Estimating Case Fatality and Case Recovery Rates of COVID-19: is this the right thing to do?

Introduction: Case fatality rates (CFRs) and case recovery rates (CRRs) are frequently used to define health consequences related to specific disease epidemics, including the COVID-19 pandemic. This study aimed to compare various methods and models for calculating CFR and CRR related to COVID-19 based on the global and national data available as of April 2020. Methods: This analytical epidemiologic study was conducted based on detailed data from 210 countries and territories worldwide in April 2020. We used three different formulas to measure CFR and CRR, considering all possible scenarios. Results: We included information for 72 countries with more than 1,000 cases of COVID-19. Overall, using first, second, and third estimation models, the CFR were 6.22%, 21.20%, and 8.67%, respectively; similarly, the CRR was estimated as 23.21%, 78.86%, 32.23%, respectively. We have shown that CFRs vary so much spatially and depend on the estimation method and timing of case reports, likely resulting in overestimation. Conclusions: Even with the more precise method of CFRs estimation, the value is overestimated. Case fatality and recovery rates should not be the only measures used to evaluate disease severity, and the better assessment measures need to be developed as indicators of countries’ performance during COVID-19 pandemic.


Formula III
This formula accounts for the lag time between an individual's disease onset and death/recovery. 4 T is the average time from emerging symptoms until the onset of death (or recovery). Since most countries had not adopted well-performing detection systems, to avoid overestimating the rates, T was considered 7 days, which is the difference of the minimum reported time between the onset of symptom to outcomes and the maximum incubation period. 19 CFR=Deaths at day x/Total cases at day x-T CRR=Recovered at day x/Total cases at day x-T

Statistical analysis
Data management and calculation were conducted in Microsoft Excel, and results (CF and CR rates) were tabulated for the three standard methods of rate estimation by countries. We reported information for the 72 countries in the body of the paper with more than 1,000 cases of COVID-19 in the main paper, and the estimates of the remaining countries (n=138) were provided as supplementary tables. Overall rates for the world were also calculated. The overall lowest and highest CFR and CRR in the European continent were estimated by model 1 and model 2, respectively ( Table 2). The highest CFR was observed in the European continent using models 1 and 3; model 2 highlighted the North American continent as the region with the highest CFR (Table 2). Moreover, the highest CRR was observed in Oceania in all three models ( Table 2).
The impact of important contributing factors affecting CFR and CRR such as the country's population, GDP, number of hospital beds per 1,000 people, number of ICU beds per 100,000 people, and number of ventilators were assessed in the three different proposed models of estimation (Table S2). Comparison among countries with high, moderate, and low CFR was illustrated in Figure 2.
Though the analysis showed a statistically nonsignificant pattern for all variables of interest, models 1 and 2 potentially provide more accurate estimates of CFR and CRR (

Discussion
We have presented a global consequence of COVID-19 in terms of CFRs and CRRs using three different estimation methods. By April 18, 2020, deceased cases reached 119,699, according to data from Worldometer. 20 We have shown that the CFR varies greatly geographically and even depends on the method of estimation implemented and case reports' timing. As a clear example of this, a CFR of 0.31 was estimated in Singapore and 98.82 in the UK. Even with the more precise CFR estimation method, 4 we hypothesize that the value is still overestimated. Other factors that could contribute to varying estimations are the pandemic stage, number and types of tests performed, strategies of diagnostics, capability of the healthcare system, and the reporting system. For example, the USA had a significant increase in testing capacity, but the preliminary estimates of CFRs did not change dramatically (CFR=3.07 on March 12, 2020 vs. 4.03 on April 18, 2020). 13 As of April 2020, most countries were testing people with severe symptoms, mainly those needing hospitalization. The important point is that it is still unclear how many cases of COVID-19 were asymptomatic, or whether similar standards for testing are being performed between countries. Cross-country comparisons cannot be reliable indicators, unless countries are comparable or important factors are adjusted for. However, if all these possible limitations are carefully acknowledged, CFR may help better appreciate the severity of COVID-19 and required mitigation steps. Given the impossibility of accurately estimating CFR and CRR while the COVID-19 pandemic has not yet ended, using different methods to estimate CFR and CRR, considering all possible scenarios, could help us to better estimate disease severity across different countries. Some researchers prefer to use the proportion of total deaths and recovered cases of COVID-19 disease to total disease cases at global and national levels to estimate CFRs and CRRs. After the end of the pandemic, observing CFR and CRR using this method can be done, but while the pandemic is still ongoing, this method is naïve and could be misleading.
The immune response to COVID-19 is not fully understood yet. Studies suggested the possible likelihood of relapse in recovered patients and existing models do not account for that. However, method III highly depends on the selected time period from where total cases are considered as the denominator. 18 The estimation of CFR using method III (6.22%) is similar to the method I (8.67%). However, because all the cases have not been resolved, method III can still be assumed to be the more precise. 18 Otherwise, we suggest merely extracting the active cases from the denominator while using method I. Undiagnosed cases are important for the disease spread, so detecting asymptomatic/undiagnosed cases is critical for the COVID-19 pandemic control. To this end, new methods based on mathematical models have been recently proposed to accurately calculate the health-related consequences of the COVID-19. 21 One of these models is the Susceptible-Exposed-Infectious-Recovered-Dead (SEIRD) Model, which could be applied to better estimate the COVID-19 transmission rate and case fatality risk worldwide. 22 CFR is used as a measure of disease severity and ideally, should be estimated by direct follow-up of cases and ascertainment of their outcome. 23 We have alternatively estimated the risk in a population within a specified period by dividing the number of deaths associated with the disease by the number of cases of that disease using different methods. In this current report, we have presented risk instead of "rate" because the numerator cases were not a subset of the denominator's population. All three methods of CFR estimation have their limitations. Common limitations of the methods are the undiagnosed cases and delays in reporting data. Another limitation of this research is removing countries with a relatively small number of COVID-19 confirmed cases in the main analyses, since CFR is a flawed metric of mortality risk when the sample size is small or very limited.
CFR is commonly used to measure disease severity and is often used to predict the course or outcome of a disease. It can also be used to evaluate the effectiveness of new therapies by reducing measures and improving methods. In the COVID-19 outbreak, widespread changes in CFR estimates can be misleading, which may lead to underestimating the potential threat of COVID-19 in symptomatic patients. It is difficult to compare estimates across the countries, as different countries use different definitions and various testing strategies that may or may not include some cases. Changes in CFR may also be impacted by testing delays, dealing with delays, and differences in the quality of care or interventions at diverse stages of the disease. country during the epidemic. To avoid this bias, timeadjusted estimates between the onset of symptoms and death should be recommended to compare CFRs across countries. 13 Therefore, the estimation of CFR in response to COVID-19 pandemic disease is a high priority, but its interpretation must be done using evidence-based strategies. Though each model has its disadvantages and pitfalls, we recommend estimating CFR using corrected model I by dividing the number of deaths on a given day by the number of patients with confirmed COVID-19 infection 14 days before, based on the assumed maximum incubation period of up to 14 days.
The WHO announced that the fatality rate of the COVID-19 is 10 times higher than that of influenza, making this research timely and relevant. 14 Due to high mortality cases around the world, accurate calculations and clear estimates of CFR for COVID-19 can inform public health interventions and policies to improve health locally and globally. CFR and CRR are not the only measures of severity of the disease, and better estimators could be explored in future research.