key: cord-347182-oj3v1x99
authors: Catala, M.; Pino, D.; Marchena, M.; Palacios, P.; Urdiales, T.; Cardona, P.-J.; Alonso, S.; Lopez-Codina, D.; Prats, C.; Alvarez Lacalle, E.
title: Robust estimation of diagnostic rate and real incidence of COVID-19 for European policymakers
date: 2020-05-06
journal: nan
DOI: 10.1101/2020.05.01.20087023
sha: 
doc_id: 347182
cord_uid: oj3v1x99

Policymakers need a clear and fast assessment of the real spread of the epidemic of COVID-19 in each of their respective countries. Standard measures of the situation provided by the governments include reported positive cases and total deaths. While total deaths immediately indicate that countries like Italy and Spain have the worst situation as of mid April 2020, on its own, reported cases do not provide a correct picture of the situation. The reason is that different countries diagnose diversely and present very distinctive reported case fatality rate (CFR). The same levels of reported incidence and mortality might hide a very different underlying picture. Here we present a straightforward and robust estimation of the diagnostic rate in each European country. From that estimation we obtain an uniform unbiased incidence of the epidemic. The method to obtain the diagnostic rate is transparent and empiric. The key assumption of the method is that the real CFR in Europe of COVID-19 is not strongly country-dependent. We show that this number is not expected to be biased due to demography nor the way total deaths are reported. The estimation protocol has a dynamic nature, and it has been giving converging numbers for diagnostic rates in all European countries as of mid April 2020. From this diagnostic rate, policy makers can obtain an Effective Potential Growth (EPG) updated everyday providing an unbiased assessment of the countries with more potential to have an uncontrolled situation. The method developed will be used to track possible improvements on the diagnostic rate in European countries as the epidemic evolves.

The evolution of the epidemic in Europe has affected Spain and Italy more strongly 2 than in other countries so far. This is clear from reported cases and fatalities in these 3 However, they lack the recipe-type nature needed sometimes to direct a policy response. 22 The focus of this paper is, thus, to introduce a method to compute the real 23 diagnostic rate and the real incidence of COVID-19 in each European country, testing 24 that the key hypothesis of the method is fulfilled and that, if they were to be slightly 25 off, they would affect all countries in the same direction. In other words, we provide a 26 recipe for policymakers that we have tested to be correct, unbiased across countries and 27 useful to make cross-country comparison provided the evolution and prognosis of the 28 disease in a patient is not strongly dependent on socio-economic factors and only on age, 29 sex and previous clinical history. 30 We must recall here that the ability to determine the diagnostic ratio is essential to 31 evaluate what the real number of infected people is. Knowledge of this number is not 32 only useful to visualize the full scope of the epidemic but also to properly estimate the 33 number of people with probable short-term immunity. In this sense, our method can be 34 added as an empirical take of other assessments about the real incidence of the disease 35 and to study the possibility of developing herd immunity. A large number of real 36 infected people would be a positive scenario for policymakers while a low number will be 37 negative. It is thus very important to err on the side of caution in all our estimates 38 giving always the less optimistic take. 39 The basic structure of the paper is the following. First, we give a general overview of 40 our framework in the methods section. Then we discuss our key assumption: the real 41 case fatality rate (CFR) in European countries experiencing a significative incidence will 42 be roughly the same, given the similar structure of the population. If the real CFR were 43 to be lower, or higher, it would affect all countries in the same way and would not affect 44 most policy decision-making since it will move all countries in the same direction. We 45 take this real CFR to be 1% and proceed to test that, effectively, there is a strong 46 correlation between the day of reported deaths with the number of cases taken 7-10 47 days before. Once a given value for the real CFR is taken, one must consider that 48 people do not die immediately from the disease, as it takes roughly 18 days after 49 infection [10] [11] [12] . In other words, the present values of the death toll can provide an 50 estimation of the number of infected people 18 days ago. Knowing the number of 51 infected people at present, not 18 days in the past, is crucial. We attack this problem 52 considering that people who become infected are usually diagnosed a few days after the 53 onset of the symptoms, which can be 8 to 14 days after infection occurs. By comparing 54 the number of people diagnosed on a certain date with our estimation of the real number of infected people, we can estimate what percentage of the cases are being 56 diagnosed. We can calculate this for different countries and regions and test how this 57 ratio has changed dynamically as the epidemic advanced. 58 In the results section, we provide a full detailed description of how this fraction has 59 become steady in the last weeks. We demonstrate that the percentage of diagnosis 60 throughout the development of the epidemic has taken values that gradually converge 61 for most countries. This gives a final clear picture showing the rate of diagnosis for each 62 country. Using this rate is straightforward to give a present-day estimate of the 63 incidence given the number of reported infected people in each country as long as we 64 can observe that the rate of diagnosis remains fairly constant. For policymakers, we 65 have constructed an index named Effective Potential Growth (EPG) that combines this 66 information with the growth rate of the epidemic to provide insight regarding which 67 countries are, comparatively and in the short-term, in the most potentially complicated 68 situation [9] . 69 

