  The use of smart devices (e.g., smartphones, smartwatches) and other
wearables for context sensing and delivery of digital interventions to improve
health outcomes has grown significantly in behavioral and psychiatric studies.
Micro-randomized trials (MRTs) are a common experimental design for obtaining
data-driven evidence on mobile health (mHealth) intervention effectiveness
where each individual is repeatedly randomized to receive treatments over
numerous time points. Individual characteristics and the contexts around
randomizations are also collected throughout the study, some may be
pre-specified as moderators when assessing time-varying causal effect
moderation. Moreover, we have access to abundant measurements beyond just the
moderators. Our study aims to leverage this auxiliary information to improve
causal estimation and better understand the intervention effect. Similar
problems have been raised in randomized control trials (RCTs), where extensive
literature demonstrates that baseline covariate information can be incorporated
to alleviate chance imbalances and increase asymptotic efficiency. However,
covariate adjustment in the context of time-varying treatments and repeated
measurements, as seen in MRTs, has not been studied. Recognizing the connection
to Neyman Orthogonality, we address this gap by introducing an intuitive
approach to incorporate auxiliary variables to improve the efficiency of
moderated causal excursion effect estimation. The efficiency gain of our
approach is proved theoretically and demonstrated through simulation studies
and an analysis of data from the Intern Health Study (NeCamp et al., 2020).
