Unequal Center Sizes, Sample Size, and Power in Multicenter Clinical Trials

In many multicenter clinical trials, the total sample size (N), the power (1-β), and the significance level (α) are decided at the time of trial design and protocol development. Although it may be recognized that equal center enrollment is the ideal, it is not practical and rational to limit enrollment per center in order to attain an equal number of subjects per center. Extreme unequal center enrollments may occur, which may lead to loss of power and loss of sensitivity to detect the treatment difference. In this manuscript, a method of computing a coefficient of imbalance (Λ) is introduced as a tool to utilize in assessing power loss in relation to unequal center sizes. This strategy is particularly useful for statistical analyses utilizing unweighted (Type III) analysis methods viewed to be most affected by extreme center imbalances in hypothesis testing and parameter estimates. Numerical examples illustrating the utility of Λ in deriving effective sample size (Ne) and adjusted power (1-βA) for center imbalances are provided utilizing published data. The advantage is that Λ, Ne, and 1-βA can be computed any time while a study is ongoing for decision purposes, even for blinded studies, since the computations do not require breaking the blind.