Cluster randomized trials are widely used when individual randomization is logistically infeasible or when correlations between observations cannot be ignored, especially in fields such as ophthalmology, infectious disease, vaccine research, and sociology. The desirability of outcome ranking (DOOR) framework evaluates patient-centric benefit-risk using an ordinal outcome and a Wilcoxon-Mann-Whitney statistic-based approach to compare outcome distributions between interventions. We propose a suite of new methods to extend DOOR to cluster trials based on properties of U-statistics and influence functions to estimate within-cluster and between-cluster treatment effects. These approaches can be applied in different scenarios, including mixtures of clusters with two treatment groups and clusters with only one group, and both small and large numbers of clusters. Simulations demonstrate that the proposed methods perform well under various scenarios regarding the number of clusters and cluster sizes. As an illustration, we apply the proposed methods to a cluster randomized crossover trial comparing delayed cord clamping and umbilical cord milking for newborns.

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