Why estimating population-based case fatality rates during epidemics may be misleading

Lucas Böttcher; Mingtao Xia; Tom Chou

In this work, we have explicitly defined a number of interpretable mathematical metrics that represent the risk of death. By rigorously defining these metrics, we are able to reveal the inherent assumptions and factors that affect their estimation. Within survival probability and SIR-type models, we explicitly illustrate how physiologically important parameters such as incubation time, death rate, cure rate, and transmissibility influence the metrics. We also discussed how statistical factors such as time of testing after infection (Ï„ 1 ) and testing ratio (f ) affect our estimates. Given the uncertainty in the testing fraction, we conclude that M 1 (t) and M 1 p (t) is best interpreted as approximately the mortality probability conditioned on being tested positive. In practice, these are probably also good estimates of mortality of patients conditioned on showing symptoms. In addition to our metrics and mathematical models, we emphasize the importance of curating individual cohort data. These data are more directly related to the probability of death M 1 (t) and are subject to the fewest confounding factors and statistical uncertainty.