The Robustness of Designs for Trials With Nested Data Against Incorrect Initial Intracluster Correlation Coefficient Estimates

In the case of trials with nested data, the optimal allocation of units depends on the budget, the costs, and the intracluster correlation coefficient. In general, the intracluster correlation coefficient is unknown in advance and an initial guess has to be made based on published values or subject matter knowledge. This initial estimate is likely to deviate from the true intracluster correlation coefficient. The current study investigates the extent to which the efficiency of a design for a trial with nested data and continuous outcome variables is influenced by an incorrect initial intracluster correlation coefficient estimate. We focus on trials with nested data in both treatment conditions as well as in one treatment condition. The investigated designs prove to be rather robust against the misspecification of the intracluster correlation coefficient. Although underestimating the intracluster correlation coefficient leads to a steeper decrease in the efficiency of a design than overestimating it, the relative efficiency of the treatment effect estimate remains above 90% as long as the population intracluster correlation coefficient is not underestimated by more than 75% or overestimated by more than 175%.