Patterns of intra-cluster correlation coefficients in school-based cluster randomised controlled trials of...

The cluster randomised trial (CRT) design is increasingly used to evaluate the impact of school-based interventions for improving social-emotional functioning outcomes in pupils. Good knowledge is required on plausible values of the intra-cluster correlation coefficient (ICC) of the outcome to calculate the required sample size in such studies. Using data from five school-based CRTs in the UK, we estimate, and describe patterns in, ICCs for social-emotional functioning outcomes.

Mixed effects linear regression models were fitted to estimate the ICC and variance components. Estimates for baseline data were obtained by fitting "null" models that had no predictor variables; estimates at follow-up were adjusted for trial arm status.

Five hundred and twenty-nine (529) ICCs were estimated. Variation across clusters in the outcomes was present at the school, year group and classroom levels. Overall, the ICCs were not markedly different between the primary and secondary school settings. Most of the school- and classroom-level ICCs were less than 0.04 for pupil-reported outcomes and less than 0.035 for parent-reported outcomes; a notable exception for pupil-reported outcomes was for outcomes that reflect a common experience shared by children, such as school climate, where the ICCs were as large as 0.1. The ICCs for teacher-reported outcomes (up to 0.1 at the school level and 0.2 at the classroom level) were larger than for pupil- and parent-reported outcomes. In the CRT that allocated schools to trial arms and only sampled one classroom from each school, the nominal school-level ICCs for teacher-reported outcomes took values up to 0.25. ICCs for teacher-reported measures of internalising behaviour problems and pro-social behaviour were larger than for externalising behaviour problems.

When randomising school clusters, sub-sampling of lower-level clusters such as classrooms should be accounted for in the sample size calculation. Teacher-reported ICCs are likely to be greater than those for pupil- and parent-reported outcomes as teachers will often provide data for many or all pupils in a given school or classroom. Differences across reporter type and across outcomes need to be considered when specifying plausible values of the ICC to calculate sample size.

STARS study (ISRCTN84130388); KiVa study (ISRCTN23999021); PACES study (ISRCTN23563048); PROMISE study (ISRCTN19083628); MYRIAD study (ISRCTN86619085).