The use of smart devices (e.g., smartphones, smartwatches) and other wearables to deliver digital interventions to improve health outcomes has grown significantly in the past few years. Mobile health (mHealth) systems are excellent tools for the delivery of adaptive interventions that aim to provide the right type and amount of support, at the right time, by adapting to an individual's changing context. Micro-randomized trials (MRTs) are an increasingly common experimental design that is the main source for data-driven evidence of mHealth intervention effectiveness. To assess time-varying causal effect moderation in an MRT, individuals are intensively randomized to receive treatment over time. In addition, measurements, including individual characteristics, and context are also collected throughout the study. The effective utilization of covariate information to improve inferences regarding causal effects has been well-established in the context of randomized control trials (RCTs), where covariate adjustment is applied to leverage baseline data to address chance imbalances and improve the asymptotic efficiency of causal effect estimation. However, the application of this approach to longitudinal data, such as MRTs, has not been thoroughly explored. Recognizing the connection to Neyman Orthogonality, we propose a straightforward and intuitive method to improve the efficiency of moderated causal excursion effects by incorporating auxiliary variables. We compare the robust standard errors of our method with those of the benchmark method. The efficiency gain of our approach is demonstrated through simulation studies and an analysis of data from the Intern Health Study (NeCamp et al., 2020).

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