Setting and data: Hubei Province, China

The first known case of SARS-CoV-2 infection was traced back to 1 December 2019 in Wuhan, the main city of Hubei Province, China [3]. The first reported death was on 11 January 2020. Human-to-human transmission of SARS-CoV-2 led to exponential growth of the reported incidence of cases (Fig 1A). On 20 January 2020, Chinese authorities implemented extensive control measures in Hubei: early identification and isolation of clinical cases, tracing and quarantining of contacts, temperature checks before accessing public areas, extension of the lunar new year holiday period, and extreme social distancing, including cancellation of mass gatherings [8]. After 3 days, a cordon sanitaire was imposed with strict traffic restrictions. From 27 January, the daily incidence of cases by date of symptom onset started to plateau and then decreased.

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Fig 1.

(A) Reported number of confirmed cases of SARS-CoV-2 infection by date of symptom onset in Hubei, China, until 11 February 2020. (B) Age distribution of the Chinese population and of the reported cases and deaths in Hubei, China. (C) Reported number of deaths associated with SARS-CoV-2 infection in Hubei, China, until 11 February 2020. (D) Age-specific contact matrix from a 2018 survey conducted in Shanghai, China [11], applied to Hubei Province. SARS-CoV-2, severe acute respiratory syndrome coronavirus 2.

https://doi.org/10.1371/journal.pmed.1003189.g001

The Chinese Center for Disease Control and Prevention (China CDC) reported the number of cases by date of symptom onset and the age distribution of cases and deaths up to 11 February 2020 in China (Fig 1B) [9]. We extracted these data together with the age distribution of the Chinese population. Death counts were obtained from a repository aggregating data from Chinese public data sources [10]. We used data about the daily number of potentially infectious contacts by age group in Shanghai [11]. We assumed that all data sources were applicable to the population of Hubei. As of 11 February, after which information about date of symptom onset was no longer available, there were 41,092 cases and 979 deaths, resulting in a CFR of 2.4%.

Setting and data: Six geographic locations in Europe

The first cases of SARS-CoV-2 infection in Europe were reported at the end of January 2020. Italy was the first country with a large epidemic after a cluster of cases, followed shortly by the first deaths, emerged in Lombardy at the end of February. As of 16 May 2020, Europe is the continent having reported the highest number of cases and deaths (more than 1,800,000 confirmed cases and 160,000 deaths) [1].

We selected European countries that reported the daily number of cases of confirmed SARS-CoV-2 infection by date of symptoms onset. In countries in which this information was available at a regional level, we selected worst-affected regions. We extracted data about the number of confirmed cases by symptom onset, the daily number of deaths, and the distribution of cases and deaths across age groups for each of the six locations: Austria, Bavaria (Germany), Baden-Württemberg (Germany), Lombardy (Italy), Spain, and Switzerland.

For Austria, we obtained all required data from published reports from 11 March to 14 April [12]. On 14 April, there were 14,151 reported cases and 399 deaths (CFR 2.8%). For Germany, we used published data from 3 March to 16 April [13]. Age distributions, available at the country level only, were applied to both regions. On 16 April, there were 31,196 cases (62% with date of onset) and 802 deaths in Baden-Württemberg (CFR 2.6%) and 36,538 cases (56% with date of onset) and 1,049 deaths in Bavaria (CFR 2.9%). For Lombardy, we collected published data from 11 February to 25 April [14, 15]. Age distributions at the national level were applied to Lombardy. On 25 April, there were 74,346 cases (77% with date of onset) and 13,263 deaths (CFR 17.8%). For Spain, we used published data from 2 March to 16 April [16]. On 16 April, 178,031 cases (79% with date of onset) and 19,478 deaths were reported (CFR 10.9%). For Switzerland, we used individual-level data from 2 March to 23 April aggregated by day of onset or day of death. On 23 April, there were 33,228 cases (11% with date of onset) and 1,302 deaths (CFR 3.9%). Further details about the data are available in S1 Text, section 1.

Age-structured model of SARS-CoV-2 transmission and mortality

We used an age-stratified SEIR compartmental model that distinguished between incubating, presymptomatic, asymptomatic, and symptomatic infections. We stratified the population into nine 10-year groups (0–9, up to 80+ years) for all locations except Austria, for which the age groups were 0–4, 5–14, and up to 75+ years. We assumed that susceptibility to SARS-CoV-2 and the risk of acquisition per contact are identical for each age group and that transmission is possible during presymptomatic and asymptomatic infections. We used age-specific contact matrices to model contact patterns according to age group (contact matrix derived by Zhang and colleagues for Hubei [11] and the POLYMOD contact matrix for the six European locations [17]). We modeled the decrease in SARS-CoV-2 transmission due to control measures using a logistic function for the transmission rate.

