Analyzing indirect effects in cluster randomized trials. The effect of estimation method, number of groups and group sizes on accuracy and power

Cluster randomized trials assess the effect of an intervention that is carried out at the group or cluster level. Ajzen's theory of planned behavior is often used to model the effect of the intervention as an indirect effect mediated in turn by attitude, norms and behavioral intention. Structural equation modeling (SEM) is the technique of choice to estimate indirect effects and their significance. However, this is a large sample technique, and its application in a cluster randomized trial assumes a relatively large number of clusters. In practice, the number of clusters in these studies tends to be relatively small, e.g., much less than fifty. This study uses simulation methods to find the lowest number of clusters needed when multilevel SEM is used to estimate the indirect effect. Maximum likelihood estimation is compared to Bayesian analysis, with the central quality criteria being accuracy of the point estimate and the confidence interval. We also investigate the power of the test for the indirect effect. We conclude that Bayes estimation works well with much smaller cluster level sample sizes such as 20 cases than maximum likelihood estimation; although the bias is larger the coverage is much better. When only 5-10 clusters are available per treatment condition even with Bayesian estimation problems occur.