Distal Causal Excursion Effects: Modeling Long-Term Effects of Time-Varying Treatments in Micro-Randomized Trials

2025-02-19

AI Summary

Existing causal methods—such as causal excursion effects—capture only short-term intervention impacts and fail to characterize long-term behavioral change, particularly in micro-randomized trials (MRTs) with time-varying interventions. Method: To address the challenge of estimating distal effects in MRTs, we formally define and identify the “Distal Causal Excursion Effect” (DCEE), quantifying the cumulative causal impact of an intervention on distal outcomes. We propose two cross-fitted, model-misspecification-robust DCEE estimators that integrate marginal structural models, inverse probability weighting, and double robustness, enabling interpretable modeling even under high-dimensional decision points. Results: Empirical evaluation on the HeartSteps dataset reveals that early activity prompts exert significantly stronger causal effects on long-term habit formation than later prompts—providing critical causal evidence for temporal optimization of digital health interventions.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• Modeling long-term effects of time-varying treatments
• Addressing limitations in causal inference for distal outcomes
• Quantifying intervention impact on long-term behavior change

Innovation

• Distal causal excursion effect for long-term outcomes
• Robust estimators with cross-fitting and without
• Application to HeartSteps MRT for habit formation