Abstract: 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. We use principal stratification to clarify the intrinsic difference between these estimands and the bias of the standard intention-to-treat analysis . 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, via either regression adjustment or inverse probability weighting. While the average treatment effect on the overall population is generally not identifiable from the observed 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. We illustrate the proposed methods via a real world application in cardiology.

https://www2.stat.duke.edu/~fl35/