Incorporating Auxiliary Variables to Improve the Efficiency of Time-Varying Treatment Effect Estimation

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).