2 b σ2 b + σw2 (1.10) Where σ2
w is the within-cluster variance and σ2b the between-cluster variance.
Historically ICCs were not explicitly published in reports of CRT’s. Nowadays, however, there are many sources of ICC estimates8, 12, 13 as well as publications which describe the general behaviour and patterns in ICCs across different therapeutic areas, outcomes and clusters.14–18 For three types of cluster that vary in size: the spouse pair; general practice and country Donner calculated the within-cluster correlation for lifestyle outcomes: hypertension; smoking status; alcohol consumption; and body fat. For all outcomes the within-cluster correlation decreased with the corresponding size of the cluster.19
The coefficient of variation in outcome
An alternative measure of clustering to the ICC is the coefficient of variation in the outcome. This is the between-cluster standard deviation divided by the parameter of interest i.e. the proportion, rate or mean within each cluster.20
k = σb
µ (1.11)
This measure is particularly useful when the primary outcome variable is a rate as an ICC cannot be calculated in that situation.
The relationship between the ICC and coefficient of variation
The clustering of outcomes must be accounted for in the sample size calculation using one of the two measures of correlation, which will be described in more detail later (Section 1.4). For binary outcomes a simple relationship exists between the two correlation measures but they make different assumptions about how the between-cluster variation differs across treatment groups and so will produce different sample size requirements. The use of the ICC is recommended for sample size
1.3. CLUSTER RANDOMISED TRIALS (CRTS)
calculations of binary outcomes unless the proportion is very small, where both methods give similar results.21
1.3.3
Prevalence of cluster based randomisation
Several reviews of CRTs have been published and are summarised in Table 1.1. Many of these reviews note that the prevalence of CRTs is increasing over time.22–30 In the review by Eldridge et al the number of cluster trials identified in primary care in 1997 had almost doubled by 1999.25 This increased use of CRTs is reflected in the increase in the methodological literature. The paper by Cornfield in 197831 was the first to highlight the fact that randomisation by cluster produces a less efficient design. Since then five textbooks have been published on cluster trials by: Murray32 in 1998; Donner and Klar6 in 2000; Hayes and Moulton7 in 2009; Eldridge and Kerry21 in 2012; and Campbell and Walters33in 2014. The journals Statistics in Medicine, Clinical Trials, Statistical Methods in Medical Research, and the American Journal of Epidemiology have each had a special issue dedicated to cluster randomised trials. Most recently, in 2015, the Trials Journal published a collection of articles on stepped-wedge designs, a type of CRT. Cluster randomised trials is a very exciting, and rapidly expanding, area of research to work in.
Table 1.1: Characteristics of 20 published reviews of cluster randomised trials
Author Dates Area Main sources N Review topic
Donner (1990)34 1979-1989 Non therapeutic intervention tri- als
Lancet, NEJM, AJE, IJE 16 Quality of methods
Simpson (1995)35 1990-1993 Primary prevention trials American Journal of Public Health, Preventive Medicine
21 Quality of methods
Chuang (2000)36 1974-1998 Computer-based clinical decision support systems
Medline, Embase, and INSPEC 24 Quality of methods
Hayes (2000)11 1986-1999 infectious diseases Medline database 21 Evaluation of de-
sign features Isaakidis (2003)23 1973-2001 Trials in Sub-Saharan Africa Medline, Cochrane Controlled Trials
Register, African Published Trials Reg- ister
51 Quality of methods
and reporting
Puffer (2003)37 1997-2002 General medicine BMJ, Lancet, NEJM 36 Risk of bias
Eldridge (2004)25 1997-2000 Primary care Cochrane Controlled Trials register ,
UK National Research Register and conference proceedings
152 Quality of methods
Varnell (2004)22 1998-2002 General medicine American Journal of Public Health,
Preventative Medicine
60 Quality of methods
Table 1.1 – continued from previous page
