There is a straightforward question that most people would like answered. If someone is infected with COVID-19, how likely is that person to die?
This question is simple, but surprisingly hard to answer.
Here we explain why that is. We’ll discuss the “case fatality rate”, the “crude mortality rate”, and the “infection fatality rate”, and why they’re all different.
The key point is that the “case fatality rate”, the most commonly discussed measure of the risk of dying, is not the answer to the question, for two reasons. One, it relies on the number of confirmed cases, and many cases are not confirmed; and two, it relies on the total number of deaths, and with COVID-19, some people who are sick and will die soon have not yet died. These two facts mean that it is extremely difficult to make accurate estimates of the true risk of death.
In the media, it is often the “case fatality rate” that is talked about when the risk of death from COVID-19 is discussed.1 This measure is sometimes called case fatality risk or case fatality ratio, or CFR.
But this is not the same as the risk of death for an infected person – even though, unfortunately, journalists often suggest that it is. It is relevant and important, but far from the whole story.
The CFR is very easy to calculate. You take the number of people who have died, and you divide it by the total number of people diagnosed with the disease. So if 10 people have died, and 100 people have been diagnosed with the disease, the CFR is [10 / 100], or 10%.
But it’s important to note that it is the ratio between the number of confirmed deaths from the disease and the number of confirmed cases, not total cases. That means that it is not the same as – and, in fast-moving situations like COVID-19, probably not even very close to – the true risk for an infected person.
Another important metric, which should not be confused with the CFR, is the crude mortality rate.
The “crude mortality rate” is another very simple measure, which like the CFR gives something that might sound like the answer to the question that we asked earlier: if someone is infected, how likely are they to die?
But, just as with CFR, it is actually very different.
The crude mortality rate – sometimes called the crude death rate – measures the probability that any individual in the population will die from the disease; not just those who are infected, or are confirmed as being infected. It’s calculated by dividing the number of deaths from the disease by the total population. For instance, if there were 10 deaths in a population of 1,000, the crude mortality rate would be [10 / 1,000], or 1%, even if only 100 people had been diagnosed with the disease.
This difference is important: unfortunately, people sometimes confuse case fatality rates with crude death rates. A common example is the Spanish flu pandemic in 1918. One estimate, by Johnson and Mueller (2002), is that that pandemic killed 50 million people.2 That would have been 2.7% of the world population at the time. This means the crude mortality rate was 2.7%.
But 2.7% is often misreported as the case fatality rate – which is wrong, because not everyone in the world was infected with Spanish flu. If the crude mortality rate really was 2.7%, then the case fatality rate was much higher – it would be the percentage of people who died after being diagnosed with the disease. [We look at the global death count of this pandemic and others here.]
Before we look at what the CFR does tell us about the mortality risk, it is helpful to see what it doesn’t.
Remember the question we asked at the beginning: if someone is infected with COVID-19, how likely is it that they will die? The answer to that question is captured by the infection fatality rate, or IFR.
To work out the IFR, we need two numbers: the total number of cases and the total number of deaths.
We may be able to estimate the total number of cases and use it to calculate the IFR – and researchers do this. But the total number of cases is not known, so the IFR cannot be accurately calculated. And, despite what some media reports imply, the CFR is not the same as – or, probably, even similar to – the IFR. Next, we’ll discuss why.
In order to understand what the case fatality rate can and cannot tell us about a disease outbreak such as COVID-19, it’s important to understand why it is difficult to measure and interpret the numbers.
Sometimes journalists talk about the CFR as if it’s a single, steady number, an unchanging fact about the disease. This is a particular bad example from the New York Times in the early days of the COVID-19 outbreak.
But it’s not a biological constant; instead, it reflects the severity of the disease in a particular context, at a particular time, in a particular population.
The probability that someone dies from a disease doesn’t just depend on the disease itself, but also on the treatment they receive, and on the patient’s own ability to recover from it.
This means that the CFR can decrease or increase over time, as responses change; and that it can vary by location and by the characteristics of the infected population, such as age, or sex. For instance, older populations would expect to see a higher CFR from COVID-19 than younger ones.
The case fatality rate of COVID-19 is not constant. You can see that in the chart below, first published in the Report of the WHO-China Joint Mission on Coronavirus Disease 2019 (COVID-19), in February 2020.10
It shows the CFR values for COVID-19 in several locations in China during the early stages of the outbreak, from the beginning of January to 20th February 2020.
You can see that in the earliest stages of the outbreak the CFR was much higher: 17.3% across China as a whole (in yellow) and greater than 20% in the centre of the outbreak, in Wuhan (in blue).
But in the weeks that followed, the CFR declined, reaching as low as 0.7% for patients who first showed symptoms after February 1st. The WHO says that that is because “the standard of care has evolved over the course of the outbreak”.
