key: cord-0722379-ldnmu5ri
authors: Luo, Guangze; Zhang, Xingyue; Zheng, Hua; He, Daihai
title: Infection fatality ratio and case fatality ratio of COVID-19
date: 2021-10-07
journal: Int J Infect Dis
DOI: 10.1016/j.ijid.2021.10.004
sha: f3a6788a3bdede7d4cea782671cb9b7b430e1f10
doc_id: 722379
cord_uid: ldnmu5ri

Infection fatality ratio (IFR) is the risk of death per infection and is one of the most important epidemiological parameters. For COVID-19, enormous efforts have been undertaken to estimate the IFR. Here, we discuss the pros and cons of several approaches and emphasize that the frequently used approach using serological survey result as the denominator and the number of confirmed deaths as the numerator will underestimate the true IFR. The most typical examples are South Africa and Peru (before official correction), wherein the confirmed deaths are only one third of the excess deaths. Our argument is that RT-PCR-based case fatality ratio (CFR) is a reliable indicator of the lethality of the COVID-19 in locations where testing is extensive. An accurate IFR is crucial for policy making and public-risk perception.

Infection fatality ratio (IFR) or case fatality ratio (CFR) defines the risk of death per infection or per case, respectively. The difference between IFR and CFR depends on the definition of the case. If one defines infection as case, then CFR equals IFR. It is very important to determine the IFR because it influences the control policy and individual risk perception. It would be straightforward to determine the IFR in a closed, small population, such as the Diamond Princess Cruise, where the CFR was 1.3% without age standardization (Russell et al. 2020 ) and 0.5% after age standardization (Faust and Del Rio 2020) . However, it is not easy to determine the true IFR in a large population, because different approaches to estimate IFR are proposed in a large population (Meyerowitz-Katz and Merone 2020; Levin et al. 2020b; Brazeau et al. 2020; Ioannidis 2021) . In this journal, Meyerowitz-Katz and Merone conducted a meta-analysis and found an IFR of 0.68% (0.53-0.82%) for the COVID-19 (Meyerowitz-Katz and Merone 2020). We discuss the pros and cons of these approaches to estimate IFR. We argue that the RT-PCR based crude case fatality rate with correction accounting for under reporting of asymptomatic cases in locations where testing is extensive should be a reliable indicator of the lethality of the COVID-19.

To estimate the IFR, one needs the number of deaths and the number of related infections. Levin et al.(Levin et al. 2020b ), Brazeau et al.(Brazeau et al. 2020 ) and Ioannidis (Ioannidis 2021) used serological survey to infer the number of infections. Levin et al.'s work was based on data up to June 2020, while many countries such as Australia experienced a severe wave in July-August, 2020. Longer time interval, particularly covering large-scale community outbreaks is preferable for reliable estimation. Even though different data and approaches were used, the age-stratified IFRs (IFR for different age groups) are largely consistent in different studies. Furthermore, Randolph and Barreiro (Randolph and Barreiro 2020) linked CFR with herd immunity to guide the distribution of health resources.

If we only consider the real time RT-PCR-confirmed COVID-19 cases and deaths, we may define the crude CFR, denoted hereafter as RT-PCR CFR, that is the reported COVID-19 deaths divided by the reported COVID-19 cases. Although the real time RT-PCR misses a significant proportion of cases, the numbers of RT-PCR confirmed cases are important indicators for informing control policies. The RT-PCR CFR is influenced by the testing policy, e.g., if only symptomatic or severe cases are tested, then RT-PCR CFR will be much larger than the IFR. Sero-RT-PCR IFR. When the numbers of deaths are RT-PCR confirmed while the numbers of infections are inferred via serological surveys, we obtain sero-RT-PCR IFR. This approach seems to be an improvement over the RT-PCR CFR, because the underreporting in the infections (i.e., the denominator) is addressed. Nonetheless, it has obvious limitations given that underreporting in deaths still exists and could be severe. For example, in South Africa and Peru, it was reported that the excess deaths (most are likely from COVID-19) tripled the reported COVID-deaths (Sguazzin 2021; Dyer 2021) . The excess deaths mean typically the difference between all-cause deaths in a pandemic year and the average number of all-cause deaths in the past five years before the pandemic. This underreporting of COVID-19 deaths is common in all countries without sufficient testing. Unless we can use postmortem serological testing, the sero-RT-PCR IFR will underestimate the true IFR by a factor of as large as onethird. Alternatively, one may use excess deaths to improve the numerator.

