Premium
Improving small‐sample inference in group randomized trials with binary outcomes
Author(s) -
Westgate Philip M.,
Braun Thomas M.
Publication year - 2010
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4101
Subject(s) - randomized controlled trial , inference , sample (material) , statistics , sample size determination , group (periodic table) , computer science , binary number , medicine , mathematics , artificial intelligence , chromatography , chemistry , arithmetic , organic chemistry
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.