Empirical power and sample size calculations for cluster-randomized and cluster-randomized crossover studies

Abstract

In recent years, the number of studies using a cluster-randomized design has grown dramatically. In addition, the cluster-randomized crossover design has been touted as a methodological advance that can increase efficiency of cluster-randomized studies in certain situations. While the cluster-randomized crossover trial has become a popular tool, standards of design, analysis, reporting and implementation have not been established for this emergent design. We address one particular aspect of cluster-randomized and cluster-randomized crossover trial design: estimating statistical power. We present a general framework for estimating power via simulation in cluster-randomized studies with or without one or more crossover periods. We have implemented this framework in the clusterPower software package for R, freely available online from the Comprehensive R Archive Network. Our simulation framework is easy to implement and users may customize the methods used for data analysis. We give four examples of using the software in practice. The clusterPower package could play an important role in the design of future cluster-randomized and cluster-randomized crossover studies. This work is the first to establish a universal method for calculating power for both cluster-randomized and cluster-randomized clinical trials. More research is needed to develop standardized and recommended methodology for cluster-randomized crossover studies.

Trial registration: ClinicalTrials.gov NCT01249625.

Figure 1. Power curves from Examples A and B.

These curves show the relationship of power with the number of clusters. The points show simulated power for 1000 datasets with a smoothed line drawn through the data to highlight the overall pattern. The solid line and gray points represent the simulations with constant baseline rates (Example A) and the open circles and dashed line represent the simulations with time-varying baseline rates (Example B).

Figure 2. Power curves from Example C.

These curves depict the relationship between power and sample size per cluster across different effect sizes. The points show simulated power for 500 datasets.