Accurate Covid-19 prevalence measurement in the field

Timely, accurate epidemic figures are necessary for informed policy. In the Covid-19 pandemic, mismeasurement can lead to tremendous waste, in health or economic output. "Random" testing is commonly used to estimate virus prevalence, reporting daily positivity rates. However, since testing is necessarily voluntary, all "random" tests done in the field suffer from selection bias. This bias, unlike standard polling biases, goes beyond demographical representativeness and cannot be corrected by oversampling (i.e. selecting people without symptoms to test). Using controlled, incentivized experiments on a sample of all ages, we show that people who feel symptoms are up to 33 times more likely to seek testing. The bias in testing propensities leads to sizable prevalence bias: test positivity is inflated by up to five times, even if testing is costless. This effect varies greatly across time and age groups, making comparisons over time and across countries misleading. We validate our results using the REACT study in the UK and find that positivity figures have indeed a very large and time varying bias. We present calculations to debias positivity rates, but importantly, suggest a parsimonious way to sample the population bypassing the bias altogether. Our estimation is both real-time and consistently close to true values. These results are relevant for all epidemics, besides covid-19, when carriers have informative beliefs about their own status.