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Defining the population of interest is central to causal inference. However, due to complexities in the timing, methods, and data required for determining eligibility, researchers may only know whether a subset of the units of interest are actually in that population, and thus, actually eligible for the study. This partial knowledge impedes researchers' pursuit of an average treatment effect which characterizes all eligible units, but only the eligible units. We define a set of estimands that make eligibility for the study explicit. We then demonstrate how to incorporate predicted eligibility into estimation procedures in order to minimize bias in treatment effect estimates.