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

2026-08-05

AI Summary

This study addresses the challenge of estimating causal effects and calculating sample size for micro-randomized trials in mobile health, where multi-category treatments influence binary proximal outcomes. The authors define a causal walk effect and propose the EMEE-catA estimator, deriving—for the first time—a sample size formula that simultaneously controls Type I error and ensures statistical power. Grounded in a causal inference framework and generalized linear models, the method is validated through Monte Carlo simulations demonstrating its validity and robustness. Application to real-world data from the Drink Less trial illustrates that this approach offers a practical, statistically efficient, and causally interpretable solution for sample size determination and implementation guidance in micro-randomized trials with categorical interventions and binary outcomes.

Abstract

Micro-randomized trials (MRTs) provide a framework for evaluating the marginal and moderated effects of mobile health (mHealth) interventions. In many applications, treatments take the form of categorical variables with multiple levels, such as different message contents or delivery strategies. Many scientifically meaningful longitudinal outcomes in mHealth studies are binary, such as whether a participant opens an app, engages with content, or completes a target behavior following a decision point at which treatment is randomized. This paper focuses on MRTs with categorical treatments and binary proximal outcomes. We define the causal excursion effect, propose an estimator called EMEE-catA, and derive a sample size formula for comparing categorical treatment levels that controls the type I error rate and guarantees power under working assumptions. We conduct extensive simulation studies to evaluate the operating characteristics of the proposed sample size formula, including robustness to violations of these assumptions. We further provide practical guidance for implementing the proposed approach to ensure adequate power in real-world MRTs. The methods are illustrated using data from the Drink Less MRT.

Problem

• Micro-randomized trials
• Categorical treatments
• Binary proximal outcome
• Causal effect estimation
• Sample size calculation

Innovation

• micro-randomized trials
• categorical treatments
• binary proximal outcome
• causal excursion effect
• sample size calculation