In a cluster randomized trial (CRT), groups of people are randomly assigned to different interventions. Existing parametric and semiparametric methods for CRTs rely on distributional assumptions or a large number of clusters to maintain nominal confidence interval (CI) coverage. Randomization-based inference is an alternative approach that is distribution-free and does not require a large number of clusters to be valid. Although it is well-known that a CI can be obtained by inverting a randomization test, this requires randomization testing a non-zero null hypothesis, which is challenging with non-continuous and survival outcomes. In this paper, we propose a general method for randomization-based CIs using individual-level data from a CRT. This fast and flexible approach accommodates various outcome types, can account for design features such as matching or stratification, and employs a computationally efficient algorithm. We evaluate this method's performance through simulations and apply it to the Botswana Combination Prevention Project, a large HIV prevention trial with an interval-censored time-to-event outcome.
Rabideau, Dustin J. and Wang, Rui, "Randomization-Based Confidence Intervals for Cluster Randomized Trials" (January 2020). Harvard University Biostatistics Working Paper Series. Working Paper 222.