In the model, after an average incubation period of 5.0 days [18], 81% (95% credible interval [CrI] 71%–89%) of infected people develop symptoms of any severity, and the rest remain asymptomatic [19, 20]. The estimated proportion of symptomatic infections was derived from outbreak investigations included in a systematic review and is implemented as a beta distribution to propagate uncertainty. Studies that have estimated the proportion of asymptomatics have not provided conclusive evidence of an age trend, so we assumed it to be constant [21]. We assumed reduced infectiousness during the period of 2.3 days preceding symptom onset (presymptomatic compartment) and also among asymptomatic individuals [18].

The model was used to compute the number of symptomatic SARS-CoV-2 infections by day of symptom onset in each age group. We applied an age-specific ascertainment proportion to the number of symptomatic infections to estimate the number of reported cases of SARS-CoV-2 infections by date of symptom onset. To identify the parameters, we assumed that 100% of infections in the oldest age group (80+ years old, 75+ years old in Austria) were reported. We assumed that mortality only occurred in symptomatic people and that the time from symptom onset to death followed a log-normal distribution with mean 20.2 days and standard deviation 11.6 [22]. This allowed us to account for the deaths occurring after the date of data collection.

Separately for Hubei and the six European locations, we simultaneously fitted our model to the data sets described above (Fig 1): (1) the number of confirmed cases by day of symptom onset, (2) the number of deaths by day of occurrence, (3) the age distribution of all confirmed cases, and (4) the age distribution of all reported deaths. We assumed a negative binomial distribution for data sets 1 and 2 and a multinomial distribution for data sets 3 and 4. All parameters were estimated from data except for the incubation period, the generation time, the contribution of presymptomatics to transmission, the presymptomatic duration, and the time from symptom onset to death.

The fitted model was used to produce estimates (median posterior distributions with 95% CrIs) of the total number of symptomatic and presymptomatic/asymptomatic infections (adjusted for preferential ascertainment) and of the total number of deaths (adjusted for right-censoring). These were then transformed into adjusted estimates of sCFR and IFR. Besides parameter values and model structure, these estimates rely on the following additional assumptions:

• The severity of symptoms differs by age group and influences the probability of reporting.
• All deaths due to SARS-CoV-2 infection have been identified and reported.
• The susceptibility to SARS-CoV-2 infection is identical across age groups.
• The average standard of care is stable for the period of interest and the next 2 months, during which a proportion of the infected people will eventually die.
• The ascertainment probability by age is constant over the periods considered.

Further details about the method are available in S1 Text, section 2.

Sensitivity analysis

From 12 February 2020, the Chinese authorities changed their criteria for reporting cases, increasing the total by more than 25,000. Reported numbers of deaths increased on 16 April, when Wuhan city reported an additional 1,290 deaths. We ran a sensitivity analysis with corrected numbers of cases and deaths in Hubei Province. We also examined the impact of assuming a 50% lower susceptibility in individuals 0–19 years old and of a lower ascertainment among those 80 years or older (from 90% to 10%, compared with a fixed proportion of 100% in the main analysis). We also refitted the model at different dates of data collection (every 5 days from 12 January to 11 February) to examine the effect of the accumulation of data over time. Additional sensitivity analyses are presented in S1 Text, section 6.

We implemented the model in a Bayesian framework using Stan [23]. All code and data are available from https://github.com/jriou/covid_adjusted_cfr.

Strengths and limitations

Our work has four important strengths. First, we distinguish between the crude CFR and two separate measures of mortality, sCFR and IFR. Second, we use a mechanistic model for the transmission of SARS-CoV-2 and the mortality associated with SARS-CoV-2 infection which directly translates the data-generating mechanisms that lead to biased observations of the number of deaths (because of right-censoring) and of cases (because of preferential ascertainment). Our model also accounts for the effect of control measures on disease transmission. We implemented the model in a Bayesian framework in order to propagate most sources of uncertainty from data and parameter values into the estimates. In Hubei, because the model captured most of the epidemic first wave, the predicted number and timing of deaths could be compared with later reports of SARS-CoV-2 deaths, providing some degree of external validation (S1 Text, section 4). Third, our model is stratified by age group, which has been shown as a crucial feature for modeling emerging respiratory infections [24]. Fourth, the model uses surveillance data that can be collected routinely, and it does not require individual-level data or studies in the general population.

