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，例如促进行为改变的推送通知。在分析此类试验时，因果偏离效应通常是首要关注点，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往往会发生额外干预，这可能会极大增加因果效应估计量的方差，因为IPW会涉及多个权重的乘积。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"每次决策IPW"。该方法适用于二元结果，且该结果可表示为在一系列子时间间隔上定义的子结果的最大值。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，我们展示了所提估计量相较于现有估计量的显著效率提升（在现实场景中，相对效率高达1.45，样本量节省高达31%）。新估计量可用于提高具有二元结果的微随机试验主要和次要分析的精度。