A method for estimating the case fatality rate during the onging epidemic- A Case Study of COVID-19

32 Human beings are constantly struggling with various epidemics. Although we gained a lot of experience and 33 success, in the face of the new epidemic, we still inevitably face pressure from public health, politics, and the 34 economy. Case fatality ratio (CFR) received widespread attention as one of the indicators describing the severity 35 of the epidemic and evaluating treatment options. However, due to the ongoing epidemic situation and the 36 constant changes in the death and diagnosis data, no scientific method for this situation to calculate the CFR 37 exists. This study proposes a method for estimating CFR in the continuation of the epidemic. CFR is estimated 38 by "ratio of the cumulative number of deaths before j days from a given day to the sum of the number of patients 39 discharged from a given day and the cumulative number of deaths before j days from a given day ".Take the 40 ongoing outbreak of COVID-19 in December 2019 as an example. The results show that, regardless of the size 41 of the estimated value or its changing trend, the estimated CFR given by the new method shows better stability 42 and better reflects the true situation of the case fatality rate; additionally, the improvement of medical conditions 43 can also be clearly reflected in the change in valuation. When j = 10, according to the data of March 10, the CFR 44 of COVID-19 in Wuhan, China and China (excluding Hubei)is 6.23%,4.46%, and 0.87%, respectively. This 45 method of estimating CFR can be used in time to evaluate the therapeutic effect of different medical schemes 46 and different regions, which is of great value and significance for the decision-making in the epidemic 47 prevention and control. 48


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Looking back on the history of civilization for thousands of years is also a review of the epic history of the 53 "war against plague ".The history of human civilization is accompanied by the pace of the plague and spiraled  were infected in China, and a total of 3,123 people died. There have been confirmed cases in 105 countries 61 overseas, with more than 30,000 people diagnosed and 760 people dead. However, due to the difficulty in 62 identifying and accounting for mild and asymptomatic infections, the number of COVID-19 cases may actually be higher. There is no doubt that the outbreak of the COVID-19 is a severe test of public health safety in China 64 and the world.

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The case fatality ratio (CFR) indicates the severity of an epidemic disease, and it also reflects the ability of 66 medical diagnosis and treatment to a certain extent. Generally, the popular method is used to calculate the CFR, 67 which is the ratio of the number of accumulated deaths to the number of diagnoses over a period of time. The 68 traditional method of calculating the CFR is certain and accurate for the epidemic situation that ended. However, 69 for the novel and ongoing epidemic, a large number of patients are still being treated in the hospital, and the 70 final treatment effect of these patients cannot be defined at the time of calculation. The data of a large number of 71 patients treated in hospital are mixed in it, which interferes with the accuracy of the calculation results of CFR.

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This defect makes the obtained results deviate greatly from the real situation, may mislead the public, and even 73 cause decision makers to misjudge the future situation. In the Report of the WHO-China Joint Mission on

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Coronavirus Disease 2019 , as of February 20, the CFR of the COVID-19 in China was 2.9% 1 , and 75 according to the data on March 8, the CRF reached about 3.9%. Although more than 60,000 people have been 76 cured and discharged, nearly 16,000 patients still remain in hospitals.

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Therefore, we propose a method to estimate the CFR during the course of the epidemic and estimate the CFR 78 of COVID-19 in order to provide important reference for the diagnosis, treatment, and containment of epidemic 79 disease.

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Determine the j value of COVID-19

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As a result of the February 12 diagnostic criteria change, resulting in a surge in cases, only the data before February 11 were selected. Taking the national data as an example, starting from February 11 and backtracking 85 to January 20, in Equation (4), j = 1, 2, 3, ..., 15 was calculated, and the CFR was calculated daily. When j = 10, 86 the value of CFR was the most stable among the days, and the coefficient of variation was the smallest.

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According to the published data, in addition to calculating the national CFR, the same calculations were China excluding Hubei reached the minimum value at j =8,10,10,10,12, respectively, indicating that this is the 91 smallest difference in the estimated value of each day.

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Dividing data into five categories as Wuhan, Hubei, Hubei excluding Wuhan, China and China excluding 94 Hubei, j = 8, 10, 12 were selected to calculate the day-to-day CFR tracking back from March5 ( Fig. 2 Table   95 S2-4). The results showed that the difference is large in the early stage and small in the near future in either 96 different j values or different data categories (Fig.2a-c). According to Table 1 and Fig.2, when j=10, if no 97 specific drugs and better treatments emerge later and no significant variation in SARS-CoV-2 pathogenicity, the 98 CFR of COVID-19 is approximately 4.46%, which is lower to the CFR of SARS (6.6%) in Mainland China. In

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Wuhan, the CFR of COVID-19 is approximately 6.23%, which is close to the CFR of SARS in Mainland China.

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Because of the large number of cases and low cure rate in Wuhan, the CFR in the Hubei province is higher 101 than the national average. The CFR of China (excluding Hubei) is the lowest, with an estimate of 0.87%. This 102 may be due to factors such as the large number of imported cases in different provinces outside Hubei, the 103 different age structure of imported cases, relatively few patients with better treatment conditions, and earlier 104 hospital admissions.