Author Dates Area Main sources N Review topic
Bland (2004)26 1983-2003 General medicine BMJ 18 Quality of methods
Murray(2008)38 2002-2006 Oncology Medline, PubMed 75 Quality of methods
Eldridge (2008)39 2004-2005 Primary care BMJ, BJGP, FP, preventive medicine,
Annals of internal medicine, journal of general internal medicine, Paediatrics
34 Internal and exter-
nal validity
Bowater (2009)40 1998-2007 Tropical parasitic disease Medline database 35 Quality of methods
Handlos (2009)27 1998-2008 Maternal and child health Pubmed, SCOPUS, Cochrane library 35 Quality of methods
Mdege (2010)24 To Jan 2010 Stepped wedge trial Medline, Embase, PsycINFO, HMIC,
CINAHL, Cochrane library, Web of Knowledge, current controlled trials register, google scholar
25 Areas of applica-
tion
Ivers (2011)30 2000-2008 General Medicine Medline database 300 Quality of methods
and reporting
Walleser (2011)41 2004-2010 Trials in children Medline, CINAHL, Embase, cochrane
central register
106 Quality of report-
ing
Crespi (2011)42 1995-2010 Cancer screening interventions PubMed, Web of Science 50 quality of analy-
sis/outcome report- ing
Brierley (2012)43 2008 General Medicine BMJ, Lancet, JAMA, NEJM 24 Bias in recruitment
Table 1.1 – continued from previous page
Author Dates Area Main sources N Review topic
Giraudeau (2012)44 2008 General Medicine Medline database 173 Reporting of in-
formed consent
Froud(2012)45 2005-2009 Oral Health PubMed and experts in the field 23 Quality of methods
and reporting Diaz-Ordaz
(2013)28
up to 2010 Trials in old age residential facil- ities
Medline database 73 Quality of methods
and reporting Diaz-Ordaz
(2013)29
up to 2010 Trials in old age residential facil- ities
Medline database 73 Reporting of in-
formed consent
Sutton (2013)46 2003-2011 Stroke PubMed 15 Quality of report-
ing
1.3. CLUSTER RANDOMISED TRIALS (CRTS)
1.3.4
Guidelines for best practice
Many of the fundamental principles of RCTs such as informed consent, randomisation, sample size and analysis are more complex with randomisation by cluster. Methodology and guidelines for best practice are not as well developed as those for individually randomised trials. The guidance that is available is described in the following sections.
Design, analysis and conduct
In addition to the published textbooks on CRTs there are some additional sources of guidance on the design, analysis and conduct of cluster randomised trials. In 1999 the methodological literature around cluster randomised trials was reviewed and synthesized into 12 methodological recommenda- tions designed to aid investigators designing and conducting these trials. The review covers study design, measures of between-cluster variation, sample size and analysis.8 With regards to sample size, the focus of my research, the advice given was to avoid designing studies with less than four clusters per group and to calculate a sample size appropriate for cluster randomisation. In 2002 the Medical Research Council (MRC) produced a brief guidance booklet on the methodological and eth- ical aspects of cluster randomised trials which provides a basic introduction to the main issues to be aware of when randomising clusters. Their advice on sample size was for a minimum of five clusters per group. (http://www.cebma.org/wp-content/uploads/Cluster-randomised-trials-Methodological- and-ethical-considerations.pdf). Guidance has also been developed for specific aspects of the cluster randomised trial such as consent procedures for trials conducted in residential facilities.29
Reporting
The CONSORT statement consists of a 25-item checklist for improving and standardising the re- porting of clinical trials. The statement was first published in 199647 and has since gone through two further revisions.48, 49 In 2004 the statement was extended for cluster randomised trials50 and this extension was updated in 2012 following the update to the main statement in 2010.51
The item which relates to describing the sample size calculation for individually randomised trials formally recommends the following descriptive elements to be reported (i) the estimated outcomes in each group (which implies the minimum important treatment effect); (ii) the level of significance