Our study has several limitations. First, an important assumption is that all cases in symptomatic individuals aged 80 years and older were reported as a result of the more severe symptoms at older ages. We cannot confirm this, but the high risk of death from SARS-CoV-2 infection among the elderly was reported very early on [3], so we believe that most old people with symptoms sought care. Sensitivity analyses show that sCFR and IFR estimates decrease linearly, with a lower ascertainment of infections among individuals aged 80 years and older (Fig 3C). For the IFR in Hubei Province to be below 0.5%, fewer than 15% of infections in individuals aged 80 years and older would have been ascertained by the local authorities.

Second, our model requires surveillance data about the incidence of cases of reported SARS-CoV-2 by date of symptom onset. When information on symptom onset is only available for a subset of cases, we have to assume that data are missing at random. Additionally, within a given geographic location, the model assumes a constant ascertainment proportion and a constant mortality for each age group during the period. When repeating the analysis at different stages of the epidemic in Hubei, we found that estimates obtained before the epidemic peak led to overestimation of the sCFR and IFR (Fig 3D). This finding could be the result of a decrease in mortality as the epidemic progresses, but it could also be attributed to a lower ability of the model to estimate the epidemic size before epidemic peak is reached, a common problem in epidemic modeling [25].

Third, we assume that the deficit of reported cases among younger age groups is a result of preferential ascertainment, whereby younger individuals have milder symptoms and are less likely to seek care, and does not reflect a lower risk of infection in younger individuals. During the pandemic of H1N1 influenza, lower circulation in older individuals was attributed to residual immunity [26]. There is no indication of preexisting immunity to SARS-CoV-2 in humans [8]. Lower susceptibility of only younger individuals for immunological reasons seems unlikely. Different contact patterns could contribute to different attack rates by age group. We include age-specific contact patterns in the model, so our results are dependent on the contact matrix used. In a sensitivity analysis with 50% reduced susceptibility in children, the estimates of age-specific IFR in other age groups did not change, but the lower number of total infections led to a higher IFR.

Fourth, the proportion of SARS-CoV-2 infections that remains asymptomatic is still uncertain. To propagate this uncertainty into the results, we implemented a prior distribution informed by the findings of outbreak investigations included in a living systematic review and meta-analysis [19, 20]. Our estimate is in agreement with the findings of a statistical modeling study of an outbreak on the cruise ship Diamond Princess, estimating an average proportion of symptomatic infections of 82.1% (95% CrI 79.8%–84.5%) [27]. Another study of 87 contacts of infected cases in Shenzhen, China, estimated that 80.4% (95% CrI 70.9%–87.4%) were symptomatic [18]. Additionally, dichotomization into asymptomatic and symptomatic is a simplification; SARS-CoV-2 causes a spectrum of symptoms that likely depend on age, sex, and comorbidities. Serological surveys in the general population will be needed to better characterize asymptomatic infections [28].

Comparison with other studies

Our model-based estimates have some degree of external validation from serological studies of previous exposure to SARS-CoV-2. In Geneva, Switzerland, a study reported an attack rate of 9.7% (95% confidence interval 6.1%–13.1%) in the city, resulting in an IFR of 0.6%, which is very close to our national estimate for Switzerland [29]. Preliminary results from a national seroprevalence study in Spain with more than 60,000 participants found an attack rate of 5.0% (95% confidence interval 4.7%–5.4%), consistent with our estimate of 5.7% (95% CrI 5.0%–6.6%) [30]. A study of excess mortality in Italy estimated 17,786 ± 269 deaths in Lombardy, which is close to our credibility interval for the number of total deaths [31]. This study did not attempt to estimate the size of the epidemic but only applied the proportion of positive tests to the population to obtain an upper limit of epidemic size, which resulted in a lower bound for the IFR of 0.6% in Lombardy.

Model-based estimates of mortality from SARS-CoV-2 in China, adjusting for bias, vary. Our estimate for Hubei Province is higher than the sCFR of 1.4% estimated in two other modeling studies [32, 33]. Differences in modeling approaches and assumptions explain the variation. Verity and colleagues used a similar modeling approach but applied their findings to all of mainland China, where mortality outside Hubei Province appeared lower [9]. This paper also assumed a homogeneous attack rate across age groups rather than simulating epidemics using an age-specific contact matrix. Wu and colleagues used another approach, assuming that susceptibility to infection varies by age. Both Verity and colleagues and Wu and colleagues used data from individuals leaving Wuhan before lockdown was implemented to infer ascertainment, while we fixed it to 100% for the oldest age group. This resulted in comparatively lower ascertainment proportions (up to 70% for the oldest age groups in Verity and colleagues, 2% for Wu and colleagues) and consequently to higher estimates of epidemic size and lower estimates of sCFR. The use of data from travelers might result in bias, especially if people who can travel are healthier than the general population.

