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Using cluster-robust standard errors when analyzing group-randomized trials with few clusters.

Francis L Huang¹, Xintong Li²

¹Missouri Prevention Science Institute, University of Missouri, 16 Hill Hall, Columbia, MO, 65211, USA. huangf@missouri.edu.

Behavior Research Methods

|September 10, 2021

Summary

This summary is machine-generated.

Cluster-randomized trials (CRTs) often have few clusters, leading to underestimated standard errors. A small sample correction (CR2 estimator) with specific degrees of freedom (dof_BM) provides unbiased results even with 10 clusters.

Keywords:

Bias-reduced linearization Cluster-randomized trials Cluster-robust standard errors Few clusters Ordinary least squares

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Area of Science:

Biostatistics
Clinical Trials Methodology
Statistical Inference

Background:

Dependent observations in cluster-randomized trials (CRTs) necessitate robust statistical methods.
Cluster-robust standard errors (CRSEs) are commonly used but can underestimate standard errors with few clusters (<50).
Logistical and financial constraints often limit the number of clusters in CRTs.

Purpose of the Study:

To investigate the performance of the CR2 estimator with empirically derived degrees of freedom (dof_BM) in CRTs with few clusters.
To assess the impact of different degrees of freedom choices on type I error and coverage rates.
To provide practical guidance and tools for analyzing CRTs with small sample sizes.

Main Methods:

Simulation study examining CR2 estimator performance under various conditions.
Comparison of CR2 estimator with dof_BM against standard CRSEs.
Analysis of type I error and coverage rates based on degrees of freedom selection.

Main Results:

The CR2 estimator with dof_BM yields unbiased results and acceptable type I error/coverage rates, even with as few as 10 clusters.
Degrees of freedom choice significantly influences coverage and type I error rates, independent of standard error adjustments.
The study provides an applied example and R syntax for analysis.

Conclusions:

The CR2 estimator combined with dof_BM is a reliable method for analyzing CRTs with a small number of clusters.
Careful consideration of degrees of freedom is crucial for accurate statistical inference in CRTs.
Accessible tools, including an SPSS add-on, are available to facilitate the implementation of these methods.