You can also see that the CFR was different in different places. By 1st February, the CFR in Wuhan was still 5.8% while it was 0.7% across the rest of China.
This shows that what we said about the CFR generally – that it changes from time to time and place to place – is true for the CFR of COVID-19 specifically. When we talk about the CFR of a disease, we need to talk about it in a specific time and place – the CFR in Wuhan on 23rd February, or in Italy on 4th March – rather than as a single unchanging value.
Case fatality ratio for COVID-19 in China over time and by location, as of 20 February 2020 – Figure 4 in WHO (2020)11
If the case fatality rate does not tell us the risk of death for someone infected with the disease, what does it tell us? And how does the CFR compare with the actual (unknown) probability?
There are two reasons why we would expect the CFR not to represent the real risk. One of them would tend to make the CFR an overestimate – the other would tend to make it an underestimate.
When there are people who have the disease but are not diagnosed, the CFR will overestimate the true risk of death. With COVID-19, we think there are many undiagnosed people.
As we saw above, in our discussion on the difference between total and confirmed cases (here), we do not know the number of total cases. Not everyone is tested for COVID-19, so the total number of cases is higher than the number of confirmed cases.
And whenever there are cases of the disease that are not counted, then the probability of dying from the disease is lower than the reported case fatality rate. Remember our imaginary scenario with 10 deaths and 100 cases. The CFR in that example is 10% – but if there are 500 real cases, then the real risk (the IFR) is just 2%.
Or in one sentence. If the number of total cases is higher than the number of confirmed cases, then the ratio between deaths and total cases is smaller than the ratio between deaths and confirmed cases. This of course assumes that there is not also significant undercounting in the number of deaths; it’s plausible that some deaths are missed or go unreported, but we’d expect the magnitude of undercounting to be less than for cases.
Importantly, this means that the number of tests carried out affects the CFR – you can only confirm a case by testing a patient. So when we compare the CFR between different countries, the differences do not only reflect rates of mortality, but also differences in the scale of testing efforts.
When some people are currently sick and will die of the disease, but have not died yet, the CFR will underestimate the true risk of death. With COVID-19, many of those who are currently sick and will die have not yet died. Or, they may die from the disease but be listed as having died from something else.
In ongoing outbreaks, people who are currently sick will eventually die from the disease. This means that they are currently counted as a case, but will eventually be counted as a death too. This means the CFR right now is an underestimate of what it will be when the disease has run its course.
This is not a problem once an outbreak has finished. Afterwards, the total number of deaths will be known, and we can use it to calculate the CFR. But during an outbreak, we need to be careful with how to interpret the CFR because the outcome (recovery or death) of a large number of cases is still unknown.
This is a common source for misinterpretation of a rising CFR in the earlier stages of an outbreak.13
This is not just a problem for statisticians: it had real negative consequences for our understanding of the outbreak. The low numbers that were published initially resulted in an underestimate of the severity of the outbreak. And the rise of the CFR over time gave the wrong impression that SARS was becoming more deadly over time. These errors made it harder to come up with the right response.
We should stress again that there is no single figure of CFR for any particular disease. The CFR varies by location, and is typically changing over time.
As this paper shows16, CFRs vary widely between countries, from 0.2% in Germany to 7.7% in Italy. But it says that this is not necessarily an accurate comparison of the true likelihood that someone with COVID-19 will die of it.
We do not know how many cases are asymptomatic versus symptomatic, or whether the same criteria for testing are being applied between countries. Without better and more standardised criteria for testing and for the recording of deaths, the real mortality rate is unknown. As the paper says, to understand the differences in CFR and how they should guide decision-making, we need better data.
But if we’re careful to acknowledge its limitations, CFR can help us to better understand the severity of the disease and what we should do about it.
This chart shows how these early CFR values compare. You can see the total number of confirmed cases of COVID-19 (on the x-axis, going across) versus the total number of deaths (on the y-axis, going up).
The grey lines show a range of CFR values – from 0.25% to 10%.
Where each country lies indicates its CFR – for instance, if a country lies along the 2% line, its current confirmed cases and death figures indicate it has a CFR of 2%.
The second chart shows how the CFR has changed over time in countries that have had over 100 confirmed cases.
We have excluded countries which still have a relatively small number of confirmed cases, because CFR is a particularly poor metric to understand mortality risk with a small sample size.
We see this if we look at the trajectory of cases and deaths in Iran: on February 24th it had 2 confirmed cases and 2 deaths, an implausible CFR of 100%. With time its CFR begins to fall, as the number of confirmed cases increases. By the time it has seen hundreds of cases, the CFR drops to around the level seen in other countries.
What we do know if that the mortality risk is higher for older populations and those with underlying health conditions such as cardiovascular disease, diabetes and respiratory disease – we look at some preliminary evidence for this in our full coverage of the COVID-19 pandemic here.