  Across research disciplines, cluster randomized trials (CRTs) are commonly
implemented to evaluate interventions delivered to groups of participants, such
as communities and clinics. Despite advances in the design and analysis of
CRTs, several challenges remain. First, there are many possible ways to specify
the causal effect of interest (e.g., at the individual-level or at the
cluster-level). Second, the theoretical and practical performance of common
methods for CRT analysis remain poorly understood. Here, we present a general
framework to formally define an array of causal effects in terms of summary
measures of counterfactual outcomes. Next, we provide a comprehensive overview
of CRT estimators, including the t-test, generalized estimating equations
(GEE), augmented-GEE, and targeted maximum likelihood estimation (TMLE). Using
finite sample simulations, we illustrate the practical performance of these
estimators for different causal effects and when, as commonly occurs, there are
limited numbers of clusters of different sizes. Finally, our application to
data from the Preterm Birth Initiative (PTBi) study demonstrates the real-world
impact of varying cluster sizes and targeting effects at the cluster-level or
at the individual-level. Specifically, the relative effect of the PTBI
intervention was 0.81 at the cluster-level, corresponding to a 19% reduction in
outcome incidence, and was 0.66 at the individual-level, corresponding to a 34%
reduction in outcome risk. Given its flexibility to estimate a variety of
user-specified effects and ability to adaptively adjust for covariates for
precision gains while maintaining Type-I error control, we conclude TMLE is a
promising tool for CRT analysis.