Other studies that attempt to adjust for right-censoring of deaths give different estimates of mortality in China than in our study. A study using a competing risk model estimated mortality at 7.2% (95% confidence interval 6.6%–8.0%) for Hubei Province [34]. Using data on exported cases, another team estimated mortality of 5.3% (95% confidence interval 3.5%–7.5%) among confirmed cases in China [35]. Another team reported a CFR of 18% (95% CrI 11%–81%) among cases detected in Hubei, accounting for the delay in mortality, and estimated the IFR at 1.0% (95% CI 0.5%–4%), based on data from the early epidemic in Hubei and from cases reported outside China [36]. Our estimate of mortality among all infected cases in Hubei is also higher than in an earlier version of this work (2.9% against 1.6%) [37]. We believe the newer estimate to be more reliable for two reasons. First, we implemented age-specific risks of transmission through a contact matrix, which partially explains the age patterns in reported SARS-CoV-2 infections and leads to lower estimates of the total number of infections, thus increasing mortality. Second, a higher estimated proportion of symptomatic people based on new data also led to higher estimates of mortality among all infected.

Interpretation and implications

In this study, we propose a comprehensive solution to the estimation of mortality from surveillance data during outbreaks using two measures of mortality [6]. Adjusted for right-censoring and preferential ascertainment of severe cases, the IFR is a measure of overall mortality associated with SARS-CoV-2 infection that can be used to assess the potential consequences of the pandemic, e.g., using theoretical estimates of final epidemic size [38]. The sCFR is a measure of mortality that is most relevant to the clinical setting for assessment of prognosis and prioritization of healthcare services. Crude CFR estimates are a poor predictor of mortality from SARS-CoV-2 infection, as demonstrated for instance by the comparison of CFR and IFR values in Switzerland (high CFR, lowest IFR) and Hubei (lowest CFR, highest IFR). In addition to the inherent biases, the wide variation in CFR between geographic locations is likely to reflect external factors, including policies for testing and differences in systems of surveillance and reporting more than differences in mortality. Crude CFR values should therefore not be used for evaluating policy or making comparisons across settings.

Our model-based estimates of the IFR and sCFR varied geographically (Fig 4A). The highest estimate of IFR was found in Hubei Province (2.9%; 95% CrI 2.4%–3.5% in the baseline analysis). The steep increase in mortality among people aged 60 years and older, reaching very high values in people aged 80 years and older, is of concern. The credibility of this estimate and of our approach for adjusting for right-censoring is supported by the model predictions of reported daily SARS-CoV-2–associated deaths in Hubei Province after 11 February (S1 Text, section 4). The estimated IFR decreases to 2.5% (95% CrI 2.1%–2.9%) when accounting for the later correction of reported cases and deaths by the local authorities and increases to 3.3% (95% CrI 2.7%–4.0%) if we consider a lower susceptibility of individuals under 20 years. We also show that applying our model at earlier stages of the epidemic would have resulted in higher estimates of sCFR and IFR and more uncertainty (Fig 3D). However, our estimates here correspond to an average value over the considered period, and it has been shown that mortality has changed over time as a result of an improvement of the standard of care [8].

The estimated IFR in Lombardy, 1.4% (95% CrI 1.1%–1.6%), was lower than in Hubei Province but higher than in five other European locations. Further research is necessary to better understand the factors associated with SARS-CoV-2 mortality. These differences highlight the importance of local factors on the outcome of SARS-CoV-2 infection, including demographic characteristics. A partial explanation for the remaining heterogeneity is the lower degree of preparedness and health service capacity in northern Italy, which in Europe was affected first by the SARS-CoV-2 epidemic. Consequently, we suggest that a single mortality estimate should not be applied to all settings to estimate the total size of the epidemic [39]. This study shows that the IFR and sCFR, adjusted for right-censoring and preferential ascertainment biases, are appropriate measures of mortality for SARS-CoV-2 infection and can be used to improve and monitor clinical and public health strategies to reduce the deaths from SARS-CoV-2 infection.