br Background Cluster randomised controlled trials CRCTs

Background Cluster randomised controlled trials (CRCTs) are increasingly used to evaluate the effectiveness of interventions for improving health (Bland, 2004; Klar & Donner, 2001). CRCTs involve the random assignment of whole clusters, such as schools, hospitals, clinics or communities, rather than individuals (Raudenbush, 1997). CRCTs are particularly useful where researchers are specifically interested in the cluster, as it order XL184 may not be feasible to randomly assign individuals to clusters such as schools or hospitals, or where they are interested in the cluster-level effects of an intervention. The advantages and disadvantages of using CRCTs have been discussed in detail in a series of publications by Donner and Klar (2001/2002/2004) (Donner & Klar, 2002; Donner & Klar, 2004; Klar & Donner, 2001). A key feature of CRCTs is that individuals in clusters are often more alike than individuals in different clusters, irrespective of treatment. This similarity within clusters needs to be taken into account when planning CRCTs to obtain adequate sample sizes, and when analysing clustered data to obtain correct estimates. The focus of this paper is on presenting estimates of the similarity of health outcomes of students within schools across a large number of European countries. Students in the same school are more similar, on average, than students selected from different schools. This is true for a range of educational and health outcomes (McKenzie, Ryan, & Di Tanna, 2014). This dependence of individuals within clusters leads to two potential problems. First, CRCTs require more subjects than RCTs to obtain adequate statistical power because observations are not independent. Secondly, the clustering of the data needs to be addressed through the use of appropriate analysis techniques (such as multilevel models), otherwise standard error estimates will be deflated resulting in an increased risk of Type I errors (false positives) (Klar & Donner, 2001; McKenzie et al., 2014). The intra-class correlation coefficient (ICC) measures the degree of within cluster dependence for a variable, and can therefore be used in power calculations to compute the necessary sample sizes for specific outcomes for CRCTs. If all observations are independent of one another, the ICC will be 0. If all the responses from observations in all clusters are exactly the same, the ICC will be 1. For trials, the greater the value of the ICC, the greater the sample size required (Klar & Donner, 2001; McKenzie et al., 2014; Raudenbush, 1997). To achieve the equivalent power of an individual level randomised un-clustered sample, the sample size has to be inflated by the design effect: Design Effect = 1+(m−1)*ICC, where m represents the average cluster size. The ICC can also be used to correct the estimates of analyses that have not taken the clustered nature of the data into account, by either retrospectively inflating the standard errors to account for the dependence, or reducing the sample size (Hedges, 2007; Hedges & Hedberg, 2007). This is potentially very important for research that compares or combines the results of analyses, such as meta-analyses. Hence Forward mutations is useful to know ICCs in advance of designing CRCTs, to ensure adequate sample size for power, and for adjusting the analysis of clustered data in meta-analysis, where clustering has not been taken into account. Knowledge of ICC׳s is important for a further reason that is often overlooked. When interpreting the impact of school level variables in multilevel models, the lower the value of the ICC, that is the lower the proportion of the variance that is at the school level and therefore the less relevant the school context is, the more likely you are to obtain a significant association between a school-level variable and the outcome (Lagerlund et al., 2015; Merlo, Wagner, Ghith, & Leckie, 2015). Researchers need knowledge of ICC׳s to accurately interpret school level variables in multilevel models.