  We present a conceptual model to measure disparity--the target study--where
social groups may be similarly situated (i.e., balanced) on allowable
covariates. Our model, based on a sampling design, does not intervene to assign
social group membership or alter allowable covariates. To address non-random
sample selection, we extend our model to generalize or transport disparity or
to assess disparity after an intervention on eligibility-related variables that
eliminates forms of collider-stratification. To avoid bias from differential
timing of enrollment, we aggregate time-specific study results by balancing
calendar time of enrollment across social groups. To provide a framework for
emulating our model, we discuss study designs, data structures, and
G-computation and weighting estimators. We compare our sampling-based model to
prominent decomposition-based models used in healthcare and algorithmic
fairness. We provide R code for all estimators and apply our methods to measure
health system disparities in hypertension control using electronic medical
records.