Framework of our methodology 71 Our analysis will be applied to European countries with a minimum of 500 deaths on 72 April 15 2020 so that we can guarantee a minimum statistical significance. The 73 analyzed countries are: Belgium, France, Germany, Italy, Netherlands, Portugal, Spain, 74 Sweden, Switzerlands and United Kingdom. Our two core assumptions are that the real 75 CFR in all European countries is roughly the same and that reported data of death due 76 COVID-19 is uniform in all European countries under consideration. We will address 77 these two hypothesis in the following sections. With these assumptions we need to carry 78 out four steps, as indicated in Fig. 1 , to obtain the percentage of diagnosis. First, using 79 a common reference CFR = 1% and, given the reported reported death count, we 80 estimate the number of cases 18 days ago. According to medical reports people die 81 between 15 and 22 days after the development of the first symptoms [13] . This time to 82 death, TtD, after the development of the first symptoms will not be country-specific for 83 demographic reasons. The estimated number of infected people with the disease at time 84 t (see process in Fig. 1 This allows us to know to estimate the number of cases 18 days ago. This value can 86 be compared with the number of cases detected 18 days ago, obtaining a diagnostic depending on the availability of tests, saturation of the health system and other 91 external factors, countries have a great variability in the time of diagnosis delay.

Countries accumulate some delay that may arrive to 18 days in the case that a 93 country detected people as late as they were detected on death. This delay to detection 94 (DD) due to lags in diagnosis corresponds to the time between the patient having the 95 first symptoms and being reported by the health system. In fact, this time in some 96 countries may vary throughout the course of the infection. Therefore we cannot assume 97 that the estimated and the reported are comparable and we need to know what the 98 diagnostic time was for each of the countries studied. 99 We can compare the reported deaths with the reported cases to find the maximal 100 correlation, see process 2 in Fig. 1(A) , to estimate the DD, see process 3 in Fig. 1(A) .

Finally the ratio between reported cases at DD with the estimated cases, see below, 102 provides an estimation for the percentage of diagnosis, see process 4 in Fig. 1(A) . Note 103 that the usual development of the reporting of a new case/death, see Fig. 1 (B), depends 104 on the particular country under consideration, which determines DD. In fact, DD also 105 includes a delay in reporting the diagnostic to death to official information systems.

The cornerstone of our analysis is that the real CFR in all European countries will not 108 be biased against any country in particular. We should point out immediately that we 109 are not arguing that there are not important uncertainties in the real CFR, what we do 110 claim and check in this methodology is that these uncertainties will not generate any 111 biased against particular countries and should not affect policy decision. We take the 112 CFR in of COVID-19 in Europe to be between 0.3-3% and we assume 1% to be the 113 benchmark scenario.

This value (1%) is the CFR observed in the initial stages of the South Korea 115 pandemic and the Diamond Princess cruise. In both cases, it was found to be around 116 1-2.6% and, in both, error margins came from different sources [14, 15] . In South Korea, 117 the ability to test all the population in contact with infected people and the tracking of 118 contagious chains was thorough, despite that, the reported CFR increased from initial 119 values around 0.5-0.7% to higher values around 2%. In the Diamond Princess cruise, 120 CFR for confirmed cases was 2% but estimation of false negatives and the possibility 121 that a fraction of the passengers never developed symptoms and was never tested put 122 the CFR again around 1%. Both South Korea and the Diamond Princess cruise provide 123 complementary evidence, one coming from a natural experiment and another from a 124 country with the ability to perform half a million tests/day from the very beginning of 125 the transmission chain [16] . If we accept the two measurements of the CFR 126 independent, the most likely interval of real CFR is between 0.5 and 2%.

