Quantifying Inequality in Underreported Medical Conditions

Abstract

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 provide a suite of experiments on synthetic and real health data that demonstrate our method's ability to recover the relative prevalence more accurately than do baselines, and the method's robustness to plausible violations of the covariate shift assumption.

A Bayesian Spatial Model to Correct Under-Reporting in Urban Crowdsourcing

“…A challenge in estimation is that, without further assumptions, unreported incidents cannot be distinguished from incidents which did not occur. This is analogous to positive-unlabeled (PU) machine learning (Liu et al 2003;Shanmugam and Pierson 2021), where datapoints are either labeled positive or unlabeled, and the latter group consists of both true positives and negatives.…”