The effect of cluster size variability on statistical power in cluster-randomized trials

Abstract

The frequency of cluster-randomized trials (CRTs) in peer-reviewed literature has increased exponentially over the past two decades. CRTs are a valuable tool for studying interventions that cannot be effectively implemented or randomized at the individual level. However, some aspects of the design and analysis of data from CRTs are more complex than those for individually randomized controlled trials. One of the key components to designing a successful CRT is calculating the proper sample size (i.e. number of clusters) needed to attain an acceptable level of statistical power. In order to do this, a researcher must make assumptions about the value of several variables, including a fixed mean cluster size. In practice, cluster size can often vary dramatically. Few studies account for the effect of cluster size variation when assessing the statistical power for a given trial. We conducted a simulation study to investigate how the statistical power of CRTs changes with variable cluster sizes. In general, we observed that increases in cluster size variability lead to a decrease in power.

Trial registration: ClinicalTrials.gov NCT01249625.

Fig 1. The annual number of articles published on CRTs (either trials themselves or methods for trials) has increased from 4 to 275 since 1997.

Source: Web of Science. Search syntax used: (TI = (“cluster random*”) OR TI = (“group random*”)) AND Document Types = (Article).

Fig 2. The negative binomial distributions used to draw the cluster sizes sets for each mean cluster size (μ) and coefficient of variance (cv).

Each set had between 5 and 120 clusters, which made up the sample size of a CRT.

Fig 3. How to find the required number of clusters (Ĉ).

First, for a given set of parameters, θ _i, hypothesis test simulations are run for each level of C ^A. Second, the results of the simulations are averaged into one point per level. Third, $\widehat{C}$ is calculated by interpolating a point at $\widehat{P}=0.8$ between (C _0.8⁻, ${\hat{P}}_{{0.8}^{-}}$) and (C _0.8⁺, ${\hat{P}}_{{0.8}^{+}}$.

Fig 4. The CRT power curves for two different parameter sets over four levels of cluster size variance.

When C ^A = 60, both fixed cluster size power estimates (${\hat{P}}_{{\theta }_{\mathit{i}}}^F$), the solid, black lines) should equal 0.8. By looking below the point (60, 0.8), one observes that power is lost as the cluster size variance increases in both scenarios. By looking to the right of the point, the observer notices that more clusters are required to attain a statistical power of 0.8 with increased variability.