Robust Estimation of Moderated Causal Excursion Odds Ratio in Micro-Randomized Trials

2025-09-24

AI Summary

To address the lack of valid estimation methods for causal excursion effects on the odds ratio scale in micro-randomized trials (MRTs), this paper introduces the first causal excursion odds ratio (CEOR) estimation framework for longitudinal binary outcomes. Methodologically, it proposes a doubly robust generalized estimating equation that integrates inverse probability weighting with regression adjustment, augmented by an association perturbation model to accommodate complex, covariate-dependent randomization mechanisms; it supports arbitrary link functions and is robust to misspecification of the association model under the null. The estimator is proven to be consistent and asymptotically normal. Simulation studies demonstrate strong finite-sample performance, and application to the Drink Less alcohol intervention trial successfully identifies the immediate effect of notification enablement rate. This work fills a critical gap in odds-ratio-scale causal inference for MRTs and expands the statistical toolkit for evaluating dynamic mobile health interventions.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Micro-randomized trials (MRTs) have become increasingly popular for developing and evaluating mobile health interventions that promote healthy behaviors and manage chronic conditions. The recently proposed causal excursion effects have become the standard measure for interventions' marginal and moderated effect in MRTs. Existing methods for MRTs with binary outcomes focus on causal excursion effects on the relative risk scale. However, a causal excursion effect on the odds ratio scale is attractive for its interpretability and valid predicted probabilities, making it a valuable supplement to causal excursion relative risk. In this paper, we propose two novel estimators for the moderated causal excursion odds ratio for MRTs with longitudinal binary outcomes. When the prespecified moderator fully captures the way interventions are sequentially randomized, we propose a doubly robust estimator that remains consistent if either of two nuisance models is correctly specified. For more general settings in which treatment randomization depends on variables beyond the chosen moderator, we propose a general estimator that incorporates an association nuisance model. We further establish the general estimator's robustness to the misspecification of the association nuisance model under no causal effect, and extend the general estimator to accommodate any link functions. We establish the consistency and asymptotic normality of both estimators and demonstrate their performance through simulation studies. We apply the methods to Drink Less, a 30-day MRT for developing mobile health interventions to help reduce alcohol consumption, where the proximal outcome is whether the user opens the app in the hour following the notification.

Problem

• Estimating moderated causal excursion odds ratio in micro-randomized trials
• Developing doubly robust estimators for longitudinal binary outcomes in MRTs
• Addressing treatment randomization dependency beyond prespecified moderators

Innovation

• Estimator for moderated causal excursion odds ratio
• Doubly robust estimator for prespecified moderators
• General estimator incorporating association nuisance model