Recent experimental results from random testing in the German city of Gangelt [17] 128 and preliminary results from Iceland [18, 19] indicate the presence of a layer of people 129 fully asymptomatic that are normally not detected. This group of people have passed 130 the disease without any knowledge seems to be larger than previously thought. These 131 preliminary studies point to a CFR of around 0.5% in zones where the epidemics was 132 not fully spread. We cannot disregard the possibility that, just as CFR inceased with 133 time even in South Korea, similar studies in countries with more cases, could have a real 134 higher CFR.

It is thus reasonable to consider CFR at 1% as an easy policy guiding principle and 136 not to use the more positive scenario of 0.5%.

Unbiased nature of CFR in Europe 138 There are three sources of possible biased CFR across countries. The disease affects 139 more strongly elder people with comorbidity problems than healthy younger ones, and 140 more men than women. In all European countries the male/female ratio is unbiased 141 except for older people. This is precisely the group with higher mortality rate. It is thus 142 very important to asses how the different demographic structure of European countries 143 could affect our central benchmark [20] . The same must be said about the relative 144 prevalence of other comorbidity factors. We proceed to show that, with the data we 145 have today: the demographic and comorbidity structure, none of these possible sources 146 of bias can have anything but a small effect. To do so, we will do a comparison with the 147 CFR of South Korea on April 15 2020, 2.1%.

148 Table 1 shows the demographic structure of South Korea and the corresponding 149 CFR for each analyzed age group reported on April 15 2020. The first row shows the 150 demographic structure according to Eurostat, but the analysis has be performed by 151 using only the three age groups shown in the second row: ≤ 49, 50 − 79 and ≥ 80 years. 152 This was done because for many countries reported cases and fatalities consider different 153 age groups, and some countries even report this two figures using different age groups. 154 The three age groups considered in the analysis were the only ones that includes all the 155 analyzed countries. As can be observed in the To analyze what is the role played by the differences in demography in Europe in the 163 COVID-19 cases and fatalities we have downloaded from Eurostat the demographic 164 distribution by age (see Table 2 ). 165 We can readily asses that, when comparing with South Korea, all the countries have 166 a larger percentage of population above 80 years (90% larger for Italy) and larger 167 median age except Sweden and United Kingdom, but the relative differences in each of 168 the cohorts in between the European countries shown in the table is small. Only Italy 169 presents a relevant larger than average ratio of people over 80.

Using this demographic data and assuming each European country presents the 171 same CFR by age group as South Korea on April 15 2020, we have computed the CFR 172 for each country. Table 3 shows the results of this analysis and the officially reported 173 CFR by the different European countries on the same date. Both values are presented 174 relative to the CFR reported by South Korea on April 15 2020, 2.16%.

As can be observed in the first column, when demography is the only difference 176 between countries, between the worst and best case of the relative CFR the differences 177 April 24, 2020 5/18

. CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 6, 2020. . having previously a very bad prognosis. We know this group is strongly affected by the 185 virus [21] . In blunt terms, we must examine the possibility that different countries are 186 counting the raw number of dead people differently.

Before entering in the detail of the analysis, let us point out that two indications go 188 against this possibility. First, Health Care systems in Europe can have different 189 April 24, 2020 6/18 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 6, 2020. . resources in different countries with different focus and priorities, but they attend There is a single exception that we know of: Belgium [22] . Belgium seems to be 195 reporting unconfirmed cases from nursing homes without tests as due to COVID-19. It 196 is quite clear that this includes a good number of people who, either, did not die from 197 COVID-19 or that COVID-19 was not an important factor in the prognosis. Therefore, 198 we will include a reminder that Belgium data is biased compared with other countries, 199 being anywhere from 20% to 50% lower given the number of reported deaths from 200 nursing homes compared with hospitals. There is a second argument regarding the 201 treatment of the elder population in other countries. If large undercounting woul be the 202 case, it should be noted in the mortality rate for people 80 years and older, which is not 203 observed in the countries where we have data.

