Robustness and Optimal Design Issues for Cluster Randomized Trials

Abstract

Cluster randomized trials (CRT), in which whole clusters instead of individuals are assigned to conditions, are not uncommon in the social, behavioral, educational, medical and organizational sciences. Though the assignment of individuals to treatment conditions is more efficient, this may not always be feasible due to ethical, financial or organizational reasons. Using a CRT has consequences with respect to the sample size and data analysis technique. The sample size should be increased to reach the same level of efficiency as with subject-level randomization and the data should be analyzed with a technique like multilevel analysis that accounts for the dependency of subjects within the same cluster. The intracluster correlation coefficient (ICC) is a measure for this dependency, but may also be seen as the proportion cluster level variance of the total variance. Thanks to extensive literature, most researchers are aware of the forenamed consequences of application of a CRT and take them into account when designing a CRT and analyzing the resulting data. However, various issues concerning design and robustness remained unclear so far and some of these issues have been covered by this thesis. In the design phase of a CRT the researcher has to determine the optimal allocation of units at the cluster and at the subject level for detecting the treatment effect -if existing- with the highest precision. The optimal allocation depends, among other things, on the magnitude of the ICC. In advance this value is unknown and the researcher has to make an educated guess. It is shown that the design is rather robust against incorrect ‘initial’ ICC estimates. The performance of multilevel structural equation modeling applied to a 2111 mediation model is investigated. It is shown that the mediation effect itself is estimated seemingly accurately. However, the parameters that determine the mediation effect are often biased, even with large sample sizes. Three different incorrect model specifications are investigated; heteroscedasticity, ignoring partially nesting, and ignoring inequality of within-cluster and contextual effects. In a CRT the variance in the experimental condition may differ from the variance in the control condition. This phenomenon is called heteroscedasticity and may be due to the treatment. When in a CRT one of the conditions consists of clusters, while the other condition consists of non-clustered individuals, the resulting data has a partially nested structure. In case a subject level covariate is taken into account, the multilevel model gives a single estimate for its effect, since the model assumes that there is no between-cluster effect. In practice the within-cluster and contextual effect may differ and when not modeled this difference is ignored. It is shown that within the framework of a CRT it is advisable to model the design specific issues appropriately when the researcher wishes to have a complete and correct view of the various effects and relations between the variables in the model. However, it is also shown that the estimation of the treatment effect and its standard error is rather robust.