A Framework for Designing Cluster Randomized Trials with Binary Outcomes

Presentation Type: Individual Paper

Category/Theme: Innovative Methods and Statistics

Title: A Framework for Designing Cluster Randomized Trials with Binary Outcomes

Abstract Body:

Introduction: Cluster randomized trials (CRTs) are becoming increasingly common as a means for evaluating the effectiveness of interventions in prevention research. In order for these CRTs to yield rigorous evidence of whether or not a program is effective, the study must be well-designed and adequately powered to detect a meaningful effect. In the past 15 years, the field has made substantial progress in terms of how to calculate statistical power for CRTs for continuous outcomes. However, in prevention research, outcomes are often binary, such as gang participation (yes/no), graduation (yes/no), and drug use (yes/no). The purpose of this paper is to establish a framework for conducting a power analysis for a CRT with a binary outcome. We apply the framework to the design of a study of a school-based intervention to prevent gang membership.

Methods: The framework we propose is based on proportions, a parameter that is likely estimable by those planning a CRT with binary outcomes. Consider a simple two-level CRT in which students are nested within schools and schools are assigned to either the new gang prevention program or business as usual. The power analysis relies on the number of students per school, the total number of schools, the proportion of gang membership in the treatment group, the proportion of gang membership in the control group, and an estimate of the reasonable upper and lower bound of gang membership in the control group.

Results: With respect to sample size, the number of schools is the key driver of statistical power. Power also increases when the upper and lower bounds for the event in the control group are smaller, or there is less variability between schools. The rareness of the event also effects the statistical power, which is why it is critical that a simple difference in proportions is not specified by the researcher, but rather the proportion of gang membership for the treatment and control schools. For intervention studies such as gang membership, where the proportion of gang membership within schools tends to be quite low, and the expected reduction in membership as a result of the interventions may be a difference in proportions of around 0.02, a large number of schools are required to power the study.

Conclusions: This paper provides a framework for conducting power analyses for CRTs with binary outcomes in a way that is intuitive for researchers planning these studies. This is critical as the number of CRTs with binary outcomes in prevention research continues to grow.