A Covid-19 case mortality rate without time delay systematics

Richard Lieu; Siobhan Quenby; Ally Bi-zhu Jiang

In a recent correspondence to Lancet [1] , the global case mortality rate of the coronavirus Covid-19 ( [2] ) was re-calculated after correcting for the finite time delay between diagnosis of the disease and death, which led to a higher estimate of the rate, namely 5.7 ± 0.2 % for the date of March 1, 2020, to be compared to the global mean value of 3.43 ± 0.01 % as computed from the data 5 in [3, 4] for the same day. The reason for the higher value in [1] is the authors' definition of the case mortality rate, as the ratio of the number of case-related deaths for the day of interest to the number of new confirmed infections for the same 1-day period two weeks earlier (obviously, this assumes distribution of time delay between infection and death is peaked at 14 days with a spread 10 of less than 1 day). The usual definition, on the other hand, is the ratio of the cumulative number of deaths to confirmed infections, both being counted to the date of interest. If the daily number of confirmed infections and deaths are constants, the two definitions will give the same answer. This is no longer so if both numbers vary. Thus, if e.g. if they both increase with time but the 15 former more steeply, the method of [1] will yield a larger result because the ratio involves a smaller denominator as a result of the smaller number of confirmed infections at an earlier time.