Efficient adjustment sets for time-dependent treatment effect estimation in nonparametric causal graphical model
David Adenyo, Mireille E Schnitzer, David Berger, Jason R Guertin, Denis Talbot
TL;DR
The paper tackles time-dependent confounding in causal graphs and introduces an extended definition of sufficient time-dependent adjustment sets that leverages conditional independencies read from the graph to reduce estimator variance. It develops a practical construction algorithm and proves that an optimal time-dependent adjustment set can be identified from the graph alone, yielding lower asymptotic variance than prior definitions. The approach is illustrated with two numerical experiments demonstrating meaningful variance reductions, and the results have practical implications for data-driven confounder selection and software support for adjustment-set identification. Overall, the work advances nonparametric causal inference in longitudinal settings by linking graph structure directly to optimal adjustment strategies and estimator efficiency.
Abstract
Criteria for identifying optimal adjustment sets yielding consistent estimation with minimal asymptotic variance of average treatment effects in parametric and nonparametric models have recently been established. In a single treatment time point setting, it has been shown that the optimal adjustment set can be identified based on a causal directed acyclic graph alone. In a time-dependent treatment setting, previous work has established graphical rules to compare the asymptotic variance of estimators based on nested time-dependent adjustment sets. However, these rules do not always permit the identification of an optimal time-dependent adjustment set based on a causal graph alone. We extend those results by exploiting conditional independencies that can be read from the graph and demonstrate theoretically and empirically that our results can yield estimators with lower asymptotic variance than those allowed by previous results. We further show how our results allow for the identification of optimal adjustment sets based on a directed acyclic graph alone in the time-dependent treatment setting.