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).

翻译：近年来，使用智能设备（如智能手机、智能手表）及其他可穿戴设备提供数字干预以改善健康结果的做法显著增长。移动健康（mHealth）系统是提供适应性干预的优质工具，旨在通过适应个体不断变化的背景，在合适的时间提供合适类型和程度的支持。微随机试验（MRTs）是一种日益常见的实验设计，是mHealth干预效果的数据驱动证据的主要来源。为了评估MRT中时变因果效应的调节作用，个体在时间维度上被密集随机分配接受处理。此外，整个研究过程中还会收集个体特征和背景等测量数据。有效利用协变量信息来改善因果效应推断的方法已在随机对照试验（RCTs）中得到充分验证，其中协变量调整用于利用基线数据解决机会不平衡问题，并提高因果效应估计的渐近效率。然而，这种方法在纵向数据（如MRTs）中的应用尚未得到深入探索。认识到与Neyman正交性的关联，我们提出了一种直观简便的方法，通过引入辅助变量来提高调节因果逸出效应的效率。我们将本方法的稳健标准误差与基准方法进行了比较。通过模拟研究和来自Intern Health Study（NeCamp等人，2020年）的数据分析，验证了我们方法的效率提升。