Multilevel analysis of group-randomized trials with binary outcomes

Objectives: Many dental studies have assessed the effectiveness of community- or group-based interventions such as community water fluoridation. These cluster trials, of which group-randomized trials (GRTs) are one type, have design and analysis considerations not found in studies with randomization of treatments to individuals (randomized controlled trials, RCTs). The purpose of this paper is to review analytic methods used for the analysis of binary outcomes from cluster trials and to illustrate these concepts and analytical methods using a school-based GRT. Methods: We examine characteristics of GRTs including intra-class correlation (ICC), their most distinctive feature, and review analytical methods for GRTs including group-level analysis, adjusted chi-square test and multivariable analysis (mixed effect models and generalized estimating equations) for correlated binary data. We consider two- and three-level modeling of data from a cross-sectional cluster design. We apply the concepts reviewed using a GRT designed to determine the effect of incentives on response rates in a school-based dental study. We compare the results of analyses using methods for correlated binary data with those from traditional methods that do not account for ICC. Results: Application of traditional analytic methods to the dental GRT used as an example for this paper led to a substantial overstatement of the effectiveness of the intervention. Conclusions: Ignoring the ICC among members of the same group in the analysis of public health intervention studies can lead to erroneous conclusions where groups are the unit of assignment. Special consideration is needed in the analysis of data from these cluster trials. Randomization of treatments to groups also should receive more consideration in the design of cluster trials in dental public health.