Estimating Time-Varying Direct and Indirect Causal Excursion Effects with Longitudinal Binary Outcomes

TL;DR

This paper develops a new statistical method to estimate time-varying causal effects in longitudinal binary outcome studies, accounting for heterogeneity and interference, with theoretical guarantees and empirical validation.

Contribution

It introduces a novel inferential procedure for causal excursion effects that handles effect heterogeneity and interference in longitudinal binary data.

Findings

Method provides consistent point and interval estimates

Theoretical guarantees of estimator's properties

Empirical validation through simulation studies

Abstract

Construction of just-in-time adaptive interventions, such as prompts delivered by mobile apps to promote and maintain behavioral change, requires knowledge about time-varying moderated effects to inform when and how we deliver intervention options. Micro-randomized trials (MRT) have emerged as a sequentially randomized design to gather requisite data for effect estimation. The existing literature (Qian et al., 2020; Boruvka et al., 2018; Dempsey et al., 2020) has defined a general class of causal estimands, referred to as "causal excursion effects", to assess the time-varying moderated effect. However, there is limited statistical literature on how to address potential between-cluster treatment effect heterogeneity and within-cluster interference in a sequential treatment setting for longitudinal binary outcomes. In this paper, based on a cluster conceptualization of the potential outcomes, we define a larger class of direct and indirect causal excursion effects for proximal and lagged binary outcomes, and propose a new inferential procedure that addresses effect heterogeneity and interference. We provide theoretical guarantees of consistency and asymptotic normality of the estimator. Extensive simulation studies confirm our theory empirically and show the proposed procedure provides consistent point estimator and interval estimates with valid coverage. Finally, we analyze a data set from a multi-institution MRT study to assess the time-varying moderated effects of mobile prompts upon binary study engagement outcomes.