  Countries officially record the number of COVID-19 cases based on medical
tests of a subset of the population with unknown participation bias. For
prevalence estimation, the official information is typically discarded and,
instead, small random survey samples are taken. We derive (maximum likelihood
and method of moment) prevalence estimators, based on a survey sample, that
additionally utilize the official information, and that are substantially more
accurate than the simple sample proportion of positive cases. Put differently,
using our estimators, the same level of precision can be obtained with
substantially smaller survey samples. We take into account the possibility of
measurement errors due to the sensitivity and specificity of the medical
testing procedure. The proposed estimators and associated confidence intervals
are implemented in the companion open source R package cape.
