Identifying and Correcting Bias from Time- and Severity- Dependent Reporting Rates in the Estimation of the COVID-19 Case Fatality Rate

Background: COVID-19 is an ongoing pandemic with over 400,000 confirmed cases and large variability in its reported case fatality rate (CFR). CFR is an epidemiological measure of severity which can affect policymaking and public health responses to the disease. As we are in the middle of an active outbreak, estimating this measure will necessarily involve correcting for time- and severity- dependent reporting of cases, and time-lags in observed patient outcomes. Methods: We carry out a theoretical analysis of current estimators of the CFR. We adapt a standard statistical technique, expectation maximization (EM), in a form previously developed for pandemic influenzas to correct for time- and severity- dependent reporting in the estimated CFR of COVID-19. Code is available at https://github.com/aangelopoulos/cfr-covid-19 . Findings: We find that the na\"{i}ve estimator of CFR is asymptotically biased for the true CFR. To compensate for both of these variables we apply an expectation maximization strategy previously developed for emerging pathogens such as pandemic influenza. We obtain a CFR estimate of 2.4% for COVID-19. We also show results of our method for relative CFR by nation. Finally, we release our code on GitHub so it can be used as more data becomes available globally. Interpretation: The current strategy of estimating the CFR by dividing the number of deaths by the number of cases should not be used anymore as it is unreliable. Moving forward we suggest instead the use of maximum likelihood models which correct for time-dependent bias. This may allow public health organizations and local, state, and national governments to more accurately direct resources (e.g. test kits and vaccines) to places that would be most in need by compensating for the time delay inherent in this urgent ongoing pandemic.