Micro-randomized trials are commonly conducted for optimizing mobile health interventions such as push notifications for behavior change. In analyzing such trials, causal excursion effects are often of primary interest, and their estimation typically involves inverse probability weighting (IPW). However, in a micro-randomized trial additional treatments can often occur during the time window over which an outcome is defined, and this can greatly inflate the variance of the causal effect estimator because IPW would involve a product of numerous weights. To reduce variance and improve estimation efficiency, we propose a new estimator using a modified version of IPW, which we call "per-decision IPW". It is applicable when the outcome is binary and can be expressed as the maximum of a series of sub-outcomes defined over sub-intervals of time. We establish the estimator's consistency and asymptotic normality. Through simulation studies and real data applications, we demonstrate substantial efficiency improvement of the proposed estimator over existing estimators (relative efficiency up to 1.45 and sample size savings up to 31% in realistic settings). The new estimator can be used to improve the precision of primary and secondary analyses for micro-randomized trials with binary outcomes.

翻译：微随机试验通常用于优化移动健康干预措施，如行为改变的推送通知。在分析此类试验时，因果瞬态效应通常是主要关注点，其估计通常涉及逆概率加权（IPW）。然而，在微随机试验中，在定义结果的时间窗口内经常可能发生额外干预，这会导致因果效应估计量的方差大幅膨胀，因为IPW涉及大量权重的乘积。为降低方差并提高估计效率，我们提出了一种使用改进版IPW的新估计量，称之为"每决策IPW"。该方法适用于二元结果可表示为一系列定义在时间子区间上的子结果最大值的情况。我们证明了该估计量的一致性和渐近正态性。通过模拟研究和实际数据应用，我们证明了所提估计量相比现有估计量具有显著的效率提升（在现实场景中相对效率最高达1.45，样本量节省最高达31%）。该新估计量可提高二元结果微随机试验中主要分析和次要分析的精度。