A Nested Dirichlet Process Analysis of Cluster Randomized Trial Data With Application in Geriatric Care Assessment

In cluster randomized trials, patients seen by the same physician are randomized to the same treatment arm as a group. Besides the natural clustering of patients due to cluster/group randomization, interactions between an individual patient and the attending physician within the group could just as well influence patient care outcomes. Despite the intuitive relevance of these interactions to treatment assessment, few studies have thus far examined their influences. Whether and to what extent these interactions affect assessment of the treatment effect remains unexplored. In fact, few statistical models provide ready accommodation for such interactions. In this research, we propose a general modeling framework based on the nested Dirichlet process (nDP) for assessing treatment effect in cluster randomized trials. The proposed methodology explicitly accounts for physician--patient interactions by assuming that the interactions follow unspecified group-specific distributions from an nDP. In addition to accounting for physician--patient interactions, the model has greatly enhanced the flexibility of traditional mixed effect models by allowing for nonnormally distributed random effects, thus, alleviating concerns about mixed effect misspecification and sidestepping verification of distributional assumptions on random effects. At the same time, the model retains the mixed models' ability to make inferences on fixed effects. The proposed method is easily extendable to more complicated hierarchical clustering structures. We introduce the method in the context of a real cluster randomized trial. A comprehensive simulation study was conducted to assess the operating characteristics of the proposed nDP model.