Sero-excess IFR. When the numbers of excess deaths are used as a proxy for COVID-19 deaths and the numbers of infections are inferred via serological surveys, we obtain a seroexcess IFR. This should be the most ideal approach to estimate the overall and age IFR of COVID-19 in a location where the COVID-19 had caused community-wide outbreak. Among these three approaches, the sero-excess IFR is the best in principle but may not be feasible at present owing to data availability.

Moreover, some previous studies were carried out in the early phase of the pandemic, e.g., up to June 2020 (Levin et al. 2020a ). The COVID-19 had not yet caused a large-scale community-wide outbreak in some countries before June 2020, e.g., Australia. This will make the estimate in these countries less representative of the true scenario. In Figure 1 , we show the instantaneous RT-PCR CFR for several countries to illustrate the effects of the choice of time interval.

We argue that the RT-PCR CFR in locations where testing is extensive should be a reliable indicator of the lethality of the COVID-19. The mean annual income of the population in these locations is high generally, death reports are of high quality, and medical system avoided a breakdown under large-scale community-wide outbreaks. Under these conditions, their RT-PCR CFR is of reference value. To show this, we include data from the beginning of the pandemic up to March 2021, much longer than the previous studies. The effects of vaccination, however, are not yet evident. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   1 1 1 1 1 1 1 1 1 1 1   1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Figure 1 : Time-varying instantaneous RT-PCR CFR which is calculated in a sliding window of 120 days for six countries. The RT-PCR CFR varies over time, which could be because of different testing policies implemented over time.

We collected COVID-19 RT-PCR cases and deaths and tests for 221 countries and regions from https://www.worldometers.info/coronavirus/coronavirus-cases/. We divided countries/regions into different categories, according to the level of successful control (thus avoiding a medical system breakdown) in terms of deaths per million population. Particularly, countries/regions where total deaths per million were between 20 and 100 were selected, which indicated large-scale community transmission but without breaking the medical system, owing to successful control measures such as extensive testing. The extensive testing typically leads to a low positive rate, i.e., low proportion of positive tests out of all tests. High deaths per million population (>100 deaths per million) or low deaths per million population (<20 deaths per million) would imply either a breakdown of the medical system or no largescale community-wide spread, respectively. However, we are interested in the typical scenario of a large-scale community-wide spread without a medical system breakdown. Furthermore, we selected countries/regions with a testing positive rate <5% (share of tests returning a positive result), which suggests extensive testing and that the pandemic is under control in a location (WHO 2020). We calculate the RT-PCR CFR using total deaths divided by the total number of confirmed cases. Although there should be a delay between the death cases and confirmed cases (about two weeks), we omitted it for simplicity. Finally, we had 14 countries/regions that satisfied the above selection criteria. The summary of selected countries/regions and the estimates of RT-PCR CFR are given in the supplementary information. The key findings have been summarized as follows:

Generally, the RT-PCR CFR falls into the range (0.005, 0.02), which is partly consistent with the serological results estimated by Levin et al.(Levin et al. 2020b ). On the one hand, the IFR range for countries with comprehensive tracing programs from Levin et al.'s estimates is (0.005, 0.018). On the other hand, Levin et al.'s estimates for countries with a large population (e.g., South Korea) are significantly lower than our estimation. The data used by Levin et al. was up to June 2020 when the instantaneous CFR was low.

