On the Measurement of Disease Prevalence

For any infectious disease, including the Covid-19 pandemic, 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 42 times more likely to seek testing. The testing propensity bias leads to sizeable prevalence bias: even under costless testing, test positivity can inflate true prevalence fivefold. The inflation factor varies greatly across time and age groups, making intertemporal and between nation comparisons misleading. We validate our results using the largest population surveillance studies of Covid-19 in England, and indeed find that the bias varies intertemporally from 4 to 23 times. We present calculations to debias positivity, but importantly, suggest a parsimonious approach to sampling the population that bypasses the bias altogether. Estimates are both real-time and consistently close to true values. Our results are relevant to any epidemic, besides Covid-19, where carriers have informative beliefs about their own status.