Fan Li is a professor in the Departments of Statistical Science, and Biostatistics and Bioinformatics at Duke University. Her primary research interest is statistical methods for causal inference, with applications to clinical trials, health and social sciences. She has developed the overlap weighting method. She also works on the interface of causal inference and machine learning, Bayesian analysis and missing data. She is an associate editor of Journal of the American Statistical Association, Bayesian Analysis, and Observational Studies.



In pragmatic cluster randomized experiments, units are often recruited after the random cluster assignment. This can lead to post-randomization selection bias, inducing systematic differences in baseline characteristics of the recruited patients between intervention and control arms. We clarify that in such situations there are two different causal estimands of average treatment effects, one on the overall population and one on the recruited population, which require different data and strategies to identify. We specify the conditions under which cluster randomization implies individual randomization. We show that under the assumption of ignorable recruitment, the average treatment effect on the recruited population can be consistently estimated from the recruited sample. While the average treatment effect on the overall population is generally not identifiable from the recruited sample alone, a meaningful weighted estimand on the overall population can be consistently estimated via applying a simple weighting scheme to the recruited sample. This estimand corresponds to the subpopulation of units who would be recruited into the study regardless of the assignment. We also develop a sensitivity analysis method for checking the ignorable recruitment assumption. The proposed methods are illustrated via a real world application in cardiology.