  Cluster randomized trials (CRTs) are a popular design to study the effect of
interventions in infectious disease settings. However, standard analysis of
CRTs primarily relies on strong parametric methods, usually mixed-effect models
to account for the clustering structure, and focuses on the overall
intent-to-treat (ITT) effect to evaluate effectiveness. The paper presents two
assumption-lean methods to analyze two types of effects in CRTs, ITT effects
and network effects among well-known compliance groups. For the ITT effects, we
study the overall and the heterogeneous ITT effects among the observed
covariates where we do not impose parametric models or asymptotic restrictions
on cluster size. For the network effects among compliance groups, we propose a
new bound-based method that uses pre-treatment covariates, classification
algorithms, and a linear program to obtain sharp bounds. A key feature of our
method is that the bounds can become narrower as the classification algorithm
improves and the method may also be useful for studies of partial
identification with instrumental variables. We conclude by reanalyzing a CRT
studying the effect of face masks and hand sanitizers on transmission of 2008
interpandemic influenza in Hong Kong.