In this framework, Spain becomes a key country. If Spain were not to have an 205 important undercounting is highly implausible to think that other countries would. We 206 proceed to analyze the data of The National Epidemiology Center (Instituto de Salud March 17 to April 18 2020 for the whole of Spain, they see that, as expected, mortality 211 is much higher than in previous years. An increase of 68% is observed. However, it is 212 interesting to compare this with the data reported for COVID-19 deaths. The reported 213 deaths by COVID-19 are roughly 20000, depending on how you attribute deaths to a 214 particular day in the calendar. On the other hand, the reported excess of deaths by the 215 MoMo surveillance system is 25000. We think that the assessment of around 20% 216 underreporting can be taken indeed as a worst-case scenario for a highly impacted 217 country. It seems reasonable to expect other countries to have underreported way below 218 or slightly below this level. All the data point out right now, that the undercounting 219 due to a different treatment of the very fragile population is highly unlikely across 220 Europe, and at most introduces changes in CFR around ±10%. Having shown that the real CFR should not present bias in European countries larger 223 than 25%, we address now how to deal with the real sources of bias in the diagnostic 224 rate for each country. To estimate DD we look for a correlation between the number of 225 reported cases (see Fig. 2A ) and the number of reported deaths (see Fig. 2B ) [1, 24] . To 226 deal with noise effects we put a weighted moving average filter on the data of both cases 227 and deaths. The correlation time between reported cases and reported deaths will be 228 named as time from diagnosis to death (DtD), and: 229 TtD = DD + DtD.

(2) Correlation between reported cumulative cases and reported cumulative deaths exploring different delays between diagnose (reported) and death for Germany (red), Spain (green) and Switzerland (green). (D) Maximum correlation is marked with a red square for each country. 99% correlation interval can be seen with black bars.

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The copyright holder for this preprint this version posted May 6, 2020. In Fig. 2C we can see the correlation [25] between reported cases and reported 230 deaths assuming different DtD for Germany, Spain and Switzerland. As you might 231 expect, correlations have values close to 1. In most cases the correlation has a concave 232 parabolic shape with a clearly defined maximum. We assume this maximum represents 233 DtD for each country. The correlation interval is estimated as the points where the 234 correlation is greater than 99% of the observed maximum. We decided to set a lower 235 limit of 4 days and a higher limit of 14 days [11] because we believe that time outside 

Diagnostic rate by country 243 As discussed in the methods, we use the same CFR = 1% in all European countries 244 instead of making small corrections for demography. The bias due to demography was 245 shown to be around 10-15%, precisely the same order of magnitude we obtain for the 246 possible bias in the counting of reported mortal cases. Given that our aim is to provide 247 a clear method for policymakers and that there is no data on how, or even if, both 248 correlate, a common CFR allows us to homogenize the results with the clear limitation 249 that we will obtain reasonable estimations and not exact results. The resulting picture 250 is expected to be closer to reality than using purely reported data, but worse than 251 correcting properly for age and diagnosis if the data of CFR for all age brackets and 252 locations (nursery homes, hospitals, individual homes) were available, which is not the 253 case. The estimation of the diagnostic rate is straightforward. From the cumulative 255 number of deceased each day, and multiplying by 100 (1% CFR) we get the cumulative 256 number of people with symptoms 18 days ago [10] [11] [12] simply by rescaling and displacing 257 backward in time the cumulated death curve of any country. To give an initial realistic 258 and homogenous diagnostic rate we must establish how many days are needed as a bare 259 minimum to be able to detect a patient from the onset of symptoms. First, the patient 260 has to feel sufficiently sick and then contact the Health Service. From this contact, the 261 doctor needs to be suspicious that the person has the disease and request a test. Then, 262 this test must be available, performed and the result received and annotated. It is clear 263 that a bare minimum of one week is needed for this process. We use the name 7-Days . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 6, 2020. . symptoms and then 7 days forward to be detectable/diagnosable. From this curve, we 270 can obtain the rate between the cumulated number of people who had symptoms for 7 271 or more days and the cumulated number of people detected 11 days ago. It is thus clear 272 that this homogenous analysis across countries could be performed assuming 5D-DR or 273 9D-DR and different CFR. It gives a proper first estimation of the situation. We argue, however, that there is indeed bias in the way people deal with the health 275 care system in normal situations and, especially, under an epidemic. Different countries 276 and populations are in fact behaving very differently. We have observed that this is the 277 case in the methods section checking the delay between diagnostic and death using 278 time-displaced correlation analysis. This is the reason why we also define the Delay to 279 Detection Diagnostic Rate (DD-DR) as the diagnostic rate computed using a time delay 280 between the appearance of symptoms and detectability different for each country. We 281 proceed to use Fig. 4 , with Spain as an example, to explain the concept behind DD-DR. 282 For Spain, the maximum correlation between cumulated death curves and cumulated 283 reported cases appears when cumulated deaths are displaced 4 days backward. This 284 suggests a DD of around two weeks (18 − 4 = 14 days). This makes sense in a situation 285 like the one in Spain during March 2020. The population receiving news that the health 286 care system is under stress may decide to delay reporting of symptoms unless they are 287 very serious. Additionally, there is the possibility that tests are not available to people 288 who report with symptoms to primary health care centers, and that the delay between 289 the test, its positive result, and its record to official information systems is not 290 negligible as well.

