School-level intra-cluster correlation coefficients and autocorrelations for children's accelerometer-measured physical activity in England by age and gender.

Background: Randomised, cluster-based study designs in schools are commonly used to evaluate children's physical activity interventions. Sample size estimation relies on accurate estimation of the intra-cluster correlation coefficient (ICC), but published estimates, especially using accelerometry-measured physical activity, are few and vary depending on physical activity outcome and participant age. Less commonly-used cluster-based designs, such as stepped wedge designs, also need to account for correlations over time, e.g. cluster autocorrelation (CAC) and individual autocorrelation (IAC), but no estimates are currently available. This paper estimates the school-level ICC, CAC and IAC for England children's accelerometer-measured physical activity outcomes by age group and gender, to inform the design of future school-based cluster trials.

Methods: Data were pooled from seven large English datasets of accelerometer-measured physical activity data between 2002-18 (> 13,500 pupils, 540 primary and secondary schools). Linear mixed effect models estimated ICCs for weekday and whole week for minutes spent in moderate-to-vigorous physical activity (MVPA) and being sedentary for different age groups, stratified by gender. The CAC (1,252 schools) and IAC (34,923 pupils) were estimated by length of follow-up from pooled longitudinal data.

Results: School-level ICCs for weekday MVPA were higher in primary schools (from 0.07 (95% CI: 0.05, 0.10) to 0.08 (95% CI: 0.06, 0.11)) compared to secondary (from 0.04 (95% CI: 0.03, 0.07) to (95% CI: 0.04, 0.10)). Girls' ICCs were similar for primary and secondary schools, but boys' were lower in secondary. For all ages, combined the CAC was 0.60 (95% CI: 0.44-0.72), and the IAC was 0.46 (95% CI: 0.42-0.49), irrespective of follow-up time. Estimates were higher for MVPA vs sedentary time, and for weekdays vs the whole week.

Conclusions: Adequately powered studies are important to evidence effective physical activity strategies. Our estimates of the ICC, CAC and IAC may be used to plan future school-based physical activity evaluations and were fairly consistent across a range of ages and settings, suggesting that results may be applied to other high income countries with similar school physical activity provision. It is important to use estimates appropriate to the study design, and that match the intended study population as closely as possible.