Clustered Treatment Assignments and Sensitivity to Unmeasured Biases in Observational Studies
Statistics and Probability
Clustered treatment assignment occurs when individuals are grouped into clusters prior to treatment and whole clusters, not individuals, are assigned to treatment or control. In randomized trials, clustered assignments may be required because the treatment must be applied to all children in a classroom, or to all patients at a clinic, or to all radio listeners in the same media market. The most common cluster randomized design pairs 2S clusters into S pairs based on similar pretreatment covariates, then picks one cluster in each pair at random for treatment, the other cluster being assigned to control. Typically, group randomization increases sampling variability and so is less efficient, less powerful, than randomization at the individual level, but it may be unavoidable when it is impractical to treat just a few people within each cluster. Related issues arise in nonrandomized, observational studies of treatment effects, but in this case one must examine the sensitivity of conclusions to bias from nonrandom selection of clusters for treatment. Although clustered assignment increases sampling variability in observational studies, as it does in randomized experiments, it also tends to decrease sensitivity to unmeasured biases, and as the number of cluster pairs increases the latter effect overtakes the former, dominating it when allowance is made for nontrivial biases in treatment assignment. Intuitively, a given magnitude of departure from random assignment can do more harm if it acts on individual students than if it is restricted to act on whole classes, because the bias is unable to pick the strongest individual students for treatment, and this is especially true if a serious effort is made to pair clusters that appeared similar prior to treatment. We examine this issue using an asymptotic measure, the design sensitivity, some inequalities that exploit convexity, simulation, and an application concerned with the flooding of villages in Bangladesh.