It is thus important to correct for this bias in the estimation of the diagnostic rate. 292 It is clearly not the same to have a time delay from symptom to the detection of 14 293 days than 7. DD-DR can be computed from Spain just like we did before for the 7D-DR 294 using the same rescaling of the cumulated dead curve as before but using a displacement 295 backward of 4 days instead of 11 days. Fig. 4 shows how the DD-DR is obtained in 296 different countries depending on the delay between symptoms and detectability.

Countries with a lower DD, such as Germany, have the same 7D-DR than DD precisely 298 because they diagnose as early as realistically possible. We notice now that both 7D-DR and DD-DR can be tracked along time, as the 300 epidemic advances we can check how these diagnostic rates changes. Each new day we 301 can look 11 days back for the 7D-DR and compute the diagnostic rate. DD-DR can be 302 tracked similarly. In Fig. 5 we show the evolution for both as a function of time for 303 three selected countries. We observe that the DD-DR reaches a steady state after the 304 initial stages of the disease while 7D-DR seems more affected by trends. This can be 305 expected since DD-DR uses, precisely, the maximum of the correlation delay so it is 306 expected to fluctuate less. The DD-DR is not only more stable but it also allows as to 307 produce a proper assessment of the errors involved. The main one is the fact that the 308 April 24, 2020 9/18 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 6, 2020. April 2020 as above 2 million in Spain and close to half million in Germany.

The table in Fig. 6 shows a list of the 7D-DR as of the beginning of mid-April of 319 2020, and the DD-DR, which seems stable, together with the associated error. To interpret estimated cumulative cases and estimated attack rate we must take into account Detection Delay, because they are computed using the reported data. Data updated on April 20 2020. Belgium data is biased due to reporting of unconfirmed death cases [22] . Best estimations might shift 20-50 %

Once the diagnostic rate is known, it is straightforward to establish a real incidence no 322 longer affected by the presence of important differences in the time delays to diagnostic 323 in different countries (see the table in Fig. 6 ). The level of diagnosis and the real 324 incidence is indeed useful for policymakers since it gives a clear general picture. However, 325 the policy response needed to improve the diagnostic rate is limited, in the short-term, 326 by the ability to increase the production of PCR kits and other diagnostic tools.

Policymakers have more ability to affect immediately mobility patterns and social 328 contact. In this sense, a key number for policymakers would be to have a reliable and 329 robust estimation of the number of infected people in each country that can propagate 330 the disease. Providing an exact number is, right now, impossible. 331 We can, however, produce an index of the effective potential growth using the 332 DD-DR and the guidelines used by the ECDC to track the epidemic. Even if the precise 333 number of people with the disease were known, and the distribution of symptoms by sex 334 and age was reported, there is no clear knowledge regarding the level of infectivity of 335 the different type of person and symptoms. For instance, it is not known the days a 336 person with mild symptoms can transmit the disease. The same can be said for people 337 with serious symptoms. Virus loads in the throat seem to be rather high across the 338 board [26] , but data on how this influence contagion is unclear. The only way to assess 339 the situation is to use a general unbiased broad measure, which is indicative of the 340 potential for infection. The ECDC uses the number of newly infected people in the last 341 14 days [27] . We use this same criterion. This number can only be obtained properly some days in the past, on the day we have a 346 typical diagnosis. After that, we would need input from new data to properly compute 347 how many people are diagnosed. So the number I 14 is strictly a measure of the recent 348 past, but good enough to give the proper picture that the system will face the following 349 days.