For these locations under our selection criteria, the RT-PCR CFR has a median of 1.37%. Locations such as Hong Kong, Australia, Japan, and South Korea that have a relatively successful control of the pandemic with measures including extensive testing, a large population size, and strong ties to other regions (e.g., Hong Kong is an important hub, and Hong Kong's data were not used given the lack of large-scale serological studies in many IFR studies) have a higher CFR than those with small populations like Iceland. We note that wide use of self-testing kits (e.g., in Japan) can lead to a higher positive testing rate due to the under-reporting of negative results in self-testing. This does not impact our estimates as long as the deaths and cases are from the same positive pool. Using RT-PCR CFR, we avoid the underestimation of IFR based on sero-RT-PCR IFR in the previous study, because of under reporting of COVID-19 deaths in places such as Peru and South Africa (O'Driscoll et al. 2021) . The Peru government website (Sala Situacional 2021) has nearly tripled its death data after completion of the study.

This report has some limitations. We note that 1.37% is the estimated RT-PCR CFR, which is higher than the true IFR. However, it is unlikely to be vastly different owing to implementation of extensive testing. In Hong Kong, South Korea, Japan, and Australia, we can assume that 80% infections are reported due to extensive testing and/or universal testing. Thus the 1.37% could be corrected to 1.37%*0.8=1.096% in a typical large population with community-wide outbreak but without medical breakdown. If the reporting rate is much lower (<<80%), then the successful control in these locations we selected is difficult to explain. Particularly in Hong Kong, universal testing of 1.5 million people only found a few cases. In Hong Kong, reported numbers include both symptomatic and asymptomatic cases. Suspected COVID-19 deaths are rigorously screened. In Hong Kong, 22% cases are imported cases which are healthier than the local cases. The CFR among imported cases is 1/10 that of the local cases. Excluded imported cases are unlikely to change our conclusion.

As the contribution of reinfection is assumed as low, it can be ignored for now. All largescale studies found that the rate of reinfection is <1% (Falahi and Kenarkoohi 2020; Roy 2020; Sheehan, Reddy, and Rothberg 2021; Okhuese 2020) . In Peru, the reported deaths (excess deaths) reached a level of 0.5% in the whole population. If we ignore the reinfection and assume that 80% of the population had been infected, the IFR would be 0.625%. In an extreme scenario (very unlikely), if 100% of the population had been infected, the IFR would be 0.5%.

The overall IFR in a population is influenced by several factors: e.g., time interval, population age profile, and the availability of medical supplies. Previous studies looked at age-stratified IFR. In Figure 2 , we compare our results from Hong Kong with three agespecific IFR estimations in previous studies (Levin et al. 2020b; Brazeau et al. 2020; O'Driscoll et al. 2021; Tao et al. 2021 ). Our RT-PCR CFR in Hong Kong matched the agespecific IFR from previous studies for most age groups, which confirms that our RT-PCR CFR, obtained effortlessly, should be a useful indicator of the lethality of the COVID-19. One should avoid using the population age profile and age-specific IFR to infer an overall IFR in a location without considering the selection criteria we used, in particular, the condition of the medical system and the availability of medical supplies. In Figure 2 , we list the point estimation and confidence interval of our study in Hong Kong (RT-PCR CFR) and other three studies. The RT-PCR CFR well matched the other three studies in most age groups; this confirms our argument that the RT-PCR CFR is a good proxy of IFR. In the elderly group (age≥75 years), the RT-PCR CFR of Hong Kong was higher, which could mean that other studies are underestimates because of improper use of serological survey in the denominator and RT-PCR confirmed deaths in the numerator.

In conclusion, we discussed the pros and cons of different approaches to estimate IFR. Our argument is that the RT-PCR CFR in locations under certain criteria (e.g., with large-scale community transmission, without medical breakdown, with extensive testing) should be considered as a reliable reference value for policy making. The sero-RT-PCR CFR may be severely bias towards low value (e.g., in South Africa and Peru) owing to different rules applied for the numerator and denominator values. 

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None.

The work described in this paper was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU C7123-20G).

All authors conceived the study, carried out the analysis, wrote the draft, discussed the results, revised the manuscript critically, and approved it for publishing.

Not applicable.

The authors declare that they have no competing interests.