How high is the Coronavirus Case Fatality Rate?

The CFR may very well be as high as 6%.

Photo: Time

Introduction

As the Coronavirus contagion nudges towards pandemic status, with its rapid spread inciting concerns over the epidemic’s global impact, it is increasingly important to understand the real threat it poses.

We use three metrics (among others) to help effectively assess the overall threat presented by the outbreak of COVID-19: 1) the initial number of people that get infected, 2) the number of days from developing the disease to death, and 3) the percentage of people that die.

Recently, I wrote a piece on how the current method of calculating the mortality rate is wrong, due to something called the lag effect — essentially, due to the nature of an ongoing contagion, the mortality rate needs to be determined on a cohort level, rather than using the overall #deaths/#cases. I also showed a condition under which the modeled number of deaths closely match the reported figures. However, I did not describe the range of possibilities under different conditions where there is a match between model and data. In this post, I simulate the spread and mortality rate of the Coronavirus under different sets of conditions to ascertain the variance of the case fatality rate.

What does Case Fatality Rate depend on?

The case fatality rate depends on multiple factors — the duration of onset-to-death, the total number of cases, patient characteristics (age, sex, health/medical conditions, etc.), proximity and repeated exposure to sick people, availability of excellent health care, etc. In this document, I will specifically explore two factors:

1. The onset-to-death: after contracting COVID-19, how many days does it take for you to die after contracting the virus? Earlier, it was thought that the incubation period ranged from 2–14 days, but Chinese authorities recently discovered a man who did not display symptoms until 27 days after contracting the disease. In addition to the incubation period, the condition of the patient after contracting the virus will determine the eventual fate. A recent study of 31 patients that died in Hubei province showed that both the mean and the median onset-to-death interval from infection were 15–16 days. The data and the histogram are shown below.

The same study found that the average number of days could be as high as 22 (see below table) using the same data but only considering deaths until January 15 (I looked at data up to the end of January).

Image: Imperial College London

2) The #/cases: depending on the number of cases, the Coronavirus mortality rate could be much higher or lower than thought. If the number of cases is underreported, (which is likely, given the scale and speed of COVID’s spread, especially in the Hubei Province) then the mortality rate would be lower. If the number of cases is lower than thought, the CFR would be higher as a larger proportion of infected people die.

Of course, the CFR can never predict the risk of mortality for any given individual, due to a large number of factors at play (age, health, etc). However, these two statistics are relevant across the board and give us a broad sense of the danger the coronavirus poses.

We model multiple different scenarios and calculate the CFR by modifying the #/cases and/or the onset-to-death.

Case 1: Assume the number of cases is the same as reported

In the first case, let’s assume the official statistics are correct: on January 22, there were 444 cases and a total of 56249 by Feb 15 in Hubei province. Below is the table depicting the modeled number of deaths, given a certain #/cases and mortality rate.

Each cell indicates the number of cumulative deaths for each scenario. For example, with a mortality rate of 2% and onset-to-death of 6 days, we would predict the number of deaths to be 765. China reports that by Feb 15, there were 1596 cumulative deaths in Hubei province. Therefore, the scenarios that result in death counts closer to 1596 predict reality more accurately. Warmer colors indicate greater deviance from that figure and the colors closer to green show the scenarios that yield a cumulative number of deaths close to 1596. Knowing this, here are some observations.

1. If the onset-to-death interval is indeed around 16 days (as shown from the data in the previous section), then the mortality rate is likely closer to 6%. If the onset-to death is closer to 20 days, then the mortality rate is likely over 7%.
2. Unless the onset-to-death interval is much more than 20 days, it is highly unlikely that the mortality rate is more than 10%
3. A low onset-to-death interval with a high mortality rate yields the highest number of deaths. In other words, the mortality rate will have to be higher if the onset-to-death is higher.
4. If the mortality rate is less than 10%, it is quite possible that the number of days until death can be as large/larger than 20 (which makes sense given that experts have recently discovered the incubation period is longer than thought.)

An interesting note: a high onset-to-death interval (everything else set equal) implies that there is much more time for the virus to spread, likely increasing the number of infections. In turn, that may cause more deaths. A shorter number of days to death will mean a shorter time for the infection to spread, causing fewer infections, but the higher mortality rate will end up causing a larger number of people to die. Thus, both cases may end up resulting in a massive amount of fatalities.

Case 2: What if the number of cases was substantially higher?

Now, it is time to examine the second case: if the total number cases were not 56249 by Feb 15, but magnitudes larger. Considering that the number of initial cases is possibly undercounted, is the mortality rate truly lower than thought? What are the implications on the mortality rate and the number of days from contracting COVID-19 to death?

Using the data (courtesy JHU) from Hubei Province, the epicenter of spread, between 1/22 to 2/15, we modeled Coronavirus’s spread. The number of deaths between 1/22 and 2/15 was 1596. In the figure above, each dot represents where situations under which the model fits the data the best. The dots represent a combination of mortality rate and days until mortality, given a certain number of initial cases, that yield a number of final deaths between 1546 and 1646. Some takeaways:

• It shows that the number of days until mortality for all cohorts is between 10 and 20. This means that if the mortality rate is 1% or above, for the model to match the data, the number of days to mortality should be between 10 and 20.
• The mortality rate can vary anywhere between 1% and 7% based on different types of conditions. However, given that onset-to-death is on the higher side, it is almost certain that the mortality rate is at least 3% (2x case) and more likely 6 or 7% given that China has reported fewer new cases (which implies that their original count may be closer to reality).
• Once the number of initial cases is multiplied by a factor of 5, there is no combination of mortality rate and days till mortality (within the set parameters) that yields a cumulative number of deaths in the range of 50 of the actual number of deaths. This tells us that the number of cases is almost certainly less than 5x, unless the number of days until death is >20 and/or the mortality rate, is less than 1%, which we know is highly unlikely as many other countries (where the data is likely more accurate) show similar high trends of mortality rates.

Caveats

A number of assumptions were made; if the real statistics deviate from any of these assumed values, my analysis will be rendered incorrect.

• The number of days until death is no less than 5 and no more than 20.
• The CFR is no less than 1% and no more than 20%.
• All people were treated the same (no segmentation).
• Note that the quality of medical care received, people’s age/sex, etc were not controlled for.

Takeaways

• The number of deaths for two different types of cases was modeled— one where we hold the number of cases the same and the second where the number of cases was modified.
• It reveals that the mortality rate has to be higher if the onset-to-death is high, which indeed may be the case.
• If people die around 16 days after being infected, the most likely mortality rate is around 6%.