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The copyright holder for this preprint this version posted May 6, 2020. . Fig 7. Schematics of the procedure to obtain incidence A 14 , recovered and estimated cases using Germany as an example. Incidence of estimated cases (blue), contagious incidence (red) and total estimated recovered cases (green). Blue shaded part is the number of cases used to compute the estimated contagious incidence. To interpret final number of total cumulative cases, recovered cumulative cases and estimated attack rate we must take into account Detection Delay, because they are computed using the reported data. Similar figures for all countries are shown in SI Fig.  2 We also consider those undetected cases which appear earlier than 14 days as 351 recovered R I . Notice that here we use the word recovered lousily. It does not mean 352 literally that all of them are fully recovered since most of them never fell ill to begin 353 with, and some of them could not have neutralized tests yet, but that those infected and 354 undetected for more than two weeks ago do not seem to pose a serious risk. 

A 14 alone, however, does not give a full picture of the situation. It is not the same to 361 have 100 contagious per 10 5 inhabitants when the number of contacts is high that when 362 the number of contacts is low. It is important to take into account the level of spreading 363 velocity of the epidemic related to the effective reproductive number (R t ).

The effective reproductive number depends on multiple factors, from the properties 365 of the virus itself to the number and type of contacts. Those, again, depend on different 366 social behavior and structure such as mobility, density or the typical size of the family 367 unit sharing a house, to name a few. The only feasible way to estimate R t is using fits 368 from SEIR models. Complex SEIR models which include spatial and contact-processes 369 have a large number of parameters which, due to the present lack of knowledge, are (3) and EPG.ρ (3) is computed using the mean value for the last three days. EPG: Effective Potential Growth described in the text. To interpret table data we must take into account Detection Delay, because they are computed using the reported data. Data updated on April 20 2020. * Belgium data is biased due to reporting of unconfirmed death cases [22] . Best estimations might shift 20-50 %.

Given the partial empiric nature of present R t , we prefer to take a fully empiric 375 surrogate as a quantitative evaluation of the level of infections. We define an alternative 376 reproductive number as the number of new cases detected today divided with the 377 number of new cases detected five days ago as N t /N t−5 . However, the high fluctuations 378 on this quantities imposes the use of averaged values over three days [9] :

where N t stand for new cases reported at day t. This rate is one if the number of new 380 cases is constant. It will be below 1 if new cases are decreasing and larger than 1 if the 381 April 24, 2020 11/18 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 6, 2020. . https://doi.org/10.1101/2020.05.01.20087023 doi: medRxiv preprint number of cases is increasing. We take 5 days as the key delay unit since this is roughly 382 the time since infected people develop symptoms if they do develop them.

There are still clear fluctuations on a day-to-day basis of this measure ρ t due to 384 common delay and irregularities in reporting. Most fluctuations can be eliminated by 385 taking the average of ρ t during three daysρ (3) 

which is normally enough to get a rather smooth measure. It is not uncommon to find 387 still some fluctuations and one-week averages can be done if required. 388 We propose the following day-to-day index EPG:

EPG is just the multiplication of the growth rate of the diseaseρ ( cases is biased by diagnosis protocols and ratios in each country, as well as by the pool 405 of asymptomatic cases. Moreover, any attempt to improve diagnosis percentage requires 406 an economic, infrastructural and logistical effort that is not always possible. In addition, 407 this health system structure is a strong conditioning that limits the possible actions to 408 carry out in this direction. The reported number of deaths, if uniformly and properly 409 recorded, provides very relevant information as a first general overview. Even in 410 countries where there is a bias on death reporting, the effort that should be made to 411 improve these data collection is much lower than the necessary effort to increase data 412 about cases.

