This page is dedicated to world-aggregated data. A comparison between the data from the countries hit harder by the pandemic is presented in two separate pages, respectively dedicated to confirmed cases and to deaths.

In the interactive graph shown in Fig. 1 the cumulative world-aggregated curves for confirmed cases and deaths are reported and compared. The control panel on the left allows the user to act on the curve of confirmed cases with two degrees of freedom: a forward shift (S) in time and the scaling by a factor (F). These two operazione allow to check how far, and with which value of the S and F parameters, the two curves, or portions of the curves, overlap. The value of the S parameter (expressed in days) optimizing the overlap, corresponds to the average time delay between diagnosis (positive test) and death. The value of the F parameter corresponds to the measured fatality rate within the sample of confirmed cases. In case S and F were constant during the pandemic, e if data contained no flaws related to the collection/reporting method, the two curves would perfectly overlap, except for intrinsic statistic fluctuations. This world-aggregated plot depicts a very complex situation, in which the time evolution indirectly reflects the geographic evolution of the pandemic (started in China, flaring in March and early April in major Western countries, and now growing elsewhere). As a consequence of this intrinsic data inhomogeneity, no combined “S+F” scale operation allows for an overlap valid across the whole considered time range. As shown here, a good agreement for the time period extending from late March to late April (based on data from April 21) is found with S = 5 days and F = 8.7%.

Further details on the estimation of the fatality rate

All “naive” fatality estimates are affected by a large error and, accordingly, by a remarkable variability according to details of data collection. The “real” value, usually called infection fatality ratio (IFR), is the fatality rate calculated on the whole infected population. The IFR value, which is presumably relatively homogeneous from country to country and in time, is notoriously lower than fatality value calculated on the sample of confirmed cases. The sample of confirmed cases is in fact not random, but enriched with strongly symptomatic patients. A higher sampling intensity (increase of tests) typically reduces the bias of the sample lowering the fatality ratio of confirmed cases. When the sampling intensity is not constant in time, F is therefore not constant. The average diagnosis-to-death time delay, estimated in the plots above by S, is also in principle dependent on the sampling procedure. Assuming the infection-to-death delay time is grossly constant in time and from place to place, early diagnoses will increase the time delay from diagnosis to death.

By applying the analysis methods made available in the interactive plot in Fig. 1 to the early part of the curve, dominated by data from the Chinese epidemic, we observe a much lower F value. This corresponds to the lower fatality rate observed in China
How does the F factor introduced here compare to the case fatality rate CFR, i.e., to the daily deaths-to-confirmed-cases ratio? CFR is a much less accurate indicator, since it is by definition not constant in time, even if the sampling policy is homogeneous and constant in time. We discuss this in the modelling section and, more extensively in this paper.

In the interactive plot reported in Fig. 2 , the world-aggregated daily increment curves for confirmed cases and deaths are reported and compared. Once more, the control panel on the left allows the user to act on the curve of confirmed cases with two degrees of freedom: a forward shift (S) in time and the scaling by a factor (F). The shape of the plots is even more clearly affected by the history of the pandemic, starting in China, temporarily decreasing in intensity and then flaring out in the rest of the world. Once more, as a consequence of this intrinsic data inhomogeneity in space and time, no combined “S+F” scale operation allows for an overlap ofr the curves across the whole considered time range. As shown here, a good agreement for the time period extending from March to late April (based on data from April 21) is found with S = 5 days and F = 13%.

Why does the optimal fit value F found in Fig. 2 differ from the value derived from Fig. 1? In Fig. 1, cumulative data are reported. Even focusing our attention on the last part of the curve, the cumulative data keep track of the earlier part of the epidemic. The daily data are instead not effected by the past and represent a relative accurate estimate of the world-averaged fatality rate of confirmed cases in March and April. This value typically exceeds the deaths-to-confirmed-cases ratio (or case fatality rate CFR), for reasons that are discussed in the section above “Further details...” and more extensively in this paper.

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