare and Emma; Ann, Carine and Tyler.
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Contents
Preface ......................................................................................................xvii
Authors .......................................................................................................xix
Glossary of Notation .................................................................................xxi
Part A: Basic Concepts
1 Introduction ........................................................................................3
1.1 Randomised Trials................................................................................3
1.1.1 Randomising Clusters ..............................................................4
1.1.2 Some Case Studies ....................................................................6
1.1.3 Overview of Book .....................................................................8
2 Variability between Clusters ..........................................................11
2.1 Introduction .........................................................................................11
2.2 The Implications of Between-cluster Variability:
Some Examples ....................................................................................12
2.3 Measures of Between-cluster Variability ........................................15
2.3.1 Introduction .............................................................................15
2.3.1.1 Binary Outcomes and Proportions .........................15
2.3.1.2 Event Data and Person-years Rates .........................15
2.3.1.3 Quantitative Outcomes and Means ........................16
2.3.2 Coeffi cient of Variation, k .......................................................16
2.3.3 Intracluster Correlation Coeffi cient, ρ ..................................17
2.3.3.1 Quantitative Outcomes .............................................17
2.3.3.2 Binary Outcomes .......................................................18
2.3.3.3 Estimation of ρ ...........................................................18
2.3.4 Relationship between k and ρ ...............................................18
2.4 The Design Effect ................................................................................19
2.4.1 Binary Outcomes .....................................................................19
2.4.2 Quantitative Outcomes ..........................................................21
2.5 Sources of Within-cluster Correlation .............................................22
2.5.1 Clustering of Population Characteristics .............................22
2.5.2 Variations in Response to Intervention ...............................22
2.5.3 Correlation Due to Interaction between Individuals .........23
3 Choosing Whether to Randomise by Cluster ...............................25
3.1 Introduction .........................................................................................25
3.2 Rationale for Cluster Randomisation ..............................................25
3.2.1 Type of Intervention ...............................................................25
ix
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x Contents
3.2.2 Logistical Convenience and Acceptability ..........................26
3.2.3 Contamination .........................................................................27
3.3 Using Cluster Randomisation to Capture Indirect
Effects of Intervention ........................................................................28
3.3.1 Introduction .............................................................................28
3.3.2 Effects of an Intervention on Infectiousness .......................29
3.3.3 Mass Effects of Intervention ..................................................31
3.3.4 Direct, Indirect, Total and Overall Effects ...........................33
3.4 Disadvantages and Limitations of Cluster
Randomisation ....................................................................................37
3.4.1 Effi ciency ..................................................................................37
3.4.2 Selection Bias ...........................................................................37
3.4.3 Imbalances between Study Arms .........................................39
3.4.4 Generalisability .......................................................................40
Part B: Design Issues
4 Choice of Clusters ............................................................................45
4.1 Introduction .........................................................................................45
4.2 Types of Cluster ..................................................................................45
4.2.1 Geographical Clusters ............................................................45
4.2.1.1 Communities ..............................................................46
4.2.1.2 Administrative Units ................................................47
4.2.1.3 Arbitrary Geographical Zones ................................48
4.2.2 Institutional Clusters ..............................................................49
4.2.2.1 Schools ........................................................................49
4.2.2.2 Health Units ...............................................................50
4.2.2.3 Workplaces .................................................................50
4.2.3 Smaller Clusters ......................................................................51
4.2.3.1 Households and Other Small Groups ....................52
4.2.3.2 Individuals as Clusters .............................................52
4.3 Size of Clusters ....................................................................................53
4.3.1 Introduction .............................................................................53
4.3.2 Statistical Considerations .......................................................53
4.3.3 Logistical Issues ......................................................................54
4.3.4 Contamination .........................................................................55
4.3.4.1 Contacts between Intervention and
Control Clusters .........................................................55
4.3.4.2 Contacts between Intervention Clusters and
the Wider Population ................................................55
4.3.4.3 Contacts between Control Clusters
and the Wider Population ........................................56
4.3.4.4 Effects of Cluster Size on Contamination ..............56
4.3.5 Transmission Zones of Infectious Diseases ........................56
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Contents xi
4.4 Strategies to Reduce Contamination ................................................58
4.4.1 Separation of Clusters.............................................................58
4.4.2 Buffer Zones .............................................................................60
4.4.3 The Fried Egg Design .............................................................62
4.5 Levels of Randomisation, Intervention, Data Collection
