Active information, missing data and prevalence estimation

The topic of this paper is prevalence estimation from the perspective of active information. Prevalence among tested individuals has an upward bias under the assumption that individuals' willingness to be tested for the disease increases with the strength of their symptoms. Active information due to testing bias quantifies the degree at which the willingness to be tested correlates with infection status. Interpreting incomplete testing as a missing data problem, the missingness mechanism impacts the degree at which the bias of the original prevalence estimate can be removed. The reduction in prevalence, when testing bias is adjusted for, translates into an active information due to bias correction, with opposite sign to active information due to testing bias. Prevalence and active information estimates are asymptotically normal, a behavior also illustrated through simulations.