The assumption of a common lethality, which has been situated around 1%, allows 414 for using the CFR as an indicator of real incidence. Current information on CFR is still 415 not complete, since many countries do not report distribution of deaths by age or sex, 416 neither provide COVID-19 mortality outside hospitals. However, we argue that the Kingdom (120,000), France (113,000) and Belgium (38,000). If we estimate the cases 426 that should have been diagnosed by that time, the ranking is lead by Italy (2,600,000) 427 and followed by France (2,400,000), Spain (2,300,000), United Kingdom (2,000,000), 428 Belgium* [22] (870,000) and Germany (580,000). Thus, differences in diagnostic rate are 429 absolutely significant when analyzing global situation in Europe. Countries like 430 Germany, Portugal and Switzerland would be diagnosing around 25% of cases, while 431 Belgium, France, Sweden and United Kingdom would be in the level of 5%.

Assessing the risk of countries to enter or remain in the epidemic growth phase is 433 essential. In this sense, the EPG index is a valuable tool for policy makers. A high EPG 434 in the situation where there is a high growth rate of the epidemic and large number of 435 active cases is a clear situation of danger, while a very low EPG because both the Reported EPG vs estimated real EPG. Different European countries in terms of the EPG computed using the reported data on the attack rate vs the EPG using our estimation of the real attach rate. The order of the different countries should be done from right to left (for the reported state of the index) and from top to bottom (for the estimated value of the index). We observe how the comparative situation of the different countries changes as of 20 April 2020. * Belgium data is biased due to reporting of unconfirmed death cases [22] . Best estimations might shift 20-50 %.

Despiteρ (3) is quite independent of the diagnostic rate, reported I 14 directly 445 depends on the level of diagnosis. Thus, if EPG is evaluated with reported data, it can 446 provide a wrong picture of the situation. Based on reported EPG, the worst situation in 447 Europe at April 20 2020 would be for Belgium, followed by Spain, United Kingdom, 448 Netherlands and Portugal. If risk is evaluated with estimated EPG, highest value would 449 still correspond to Belgium as well, but followed by Sweden, United Kingdom, Spain, 450 Netherlands and Italy. Portugal is in much better position that its reported data 451 suggest. Actually, countries with similar reported EPG like Portugal, and Netherlands 452 have, in fact, totally different estimated EPG, being the last country at significantly 453 higher risk than the former 9. 454 We have shown in the Methods section that the basis for obtaining estimated I 14 455 and A 14 is not biased due to demographic differences and, right now, there is no 456 indication that it is biased due to a different way of accounting for the cumulative dead 457 toll of the epidemic. There is also no indication that comorbidity factors are largely 458 different in different countries or that CFR is higher on some countries given that ICU 459 units and hospitals are not available for people that would need it, at least so far. If this 460 were the case, under any scenario where the situation occurs, the epidemic in that 461 country will have such a larger number of cases, attack rate and growth that the EPG 462 will be extremely high. The only real limitation is that the social and environmental 463 issues could affect the prognosis of the infected. If living in a small house with other 464 people infected could lead to worse prognosis than staying in a large house alone, a new 465 analysis regarding the unbiased nature of the CFR would need to be done.

It is important to indicate that not only I 14 is unbiased, as analysed in previous 467 sections, but thatρ (3) is not biased as well. Even though absolute reported cases is 468 biased, as we have shown, ρ t deals with ratios and its evolution. As long as the diagnosis 469 and recording of the people with disease follows roughly the same criteria along time in 470 each country, ρ t is a good measure of the growth the epidemic. Indeed, if evaluated 471 diagnosis percentage is more or less constant in time, we can assume that ρ t correctly 472 reveals tendencies in contagiousness. If a change in criteria in reporting the cases occurs 473 (i. e., a large increase in the number of tests per day leading to an increase of cases due 474 to more testing), ρ t will be temporally affected but will go back to be a good measure 475 once the new criteria is established. In this case, EPG will provide a wrong picture for a 476 while as well, until stationary conditions in diagnosing and reporting are achieved again. 477 There is another important point to address in order to guarantee that ρ t is a robust 478 measure. As soon as we are estimating real number of cases, we can determine the 479 associated ρ t . It is expected that both ρ t behave similarly but with a certain delay.

This delay can be determined by translating both ρ t in time until error between both is 481 minimized. We show this detailed analysis in the Supplement Material SI File where we 482 evaluate that both the reported ρ t and the inferred ρ t are indeed different but that 483 follow the same type of evolution once the proper delay is accounted for SI Fig. 3 .

