Micro-randomized trials (MRTs) are increasingly utilized for optimizing mobile health interventions, with the causal excursion effect (CEE) as a central quantity for evaluating interventions under policies that deviate from the experimental policy. However, MRT often contains missing data due to reasons such as missed self-reports or participants not wearing sensors, which can bias CEE estimation. In this paper, we propose a two-stage, doubly robust estimator for CEE in MRTs when longitudinal outcomes are missing at random, accommodating continuous, binary, and count outcomes. Our two-stage approach allows for both parametric and nonparametric modeling options for two nuisance parameters: the missingness model and the outcome regression. We demonstrate that our estimator is doubly robust, achieving consistency and asymptotic normality if either the missingness or the outcome regression model is correctly specified. Simulation studies further validate the estimator's desirable finite-sample performance. We apply the method to HeartSteps, an MRT for developing mobile health interventions that promote physical activity.

翻译：微随机化试验（MRT）正日益广泛地应用于优化移动健康干预措施，其中因果偏移效应（CEE）是评估偏离实验策略的干预策略下干预效果的核心指标。然而，由于自我报告遗漏或参与者未佩戴传感器等原因，MRT常包含缺失数据，这可能导致CEE估计产生偏差。本文针对纵向结局随机缺失的MRT，提出了一种两阶段双重稳健的CEE估计方法，适用于连续型、二分类与计数型结局。我们的两阶段方法允许对两个干扰参数（缺失机制模型与结局回归模型）采用参数化或非参数化建模方式。我们证明了该估计量具有双重稳健性：只要缺失机制模型或结局回归模型之一设定正确，估计量即具有一致性与渐近正态性。模拟研究进一步验证了估计量在有限样本下的优良性能。我们将该方法应用于HeartSteps研究——一项旨在开发促进身体活动的移动健康干预措施的微随机化试验。