  In mobile health, tailoring interventions for real-time delivery is of
paramount importance. Micro-randomized trials have emerged as the
"gold-standard" methodology for developing such interventions. Analyzing data
from these trials provides insights into the efficacy of interventions and the
potential moderation by specific covariates. The "causal excursion effect", a
novel class of causal estimand, addresses these inquiries. Yet, existing
research mainly focuses on continuous or binary data, leaving count data
largely unexplored. The current work is motivated by the Drink Less
micro-randomized trial from the UK, which focuses on a zero-inflated proximal
outcome, i.e., the number of screen views in the subsequent hour following the
intervention decision point. To be specific, we revisit the concept of causal
excursion effect, specifically for zero-inflated count outcomes, and introduce
novel estimation approaches that incorporate nonparametric techniques.
Bidirectional asymptotics are established for the proposed estimators.
Simulation studies are conducted to evaluate the performance of the proposed
methods. As an illustration, we also implement these methods to the Drink Less
trial data.