and Inference .......................................................................................64
5 Matching and Stratification ............................................................65
5.1 Introduction .........................................................................................65
5.2 Rationale for Matching ......................................................................65
5.2.1 Avoiding Imbalance between Treatment Arms .................66
5.2.2 Improving Study Power and Precision ................................68
5.3 Disadvantages of Matching ...............................................................70
5.3.1 Loss of Degrees of Freedom ..................................................70
5.3.2 Drop-out of Clusters ...............................................................72
5.3.3 Limitations in Statistical Inference for Matched Trials .....74
5.3.3.1 Adjustment for Covariates .......................................74
5.3.3.2 Testing for Variation in Intervention Effect ...........74
5.3.3.3 Estimation of Intracluster Correlation
Coeffi cient and Coeffi cient of Variation .................75
5.4 Stratifi cation as an Alternative to Matching ...................................75
5.5 Choice of Matching Variables ...........................................................77
5.5.1 Estimating the Matching Correlation ..................................77
5.5.2 Matching on Baseline Values of Endpoint of Interest........78
5.5.3 Matching on Surrogate Variables .........................................79
5.5.4 Matching on Multiple Variables ............................................79
5.5.5 Matching on Location .............................................................80
5.6 Choosing Whether to Match or Stratify ..........................................81
5.6.1 Introduction .............................................................................81
5.6.2 Trials with a Small Number of Clusters ..............................81
5.6.3 Trials with a Larger Number of Clusters.............................83
6 Randomisation Procedures .............................................................85
6.1 Introduction .........................................................................................85
6.2 Restricted Randomisation .................................................................86
6.2.1 Basic Principles ........................................................................86
6.2.2 Using Restricted Randomisation to Achieve Overall
Balance ......................................................................................87
6.2.3 Balance Criteria .......................................................................89
6.2.4 Validity of Restricted Randomisation ..................................94
6.2.5 Restricted Randomisation with More than Two
Treatment Arms ......................................................................99
6.3 Some Practical Aspects of Randomisation .....................................99
6.3.1 Concealment of Allocation ....................................................99
6.3.2 Public Randomisation ............................................................99
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xii Contents
7 Sample Size .....................................................................................105
7.1 Introduction .......................................................................................105
7.2 Sample Size for Unmatched Trials .................................................106
7.2.1 Event Rates .............................................................................107
7.2.2 Proportions ............................................................................109
7.2.3 Means ......................................................................................110
7.2.4 Variable Sample Size per Cluster ........................................111
7.2.5 Sample Size Calculations Based on Intracluster
Correlation Coeffi cient .........................................................111
7.3 Sample Size for Matched and Stratifi ed Trials .............................113
7.3.1 Matched Trials .......................................................................113
7.3.1.1 Event Rates ...............................................................114
7.3.1.2 Proportions ...............................................................114
7.3.1.3 Means ........................................................................114
7.3.2 Stratifi ed Trials ......................................................................116
7.4 Estimating the Between-cluster Coeffi cient
of Variation ........................................................................................117
7.4.1 Unmatched Trials ..................................................................117
7.4.1.1 Event Rates ...............................................................118
7.4.1.2 Proportions ...............................................................119
7.4.1.3 Means ........................................................................120
7.4.2 Matched and Stratifi ed Trials ..............................................120
7.4.2.1 Event Rates ...............................................................120
7.4.2.2 Proportions and Means ..........................................121
7.5 Choice of Sample Size in each Cluster ...........................................121
7.6 Further Issues in Sample Size Calculation....................................124
7.6.1 Trials with More than Two Treatment Arms ....................124
7.6.2 Trials with Treatment Arms of Unequal Size ...................124
7.6.3 Equivalence Trials .................................................................125
7.6.4 Power and Precision .............................................................126
7.6.5 Assumptions about Intervention Effects ...........................127
8 Alternative Study Designs ............................................................129
8.1 Introduction .......................................................................................129
8.2 Design Choices for Treatment Arms..............................................129
8.2.1 Trials with Several Treatment Arms ..................................129
8.2.2 Factorial Trials .......................................................................130
8.2.2.1 Independent Effects ................................................130
8.2.2.2 Non-independent Effects........................................132
8.2.3 Crossover Design ..................................................................135
8.2.4 Stepped Wedge Design ........................................................136
8.3 Design Choices for Impact Evaluation ..........................................141
8.3.1 Introduction ...........................................................................141
8.3.2 Repeated Cross-sectional Samples .....................................142
8.3.3 Cohort Follow-up ..................................................................143
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