  Large-scale testing is considered key to assess the state of the current
COVID-19 pandemic. Yet, the link between the reported case numbers and the true
state of the pandemic remains elusive. We develop mathematical models based on
competing hypotheses regarding this link, thereby providing different
prevalence estimates based on case numbers, and validate them by predicting
SARS-CoV-2-attributed death rate trajectories. Assuming that individuals were
tested based solely on a predefined risk of being infectious implies the
absolute case numbers reflect the prevalence, but turned out to be a poor
predictor, consistently overestimating growth rates at the beginning of two
COVID-19 epidemic waves. In contrast, assuming that testing capacity is fully
exploited performs better. This leads to using the percent-positive rate as a
more robust indicator of epidemic dynamics, however we find it is subject to a
saturation phenomenon that needs to be accounted for as the number of tests
becomes larger.
