Incorporating nonparametric methods for estimating causal excursion effects in mobile health with zero-inflated count outcomes

In the domain of 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, backed by current semiparametric inference techniques. Yet, existing methods mainly focus 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, the number of screen views in the subsequent hour following the intervention decision point. In the current paper, we revisit the concept of causal excursion effects, specifically for zero-inflated count outcomes, and introduce novel estimation approaches that incorporate nonparametric techniques. Bidirectional asymptotics are derived for the proposed estimators. Through extensive simulation studies, we evaluate the performance of the proposed estimators. As an illustration, we also employ the proposed methods to the Drink Less trial data.