Causal Inference in Randomized Trials with Partial Clustering and Imbalanced Dependence Structures

In many randomized trials, participants are grouped into clusters, such as neighborhoods or schools, and these clusters are assumed to be the independent unit. This assumption, however, might not reflect the underlying dependence structure, with serious consequences to statistical power. First, consider a cluster randomized trial where participants are artificially grouped together for the purposes of randomization. For intervention participants the groups are the basis for intervention delivery, but for control participants the groups are dissolved. Second, consider an individually randomized group treatment trial where participants are randomized and then post-randomization, intervention participants are grouped together for intervention delivery, while the control participants continue with the standard of care. In both trial designs, outcomes among intervention participants will be dependent within each cluster, while outcomes for control participants will be effectively independent. We use causal models to non-parametrically describe the data generating process for each trial design and formalize the conditional independence in the observed data distribution. For estimation and inference, we propose a novel implementation of targeted minimum loss-based estimation (TMLE) accounting for partial clustering and the imbalanced dependence structure. TMLE is a model-robust approach, leverages covariate adjustment and machine learning to improve precision, and facilitates estimation of a large set of causal effects. In finite sample simulations, TMLE achieved comparable or markedly higher statistical power than common alternatives. Finally, application of TMLE to real data from the SEARCH-IPT trial resulted in 20-57\% efficiency gains, demonstrating the real-world consequences of our proposed approach.