Distal Causal Excursion Effects: Modeling Long-Term Effects of Time-Varying Treatments in Micro-Randomized Trials
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远期因果偏离效应：微随机试验中时变处理的长期效应建模
- 研究问题
- 微随机试验反复随机分配干预，如何衡量某次干预对长期行为的影响，并以简洁模型区分干预时点的作用？
- 方法与思路
- 作者定义远期因果偏离效应，比较两种偏离策略下的远期结局，并提出采用与不采用交叉拟合的两类估计量。
- 材料陈述的贡献
- 摘要称两类估计量均对结局模型误设稳健，并建立渐近性质；HeartSteps应用提示较早提示的长期效应更强。
- 阅读关注点
- 应核对偏离策略及远期结局的定义、其他处理分配如何被边际化，以及模型误设稳健性和渐近推断所需条件。
- 阅读边界
- 这是arXiv预印本，不能据此确认同行评审或期刊接收；摘要未说明识别条件、效应大小及习惯形成的具体测量。
原文摘要
Micro-randomized trials (MRTs) play a crucial role in optimizing digital interventions. In an MRT, each participant is sequentially randomized among treatment options hundreds of times. While the interventions tested in MRTs target short-term behavioral responses (proximal outcomes), their ultimate goal is to drive long-term behavior change (distal outcomes). However, existing causal inference methods, such as the causal excursion effect, are limited to proximal outcomes, making it challenging to quantify the long-term impact of interventions. To address this gap, we introduce the distal causal excursion effect (DCEE), a novel estimand that quantifies the long-term effect of time-varying treatments. The DCEE contrasts distal outcomes under two excursion policies while marginalizing over most treatment assignments, enabling a parsimonious and interpretable causal model even with a large number of decision points. We propose two estimators for the DCEE -- one with cross-fitting and one without -- both robust to misspecification of the outcome model. We establish their asymptotic properties and validate their performance through simulations. We apply our method to the HeartSteps MRT to assess the impact of activity prompts on long-term habit formation. Our findings suggest that prompts delivered earlier in the study have a stronger long-term effect than those delivered later, underscoring the importance of intervention timing in behavior change. This work provides the critically needed toolkit for scientists working on digital interventions to assess long-term causal effects using MRT data.