Group Randomized Trials (GRTs) randomize groups of people to treatment or control arms instead of individually randomizing subjects. When each subject has a binary outcome, over-dispersed binomial data may result, quantified as an intra-cluster correlation (ICC). Typically, GRTs have a small number, bin, of independent clusters, each of which can be quite large. Treating the ICC as a nuisance parameter, inference for a treatment effect can be done using quasi-likelihood with a logistic link. A Wald statistic, which, under standard regularity conditions, has an asymptotic standard normal distribution, can be used to test for a marginal treatment effect. However, we have found in our setting that the Wald statistic may have a variance less than 1, resulting in a test size smaller than its nominal value. This problem is most apparent when marginal probabilities are close to 0 or 1, particularly when n is small and the ICC is not negligible. When the ICC is known, we develop a method for adjusting the estimated standard error appropriately such that the Wald statistic will approximately have a standard normal distribution. We also propose ways to handle non-nominal test sizes when the ICC is estimated. We demonstrate the utility of our methods through simulation results covering a variety of realistic settings for GRTs. Copyright © 2010 John Wiley & Sons, Ltd.
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