  Personalized interventions in social services, education, and healthcare
leverage individual-level causal effect predictions in order to give the best
treatment to each individual or to prioritize program interventions for the
individuals most likely to benefit. While the sensitivity of these domains
compels us to evaluate the fairness of such policies, we show that actually
auditing their disparate impacts per standard observational metrics, such as
true positive rates, is impossible since ground truths are unknown. Whether our
data is experimental or observational, an individual's actual outcome under an
intervention different than that received can never be known, only predicted
based on features. We prove how we can nonetheless point-identify these
quantities under the additional assumption of monotone treatment response,
which may be reasonable in many applications. We further provide a sensitivity
analysis for this assumption by means of sharp partial-identification bounds
under violations of monotonicity of varying strengths. We show how to use our
results to audit personalized interventions using partially-identified ROC and
xROC curves and demonstrate this in a case study of a French job training
dataset.