The third important outcome of this analysis is the estimation of recovered people. 485 This is an important number to assess the possibility of herd immunity discussed as a 486 possible exit strategy. The idea is that those that recover might have immunity and act 487 as barrier in the transmission of the disease. A recent study from the Fudan University 488 at Shangai [21] has analyzed antibody titters of 175 adult COVID-19 recovered patients. 489 The study is based in the detection in plasma of Spike-binding antibody using RBD, S1, 490 and S2 proteins of SARS-CoV-2 using an ELISA technique. It is also the first study 491 that looks after neutralizing antibodies (NAbs) specific for SARS-CoV-2 using a gold 492 standard to evaluate the efficacy of vaccines against smallpox, polio and influenza 493 viruses.

The study highlights the correlation between the NAb titters and Spike-binding 495 antibodies that were detected in patients from day 10-15 after the onset of the disease, 496 remaining afterwards. Middle and elderly age patients had higher titters compared with 497 young age patients, in which in 10 cases the titters were under the limit of detection.

NAb titters had a positive and negative correlation with C-reactive protein (CRP) levels 499 and lymphocyte counts, respectively. This indicates that the severity of the disease, in 500 terms of inflammatory response (CRP levels), usually worse in middle and elderly age, 501 favors the increase of antibody titters. Equally, the negative correlation with 502 lymphocyte counts suggests an association between cellular and humoral response. 503 Therefore, it is possible that the immunity reached by young people, which were mostly 504 asymptomatic, is residual. In that case, this sub-population would keep being carriers of 505 COVID-19. Serological studies that many countries are designing and carrying out 506 should provide further information on post-infection immunity.

Even if the entire recovered population acquires middle-term immunity, current 508 incidence situates European countries far from herd immunity. Nevertheless, it is 509 feasible that regions with highest affectation were closer to use herd immunity as a 510 strategy for de-confinement. Governments might wish to explore the possibility of local 511 deconfinement.

There are two possible limitations of this present study. It could be possible, in theory, 514 that some countries present an intrinsically different CFR if they are able to isolate 515 completely and significantly its elder population more than others. The epidemics real 516 CFR is a measure of the case fatalities if all the population, or a representative sample 517 of it, has become infected. If one country would effectively prevent all infections among 518 all its elder population from contagious forever, it will certainly have a different CFR. 519 Right now, it is impossible to assess if this is indeed the case in different countries given 520 the lack of reported cases and mortality rates by age and sex. We should notice however 521 that, if this disaggregation were to be provided, we could proceed with exactly the same 522 methodology but instead of using the whole country as a whole we would divide it into 523 different age brackets and treat them separately.

The second limitation is related to the first one but coming from a more structural 525 perspective. A clear possibility is that countries under stress could be failing in 526 providing the same medical support changing the CFR. We must notice that Health 527 Care in European countries, even under stress, has been able to increase dramatically 528 its number of health personnel, of beds and hospitalization in short notice [28, 29] . Italy 529 and Spain present some regions under stress but not the whole country [30] . Finally, one 530 cannot disregard the possibility that complex mechanisms of mutations and repetitive 531 exposure to the virus may change the prognosis depends on the type of residence and, 532 hence on socio-economic factors, which are clearly different across countries. If any 533 proof that a close environment not only increases the level of infections, which they 534 obviously do, but also changes the disease evolution in the patient, one should again test 535 that the uniform/unbiased CFR hypothesis holds with the proper knowledge at hand. to obtain DtD for each country and the corresponding evolution of the diagnostic rate. 546 We also provide fore each country the evolution of recovered and the attack rate in the 547 last 14 days A 14 . We also provide the demonstration thatρ (3) is also unbiased showing 548 the correlations between real and estimated growth rates. Fig. 2 Series of figures showing the evolution of the estimated cases for 557 different European countries. In blue, incidence of estimated cumulative cases. In 558 green, estimated incidence of cumulative recovered cases. In red, estimated incidence of 559 attack rate lasts 14 days (A 14 ). Day 1 is considered the first day where cumulative cases 560 was over 100 cases, it is different for each country. Data extended till April 20 2020. . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted May 6, 2020. . growth rate and, in blue, reported cases growth rate. (B) The gorwth rate of estimated 564 cases is displaced to find better match with the growth rate of reported cases. (C) Error 565 between estimated and reported growth rates using differents delays. Minimum delay is 566 marked and is the one used in (B). 

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