Nonparametric Methods for the Analysis of Cluster Randomization Trials with Multiple Endpoints
Abstract
Cluster randomized trials or cluster trials, which randomize groups of individuals rather than individuals, can simplify the delivery of complex interventions and mitigate the risk of contamination. When diseases and their interventions are complex, impacting multiple dimensions of health, cluster trials may employ multiple primary endpoints to ensure treatment effects are fully characterized. However, analysis is complicated by correlation among endpoints and intracluster correlation, which may differ by endpoint. When multiple endpoints are aggregated into a single composite endpoint, the correlation structure is simplified significantly. There is no need to specify the within-subject between-endpoint correlation structure, and there is only one source of intracluster correlation. However, composites are challenging to construct when endpoint distributions differ or are "noncongruent" and can result in misleading effect estimates when endpoints differ in priority or severity. This thesis deals with both problems by extending nonparametric methods developed by Zou (2021) for cluster randomization trials with a single endpoint. Specifically, by defining the treatment effect as the probability that a participant in the treatment group will have a better outcome than (or win over) a control participant, or "the win probability," this thesis develops nonparametric methods for cluster randomization trials with multiple endpoints of different types. Two extensions of the win probability for composite endpoints are considered: (1) the prioritized win probability, resulting from counting wins for the multiple endpoints in order of priority, and (2) the global win probability, equal to the (weighted) average of multiple win probabilities. Simulation results suggest that the proposed methods perform very well. Case studies based on a cluster randomization trial in Crohn’s disease and corresponding SAS and R scripts are provided.