Fishing in the Bay

28 March 2022

The Case of the Fatal Ratio

We can all limit our chance of getting Covid. If we get vaccinated and follow the advice about masks and physical distancing, the chance will be much lower. What you and I cannot control is our chance of dying if we get infected. The concept of the case fatality rate (CFR) is apparently straight-forward. If I get infected what is the chance that I die? That’s the bottom line surely.

How would we estimate this? By a simple ratio. How many of those infected say one month ago ended up dying? A kid in grade 4 could understand it. When I went to school, we could have calculated it using long-division. Alas, no longer…

This empirical CFR usually goes down over time. Why? There are several reasons.

First, the true CFR goes down. The true CFR is your actual probability of dying if you are infected, as distinct from our data-based empirical estimate of it. There are two reasons that the true CFR will go down over time. First, the most vulnerable die first so the CFR of the remaining population is lower. So, the CFR is not so straightforward. It depends on who we are talking about and as the disease progresses this changes. Secondly, it goes down as we learn better how to treat the disease. So, CFR is not a property of the disease alone. It is a property of the disease, who we are talking about and our ability to deal with it.

Even if the true CFR remained constant – and it is the true CFR that we really care about – the empirical CFR will almost inevitably trend downwards over time. Indeed, our initial estimates are almost always a gross exaggeration of the lethality of any disease. Initial naïve estimate of the CFR for Covid were around 3%!

The reason is that we become better at identifying how many people are infected. When there were no tests, as at the beginning of 2020, it was very hard to know this number. But with more accurate tests and more testing we know, better and better, how many are infected.

We have to admit that Donald Trump was right when he said higher infection counts were (partly) due to more testing. But he did not include the word “partly” and seemed to think the solution was less testing. Of course, testing is mainly important for limiting the spread, not just so data nerds can get a better estimate of the CFR or so politicians can look good.

But keep in mind that we are still probably severely undercounting the number of infections each day, right now with all that testing. Because many infected people, perhaps most, will not have symptoms and there are financial dis-incentives to getting tested. So, the final estimate of the CFR for current Covid strains will probably end up much smaller than the current empirical estimates (perhaps around 1 in 200) though this varies drastically across age-groups.

What else can we say about the CFR?

Almost by definition, it is supposed to be independent of the infection rate on the denominator. The CFR is the proportion of those who are infected who die. This language suggests that it does not matter if there are 100 deaths from 10,000 cases or 10 deaths from 1000 cases. But when the infection rate gets high enough to swamp the health system, the true CFR increases.

So, what have we learned?

The CFR is important but it is not a single number. It depends on who has already died, who remains, how vulnerability a person is, what health professionals have learned about how to treat the disease and how successful we have been in “flattening the curve”. And we have also learned that it is hard to estimate early in a pandemic and almost always the early data makes a disease look way more lethal than it really is.

A simple ratio really does not cut it, and polemical blogposts that focus on the CFR as if it were a single number that is easy to measure almost invite the misinterpretation that follows.

Modern epidemiologists do not ignore such nuances and fallacies.

They run complex simulations that try to take account of how people mix, how testing and vaccination changes over time, how capacity constraints will limit treatment and lead to more deaths and severe illness, and how vaccinated and unvaccinated sub-populations will fare under different scenarios. 

While I personally believe that the government became unhealthily obsessed with justifying all their actions solely on health advice (rather than economists, ethicists and mental health professionals), I judge that the epidemiologists have been providing very good predictions of the consequences of different policies under difficult conditions of extreme uncertainty.