  Micro-randomized trial (MRT) is a sequential randomized experimental design
to empirically evaluate the effectiveness of mobile health (mHealth)
intervention components that may be delivered at hundreds or thousands of
decision points. The MRT context has motivated a new class of causal estimands,
termed "causal excursion effects", for which inference can be made by a
weighted, centered least squares approach (Boruvka et al., 2017). Existing
methods assume between-subject independence and non-interference. Deviations
from these assumptions often occur which, if unaccounted for, may result in
bias and overconfident variance estimates. In this paper, causal excursion
effects are considered under potential cluster-level correlation and
interference and when the treatment effect of interest depends on cluster-level
moderators. The utility of our proposed methods is shown by analyzing data from
a multi-institution cohort of first year medical residents in the United
States. The approach paves the way for construction of mHealth interventions
that account for observed social network information.
