Improving small-sample inference in group randomized trials with binary outcomes
Article first published online: 5 NOV 2010
Copyright © 2010 John Wiley & Sons, Ltd.
Statistics in Medicine
Volume 30, Issue 3, pages 201–210, 10 February 2011
How to Cite
Westgate, P. M. and Braun, T. M. (2011), Improving small-sample inference in group randomized trials with binary outcomes. Statist. Med., 30: 201–210. doi: 10.1002/sim.4101
- Issue published online: 7 JAN 2011
- Article first published online: 5 NOV 2010
- Manuscript Accepted: 8 SEP 2010
- Manuscript Received: 7 APR 2010
- bias correction;
- correlated data;
- pseudo-Wald tests;
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.