  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.
