Estimating Causal Effects for Binary Outcomes Using Per-Decision Inverse Probability Weighting

TL;DR

This paper introduces two novel estimators based on a modified inverse probability weighting method, called 'per-decision IPW', to more efficiently estimate causal effects in micro-randomized trials with binary outcomes, reducing variance and improving precision.

Contribution

The paper proposes two new estimators using per-decision IPW and semiparametric efficiency theory to improve causal effect estimation in micro-randomized trials with binary outcomes.

Findings

Significant variance reduction demonstrated in simulations.

Enhanced estimation efficiency shown in real data applications.

Estimators are consistent and asymptotically normal.

Abstract

Micro-randomized trials are commonly conducted for optimizing mobile health interventions such as push notifications for behavior change. In analyzing such trials, causal excursion effects are often of primary interest, and their estimation typically involves inverse probability weighting (IPW). However, in a micro-randomized trial, additional treatments can often occur during the time window over which an outcome is defined, and this can greatly inflate the variance of the causal effect estimator because IPW would involve a product of numerous weights. To reduce variance and improve estimation efficiency, we propose two new estimators using a modified version of IPW, which we call "per-decision IPW". The second estimator further improves efficiency using the projection idea from the semiparametric efficiency theory. These estimators are applicable when the outcome is binary and can be expressed as the maximum of a series of sub-outcomes defined over sub-intervals of time. We establish the estimators' consistency and asymptotic normality. Through simulation studies and real data applications, we demonstrate substantial efficiency improvement of the proposed estimator over existing estimators. The new estimators can be used to improve the precision of primary and secondary analyses for micro-randomized trials with binary outcomes.