  Estimating the prevalence of a medical condition, or the proportion of the
population in which it occurs, is a fundamental problem in healthcare and
public health. Accurate estimates of the relative prevalence across groups --
capturing, for example, that a condition affects women more frequently than men
-- facilitate effective and equitable health policy which prioritizes groups
who are disproportionately affected by a condition. However, it is difficult to
estimate relative prevalence when a medical condition is underreported. In this
work, we provide a method for accurately estimating the relative prevalence of
underreported medical conditions, building upon the positive unlabeled learning
framework. We show that under the commonly made covariate shift assumption --
i.e., that the probability of having a disease conditional on symptoms remains
constant across groups -- we can recover the relative prevalence, even without
restrictive assumptions commonly made in positive unlabeled learning and even
if it is impossible to recover the absolute prevalence. We conduct experiments
on synthetic and real health data which demonstrate our method's ability to
recover the relative prevalence more accurately than do baselines, and
demonstrate the method's robustness to plausible violations of the covariate
shift assumption. We conclude by illustrating the applicability of our method
to case studies of intimate partner violence and hate speech.
