A unique observed-data functional for direct effects that equals the ATE if the focal variable is pre-exposure and an interventional direct effect if post-exposure, under a no-additive-interaction condition.
Therefore the test that rejects whenp max < αhas size at mostαunder the union null
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Model-Robust Direct Effect Under Confounder-Mediator Ambiguity
A unique observed-data functional for direct effects that equals the ATE if the focal variable is pre-exposure and an interventional direct effect if post-exposure, under a no-additive-interaction condition.