## 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.

Original language | English |
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Pages (from-to) | 201-210 |

Number of pages | 10 |

Journal | Statistics in Medicine |

Volume | 30 |

Issue number | 3 |

DOIs | |

State | Published - Feb 10 2011 |

## Keywords

- Bias correction
- Correlated data
- Overdispersion
- Pseudo-Wald tests
- Quasi-likelihood

## ASJC Scopus subject areas

- Epidemiology
- Statistics and Probability