Modeling Time-Varying Effects of Mobile Health Interventions Using Longitudinal Functional Data from HeartSteps Micro-Randomized Trial

TL;DR

This paper develops a novel semiparametric model to analyze how mobile health intervention effects vary over time and with context using longitudinal data from a micro-randomized trial, providing insights into individual response patterns.

Contribution

It introduces the first semiparametric causal excursion effect model with varying coefficients for longitudinal functional data in mobile health studies.

Findings

Identified how intervention effects change over time and context.

Demonstrated robustness of the estimator through simulations.

Provided new insights into response profiles and moderation factors.

Abstract

To optimize mobile health interventions and advance domain knowledge on intervention design, it is critical to understand how the intervention effect varies over time and with contextual information. This study aims to assess how a push notification suggesting physical activity influences individuals' step counts using data from the HeartSteps micro-randomized trial (MRT). The statistical challenges include the time-varying treatments and longitudinal functional step count measurements. We propose the first semiparametric causal excursion effect model with varying coefficients to model the time-varying effects within a decision point and across decision points in an MRT. The proposed model incorporates double time indices to accommodate the longitudinal functional outcome, enabling the assessment of time-varying effect moderation by contextual variables. We propose a two-stage causal effect estimator that is robust against a misspecified high-dimensional outcome regression nuisance model. We establish asymptotic theory and conduct simulation studies to validate the proposed estimator. Our analysis provides new insights into individuals' change in response profiles (such as how soon a response occurs) due to the activity suggestions, how such changes differ by the type of suggestions received, and how such changes depend on other contextual information such as being recently sedentary and the day being a weekday.