Case fatality risk estimated from routinely collected disease surveillance data: application to COVID–19

Case fatality risk (CFR) is the probability of death among cases of a disease. A crude CFR estimate is the ratio of the number deaths to the number of cases of the disease. This estimate is biased, however, particularly during outbreaks of emerging infectious diseases such as COVID-19, because the death time of recent cases is subject to right censoring. Instead, we propose deconvolution methods applied to routinely collected surveillance data of unlinked case and death counts over time. We begin by considering the death series to be the convolution of the case series and the fatality distribution, which is the subdistribution of the time between diagnosis and death. We then use deconvolution methods to estimate this fatality distribution. This provides a CFR estimate together with information about the distribution of time to death. Importantly, this information is extracted without the need to make strong assumptions used in previous analyses. The methods are applied to COVID-19 surveillance data from a range of countries illustrating substantial CFR differences. Simulations show that crude approaches lead to underestimation, particularly early in an outbreak, and that the proposed approach can rectify this bias. An R package called covidSurv is available for implementing the analyses