# Estimating Time-Varying Causal Excursion Effect in Mobile Health with Binary Outcomes

arXiv: https://arxiv.org/abs/1906.00528 · HTML: https://mlsanity.com/paper/1906.00528/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2019.

## Built on by (most cited first, 6 of 6)

- [Did we personalize? Assessing personalization by an online reinforcement learning algorithm using resampling](https://mlsanity.com/paper/2304.05365/) (2023)
- [Thompson sampling for zero-inflated count outcomes with an application to the Drink Less mobile health study](https://mlsanity.com/paper/2311.14359/) (2023)
- [Minimum information divergence of Q-functions for dynamic treatment resumes](https://mlsanity.com/paper/2211.08741/) (2022)
- [A Meta-Learning Method for Estimation of Causal Excursion Effects to Assess Time-Varying Moderation](https://mlsanity.com/paper/2306.16297/) (2023)
- [Reconciling Causality and Non-Equilibrium Thermodynamics with Hamiltonian Causal Models](https://mlsanity.com/paper/2606.04822/) (2026)
- [When AI Generates Covariates: Causal Typing and Estimand Drift in Sequential Experiments](https://mlsanity.com/paper/2609.17772/) (2026)

## Abstract (arXiv)

Advances in wearables and digital technology now make it possible to deliver behavioral mobile health interventions to individuals in their everyday life. The micro-randomized trial (MRT) is increasingly used to provide data to inform the construction of these interventions. In an MRT, each individual is repeatedly randomized among multiple intervention options, often hundreds or even thousands of times, over the course of the trial. This work is motivated by multiple MRTs that have been conducted, or are currently in the field, in which the primary outcome is a longitudinal binary outcome. The primary aim of such MRTs is to examine whether a particular time-varying intervention has an effect on the longitudinal binary outcome, often marginally over all but a small subset of the individual's data. We propose the definition of causal excursion effect that can be used in such primary aim analysis for MRTs with binary outcomes. Under rather restrictive assumptions one can, based on existing literature, derive a semiparametric, locally efficient estimator of the causal effect. We, starting from this estimator, develop an estimator that can be used as the basis of a primary aim analysis under more plausible assumptions. Simulation studies are conducted to compare the estimators. We illustrate the developed methods using data from the MRT, BariFit. In BariFit, the goal is to support weight maintenance for individuals who received bariatric surgery.