Electronic Thesis and Dissertation Repository

Thesis Format



Doctor of Philosophy


Epidemiology and Biostatistics

Collaborative Specialization



Zou, Guangyong

2nd Supervisor

Jairath, Vipul

Joint Supervisor


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.

Summary for Lay Audience

Randomized controlled trials (RCTs) are scientific experiments used to evaluate medical treatments. Participants are randomly allocated to receive experimental treatment or a control, e.g., placebo. Random allocation helps ensure that groups have similar characteristics. Researchers can then compare outcomes between the experimental and control groups to determine whether the treatment has a significant effect. Cluster randomized trials, or cluster trials, are a special type of RCT where clusters or groups of people, e.g., families or clinics, are randomly allocated rather than individuals. They make it easier to deliver complex treatments and reduce the chances of treatment mix-ups since all individuals within the same cluster receive the same treatment. When diseases impact multiple aspects of health, cluster trials might measure multiple outcomes to fully understand the effects of treatment. Analyzing data from these trials is difficult because of relationships between outcomes within a cluster and within individuals. That is, people within the same cluster respond similarly, and outcomes may influence one another. To simplify analysis, researchers sometimes combine multiple outcomes into one overall measure. This reduces some complications, like figuring out relationships between different outcomes, but introduces others when the outcomes have different numeric properties or levels of importance. This thesis uses tournament-style evaluation to analyze cluster trials with multiple outcomes. Treatment patients compete head-to-head with control patients, with a “win" declared if the treatment patient is in better health. The number of wins divided by the number of competitions yields ``the win probability." The win probability is the probability that a treatment patient does as well as or better than a control patient and is congruent with the Hippocratic Oath, “to help, or at least, do no harm." The “prioritized win probability" results from comparing outcomes in order of their priority. The “global win probability" results from averaging the win probability for each outcome. Computer simulation studies show that the new methods work well. Examples of how these methods could be used to analyze cluster trials for Crohn's disease and programs in SAS and R are provided.

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

Available for download on Tuesday, July 15, 2025