Intra-cluster correlations from the CLustered OUtcome Dataset bank to inform the design of longitudinal cluster trials

Abstract

Background: Sample size calculations for longitudinal cluster randomised trials, such as crossover and stepped-wedge trials, require estimates of the assumed correlation structure. This includes both within-period intra-cluster correlations, which importantly differ from conventional intra-cluster correlations by their dependence on period, and also cluster autocorrelation coefficients to model correlation decay. There are limited resources to inform these estimates. In this article, we provide a repository of correlation estimates from a bank of real-world clustered datasets. These are provided under several assumed correlation structures, namely exchangeable, block-exchangeable and discrete-time decay correlation structures. Methods: Longitudinal studies with clustered outcomes were collected to form the CLustered OUtcome Dataset bank. Forty-four available continuous outcomes from 29 datasets were obtained and analysed using each correlation structure. Patterns of within-period intra-cluster correlation coefficient and cluster autocorrelation coefficients were explored by study characteristics. Results: The median within-period intra-cluster correlation coefficient for the discrete-time decay model was 0.05 (interquartile range: 0.02–0.09) with a median cluster autocorrelation of 0.73 (interquartile range: 0.19–0.91). The within-period intra-cluster correlation coefficients were similar for the exchangeable, block-exchangeable and discrete-time decay correlation structures. Within-period intra-cluster correlation coefficients and cluster autocorrelations were found to vary with the number of participants per cluster-period, the period-length, type of cluster (primary care, secondary care, community or school) and country income status (high-income country or low- and middle-income country). The within-period intra-cluster correlation coefficients tended to decrease with increasing period-length and slightly decrease with increasing cluster-period sizes, while the cluster autocorrelations tended to move closer to 1 with increasing cluster-period size. Using the CLustered OUtcome Dataset bank, an RShiny app has been developed for determining plausible values of correlation coefficients for use in sample size calculations. Discussion: This study provides a repository of intra-cluster correlations and cluster autocorrelations for longitudinal cluster trials. This can help inform sample size calculations for future longitudinal cluster randomised trials.

Power considerations for generalized estimating equations analyses of four‐level cluster randomized trials

“…When there is a large uncertainty for components of 𝜶, we strongly recommend conducting a sensitivity analysis by considering a range of values for ICCs in power analysis, as we already demonstrated in Section 5. Finally, we wish to note that publishing ICCs has long been advocated; for example, see Murray et al (2004) for a table listing 14 research articles presenting ICCs for a variety of endpoints, groups and populations; Preisser et al (2007) for published ICCs for nine binary youth alcohol use measures from the Youth Survey of the Enforcing Underage Drinking Laws Program; and Korevaar et al (2021) for published ICC estimates from the CLustered OUtcome Dataset bank to inform the design of longitudinal CRTs for a wide range of outcomes. We encourage more such efforts to assist the planning for complex multilevel CRTs and to strengthen the connection between the methodological development on study design and statistical practice.…”

“…(2007) for published ICCs for nine binary youth alcohol use measures from the Youth Survey of the Enforcing Underage Drinking Laws Program; and Korevaar et al. (2021) for published ICC estimates from the CLustered OUtcome Dataset bank to inform the design of longitudinal CRTs for a wide range of outcomes. We encourage more such efforts to assist the planning for complex multilevel CRTs and to strengthen the connection between the methodological development on study design and statistical practice.…”

Model misspecification in stepped wedge trials: Random effects for time or treatment

“…In our motivating example, we used the data to inform assumptions about values of true variance parameters. To use this method for creating a prespecified analysis, assumptions about true variance parameters would be based on pre‐existing data 17 and scientific beliefs instead of being estimated from the data of interest. This may sometimes be difficult, but we hope researchers can draw on their experience in estimating power for SWTs, since the methods of making assumptions about variance components before data collection should be similar.…”

Random effect misspecification in stepped wedge designs

“…In addition to a random cluster effect, denoted by u i , models for the analysis of SWT often include random effects for time and/or treatment to account for random variations in the time trend or treatment effect, respectively, between clusters. 7,8 In the random time effect model, a i = ( u i , w i 1 ,… , w iJ ) T , where w ij is the random time effect (here, time is treated as categorical for maximum flexibility). The covariance matrix of the random effects is G = diag ( τ 2 , γ 2 ,… , γ 2 ) , a diagonal matrix with dimension J + 1.…”