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Estimates of CFR q1, q2, qj vary over the duration of the epidemic (Fig.3). The difference among the three is 107 large at the beginning of the epidemic, but over time, the difference between the three becomes smaller and 108 smaller, and when the epidemic is over and treatment is over, the three are bound to present the same value.

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It can be seen from Figure 3 and Table 2 that the estimated value of qj is between the estimated values of q1 110 and q2. Over time, the estimated values of q1 and q2 move closer to the middle, regardless of the size of the 111 estimated value or its changing trend. The estimated value of qj shows better stability, indicating that the qj value 112 can better reflect the true situation of mortality. By comparing the current q1, q2, and qj estimates, the q1and q2 113 estimates exactly give an interval estimate of CFR (Table 2).

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It is known from figure 2 and figure 3 that the CFR estimates vary with time. In the course of treatment, two

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The regression analysis results are showed in Table 3. First, the estimated value of qj is basically stable. In the 122 analysis of the five data categories, the correlation between the value of qj and time t is not significant. This 123 result is consistent with its definition. The estimated value of q1 and q2 is highly correlated with time t, in which 124 the q1 estimate is rapidly decreasing, while the q2 estimate is significantly increasing. Second, on February 12, 125 as a result of changes in diagnostic criteria, a large number of suspected cases were converted to diagnosis cases, but it exhibits a relatively small impact on the CFR estimates.

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The significant reduction in deaths after February 23 is due to the large number of square cabin hospitals in 128 use, the improvement of related medical conditions, and the large-scale entry of traditional Chinese medicine 129 into the anti-epidemic battlefield, which effectively avoided mild to severe illness, severe to critical illness, and 130 reduced CFR in severe cases; therefore, these improvements of medical treatment have a relatively large impact 131 on CFR estimates.  (Table S1).

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The definition, model and correction of case fatality rate 139 "Cure" means the patient was recovered and discharged from the hospital at the end of treatment, and "death 140 from illness" is the end of treatment due to death. (1)

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On this basis, several different CFR can be estimated using different data: Bring the cumulative number of patients cured and discharged on the day (n) (Σxi) and the cumulative number 148 of death (Σyi) on the day into formula (1) to calculate the CFR, that is:

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In fact, this estimate has not been used in reality. The possible reason is that the method highly overestimates 152 CFR.

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The widely accepted estimate of CFR in real life is calculated using the " ratio of the cumulative number of dead 154 patients on the day (∑yi) to the cumulative number of patients diagnosed on that day (ΣTi)", which is called the 155 crude fatality rate, and is recorded as:

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As the epidemic is ongoing, diagnosed patients present as the following three types: as cured and discharged, 159 died of illness, or hospitalized. It is unclear whether the diagnosed patients treated in the hospital will eventually 160 be cured or die. Therefore, the results are inaccurate by using the above formula to calculate the CFR directly

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According to the results of clinical research, COVID-19 is a self-limiting disease with milder early symptoms.

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After one week, the condition may worsen, and the patient can gradually recover as long as the patient passes 173 the most dangerous period of time. In addition, according to the treatment plan, the cured patients must wait for 174 all symptoms to disappear and be negative for two SARS-CoV-2 nucleic acid tests before they can reach the 175 discharge standard for to be considered cured.

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According to statistical theory, if the COVID-19 epidemic event satisfies the statistical random event 177 hypothesis, and the virus is not mutated without considering the discovery of future specific medicines and 178 special medical treatments, the estimated daily CFR should be theoretically stable.

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According to this idea, formula (4) can be used to perform simulation calculations on actual data. Two

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Vent study

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The definitions of q1 and q2 are not required to meet the premise that "the CFR is theoretically stable."

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Although the definition of qj meets the premise that "assuming that the medical conditions and medical care 187 technology level are unchanged, and the virus has not mutated, then the daily CFR is theoretically stable", but in 188 fact, the value of the three may change over time due to the occurrence of the epidemic and the medical events in the development process. Therefore, in order to detect the stability of CFR estimates and the effects of 190 medical events, this study used a statistical model: Here, t is time, and the D is a dummy variable.

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About j value

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The CFR estimate is negatively correlated with the j value size. The larger the j value, the smaller the CFR 197 estimates; the smaller the j value, the larger CR estimates. In relation to the estimated value of CFR, CFR will 198 vary with the value of j. Therefore, to obtain accurate estimates of CR and CFR, we need to choose a j value,

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which is also worthy of further study. However, using this strategy and method is certainly more reasonable than

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According to clinical experience, the median time from onset to clinical recovery is approximately 2 weeks 207 for mild and approximately 3-6 weeks for severe or critical illness. The time from onset to progression to severe 208 illness such as hypoxia is 1 week, and among patients who die, the time from onset to death ranges from 2-8 209 weeks 1 . In this article, j = 10 was consistent with the development of the disease course.
Some researchers also noticed that when estimating the CRF, the selected data ignored a large number of

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The strong transmission of SARS-CoV-2, the uncertainty that causes death in high-risk groups, and the