Unequal Center Sizes, Sample Size, and Power in Multicenter Clinical Trials
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Unequal Center Sizes, Sample Size, and Power in Multicenter Clinical Trials
Francis Ruvuna, PLD
ILEXrM Oncologv. Biostatistics, Inc., San Antonio, Texas
Key Words Multicenter clinical trials; Center imbalance; Power; Effective sample size; Coefficient of imbalance Correspondence Address Francis Ruvuna, BioNumerik Pharmaceuticals, Inc., 8122 Datapoint Drive, Suite 400, San Antonio, TX 78229. (e-mail: [email protected]).
In many multicenter clinical trials, the total sample size (N), the power (I+), and the significance level (a)are decided a t 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 computinz a coefficient ofi;rtbalance is'in trohuceduas a tool to utilize in assessing power loss in
(a)
INTRODUCTION Many clinical trials in the pharmaceutical industry are conducted at several centers. The two most plausible benefits of multicenter trials are: 1. To achieve quick enrollment within a practical time frame, and 2. To take advantage of the evidence from multiple centers to possibly generalize the results to a broader population of clinical centers.
However,a major drawback associated with multicenter clinical trials is that the center enrollments in a study can vary greatly, resulting in a loss of power and sensitivity due to extreme center size imbalances. Senn (1)pointed out that it is common in clinical trials to find that the largest center has twice as many enrolled subjects as the smallest center. Usually at the time of study design, standard sample size formulas are applied to calculate the total sample size required based on specified power to detect the desired treatment difference at a specified statistical significance level. The estimated sample size is used, along with the desired duration of enrollment, for an initial "guesstimate" of the enrollment rate and the
relation to unequal center sizes. This strategy is particularly useful for statistical analyses utilizing unweighted (Type 111) analysis methods viewed to be most affected by extreme center imbalances in hypothesis testing and parameter estimates. Numerical examples illustrating the utility of A in deriving effective sample size ( N J and adjusted power (l-pJ for center imbalances are provided utilizing published data. The advantage is that A, Ne, a n d l-pA 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.
number of centers required for the trial. The implicit assumption embedded in these calculations is equal enrollment at all centers. As Senn (2) pointed out, attempts to enroll equal numbers of subjects per center in multicenter clinical trials would tak
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