Methods: Mind the Gap

Webinar Series

Toward Causal Inference in Cluster Randomized Trials: Estimands and Reflection on Current Practice

November 3, 2022
Fan Li
Fan Li, Ph.D.

Yale School of Public Health

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About the Webinar

Cluster randomized trials (CRTs) involve randomizing groups of individuals to different interventions. While model-based methods are extensively studied for analyzing CRTs, there has been little reflection around the treatment effect estimands at the outset. In the first part of this presentation, we described two relevant estimands that can be addressed through CRTs and pointed out that they can differ when the treatment effects vary according to cluster sizes. As a cautionary note, we demonstrated how choices between different analytic approaches can impact the interpretation of results by fundamentally changing the question being asked. In the second part, we revisited the linear mixed model as the most commonly used method for analyzing CRTs. The linear mixed model makes stringent assumptions, including normality, linearity, and typically a compound symmetric correlation structure, all of which may be challenging to verify. However, under certain conditions, we showed that the linear mixed model consistently estimates the average causal effect under arbitrary misspecification of its working model. Under equal randomization, its model-based variance estimator, surprisingly, remains consistent under model misspecification, justifying the use of confidence intervals output by standard software. These results hold under both simple and stratified randomization, and serve as an important causal inference justification for linear mixed models. Caveats and extensions of our findings were also mentioned.

About Fan Li

Dr. Fan Li is an Assistant Professor in the Department of Biostatistics at Yale School of Public Health, and faculty member in the Center for Methods in Implementation and Prevention Science and the Yale Center for Analytical Sciences. He received his Ph.D. in biostatistics from Duke University in May 2019, and joined the Yale Biostatistics faculty in July 2019. His main expertise is in the development of methods for designing and analyzing pragmatic cluster randomized trials, causal inference for randomized trials and observational studies, and techniques for improving internal and external validity for treatment comparison under different study designs. He is the Principal Investigator of a Patient-Centered Outcomes Research Institute (PCORI)-funded methods award that investigates new study planning methods and software for testing treatment effect heterogeneity in cluster randomized trials. His research has also been supported by several additional PCORI-funded and NIH-funded awards. Since 2013, Dr. Li has joined the Biostatistics and Study Design Core at the NIH Pragmatic Trials Collaboratory and contributed to the application of new methods to existing Demonstration Projects that adopted the cluster randomized design. He is also an Executive Committee member of the Design and Statistics Core at the NIA IMPACT Collaboratory. He currently serves as an Associate Editor for Statistics in Medicine, Clinical Trials (Journal of the Society for Clinical Trials), Implementation Science, and Epidemiologic Methods. 

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