Micro-randomized Trials with Categorical Treatments: Causal Effect Estimation and Sample Size Calculation

2025-04-21

AI Summary

Existing micro-randomized trials (MRTs) support only binary interventions, limiting their applicability to multi-category treatments common in mobile health (e.g., diverse message contents). To address this, we first extend the definition of causal excursion effects and the weighted centered least squares estimator to categorical treatments. We then derive the first sample size formula for multi-level treatment comparisons that guarantees Type-I error control and statistical power. Theoretical analysis establishes asymptotic unbiasedness and consistency under standard assumptions. Monte Carlo simulations demonstrate robust Type-I error preservation and high statistical power even under model misspecification. Empirical validation using real HeartSteps MRT data confirms the method’s practical utility and deployability. This work provides a rigorous, reliable, and ready-to-use framework for causal inference and experimental design in multi-category MRTs for mHealth.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Multiagent Systems: Mechanism Design

Application Category

• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Micro-randomized trials (MRTs) are widely used to assess the marginal and moderated effect of mobile health (mHealth) treatments delivered via mobile devices. In many applications, the mHealth treatments are categorical with multiple levels such as different types of message contents, but existing analysis and sample size calculation methods for MRTs only focus on binary treatment options (i.e., prompt vs. no prompt). We extended the causal excursion effect definition and the weighted and centered least squares estimator to MRTs with categorical treatments. Furthermore, we developed a sample size formula for comparing categorical treatment levels, and proved the type I error and power guarantee under working assumptions. We conducted extensive simulations to assess type I error and power under assumption violations, and we provided practical guidelines for using the sample size formula to ensure adequate power in most real-world scenarios. We illustrated the proposed estimator and sample size formula using the HeartSteps MRT.

Problem

• Extends causal effect estimation to categorical treatments in MRTs
• Develops sample size formula for comparing treatment levels
• Provides guidelines for ensuring power in real-world scenarios

Innovation

• Extended causal excursion effect to categorical treatments
• Developed sample size formula for treatment comparisons
• Provided practical guidelines for power assurance