Bao Yihan, Bell Lauren, Williamson Elizabeth, Garnett Claire, Qian Tianchen
Department of Statistics and Data Science, Yale University, 266 Whitney Avenue, New Haven, CT 06511, United States.
Leeds Institute of Clinical Trials Research, University of Leeds, Level 10 Worsley Building Clarendon Way, Leeds, LS2 9NL, United Kingdom.
Biostatistics. 2024 Dec 31;26(1). doi: 10.1093/biostatistics/kxae025.
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 two new estimators using a modified version of IPW, which we call "per-decision IPW." The second estimator further improves efficiency using the projection idea from the semiparametric efficiency theory. These estimators are 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 estimators' consistency and asymptotic normality. Through simulation studies and real data applications, we demonstrate substantial efficiency improvement of the proposed estimator over existing estimators. The new estimators can be used to improve the precision of primary and secondary analyses for micro-randomized trials with binary outcomes.
微随机试验通常用于优化移动健康干预措施，如用于行为改变的推送通知。在分析此类试验时，因果偏移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通常会出现额外的治疗，这可能会极大地增加因果效应估计量的方差，因为IPW会涉及大量权重的乘积。为了减少方差并提高估计效率，我们提出了两种使用IPW修改版本的新估计量，我们称之为“逐决策IPW”。第二种估计量利用半参数效率理论中的投影思想进一步提高了效率。当结果为二元且可表示为在时间子区间上定义的一系列子结果的最大值时，这些估计量适用。我们建立了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，我们证明了所提出的估计量相对于现有估计量在效率上有显著提高。新的估计量可用于提高具有二元结果的微随机试验的主要和次要分析的精度。
