title: Improving small-sample inference in group randomized trials with binary outcomes.
abstract: 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.
authors.affiliation: Department of Biostatistics, School of Public Health, University of Michigan, Ann Arbor, MI 48109, USA. pwestgat@umich.edu
authors.forename: Philip M
authors.initials: PM
authors.lastname: Westgate
authors.forename: Thomas M
authors.initials: TM
authors.lastname: Braun
mesh_terms: D000465:Algorithms; D015982:Bias; D016000:Cluster Analysis; D003198:Computer Simulation; D006801:Humans; D016015:Logistic Models; D015233:Models, Statistical; D011336:Probability; D016032:Randomized Controlled Trials as Topic / Q000379:methods*; D018401:Sample Size; D016008:Statistical Distributions; D016896:Treatment Outcome