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Estimating causal effects for binary outcomes using per-decision inverse probability weighting
Yihan Bao1, Lauren Bell2, Elizabeth Williamson3
1Department of Statistics and Data Science, Yale University, 266 Whitney Avenue, New Haven, CT 06511, United States.
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.
Insights
New methods for analyzing micro-randomized trials improve causal effect estimation. Per-decision inverse probability weighting (IPW) reduces variance in mobile health intervention studies with binary outcomes.
Area of Science:
- Biostatistics
- Digital Health
- Behavioral Science
Background:
- Micro-randomized trials (MRTs) are crucial for optimizing mobile health interventions.
- Estimating causal excursion effects in MRTs often relies on inverse probability weighting (IPW).
- Standard IPW can suffer from high variance in MRTs due to numerous time-varying treatments.
Purpose of the Study:
- To develop novel, more efficient estimators for causal effects in MRTs.
- To address the variance inflation issue in IPW for complex MRT designs.
- To enhance the precision of analyses for binary outcomes in mobile health research.
Main Methods:
- Proposed two new "per-decision IPW" estimators for binary outcomes in MRTs.
- The second estimator incorporates semiparametric efficiency theory using projection.
- Methods are validated for consistency and asymptotic normality.
Main Results:
- The proposed per-decision IPW estimators demonstrate substantial efficiency improvements over existing methods.
- Simulations and real-world data applications confirm the enhanced precision.
- The new estimators effectively reduce variance in causal effect estimation.
Conclusions:
- The novel per-decision IPW estimators offer a significant advancement for analyzing MRTs.
- These methods improve the precision of primary and secondary analyses in mobile health intervention studies.
- The proposed estimators enhance the reliability of findings from micro-randomized trials with binary outcomes.
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