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Estimating the prevalence of a medical condition, or the proportion of thepopulation in which it occurs, is a fundamental problem in healthcare andpublic 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 groupswho are disproportionately affected by a condition. However, it is difficult toestimate relative prevalence when a medical condition is underreported. In thiswork, we provide a method for accurately estimating the relative prevalence ofunderreported medical conditions, building upon the positive unlabeled learningframework. We show that under the commonly made covariate shift assumption --i.e., that the probability of having a disease conditional on symptoms remainsconstant across groups -- we can recover the relative prevalence, even withoutrestrictive assumptions commonly made in positive unlabeled learning and evenif it is impossible to recover the absolute prevalence. We conduct experimentson synthetic and real health data which demonstrate our method's ability torecover the relative prevalence more accurately than do baselines, anddemonstrate the method's robustness to plausible violations of the covariateshift assumption. We conclude by illustrating the applicability of our methodto case studies of intimate partner violence and hate speech.

Quantifying disparities in intimate partner violence: a machine learning method to correct for underreporting