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

Oregon Convention Center 

Micro-randomized trials (MRTs) 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 MRT, 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 a new estimator using a modified version of IPW, which we call "per-decision IPW". It is 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 estimator's 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 estimator can be used to improve the precision of primary and secondary analyses for MRTs with binary outcomes.

causal excursion effect

inverse probability weighting

log relative risk

micro-randomized trial

per-decision importance weighting

mobile health 

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