What is the Mortality Rate? Update 2

Given the recently announced antibody tests from NY, I wanted to take a closer look at my model and compare the results.  It is important to be cautious about overinterpreting preliminary results like this; it is using a new test, for a new disease, on a sample for which we do not know how well it represents the population, but it is also the best test we have so far.

In my simple model for daily death, there are 2 inputs: speed of transmission, R0, and mortality rate.  Given that we only know the output, we cannot fully determine the value of both inputs, however to fit the empirical evidence it must be that if the mortality rate is lower then the speed of transmission must be higher and vice versa.  In other words, each mortality rate has an associated path of transmission and thus a path which determines the total number of infections/deaths.

The model can tell us which combinations of transmission and mortality are possible but not what either of them is.  To do that we need to look at other data.  In my first post on mortality, I focused on studies that estimated mortality rate directly, from which we then estimate the transmission rate.  The other approach is to focus on the number of infections to give a rate of transmission and then see what that implies for mortality rate.

When looking directly at studies on mortality, I concluded that 1% was my best estimate.  The New York test is the other approach, looking at the number of infections.  We can now look at what a completely different data set tells us.  I have drawn 3 paths for NY infections below, all of which can fit the basic data we have seen on death rates.

There is clearly a non-linear relationship between % mortality and % infections in the population.  If I take 1% as the base case, then a rate of 0.5% would require a far higher infection rate while a rate of 1.5% instead would not change the number of infected people nearly as much.

My model predicts a mortality rate of 1% and current deaths data, then the population infection rate would be 12% of the NY State population.  This is remarkably close to the estimate from the NY test result of just under 14%.

The NY test could imply mortality rate a little below 1%, but on the other hand we know there is material underreporting of COVID deaths and so, one could equally argue that the mortality rate is a little over 1%, consistent with the same data.  Some media outlets are using the results to suggest the mortality rate is 0.5%, a poor estimate and a bad way to use statistics.  This ignores the important lag between infections and death as well as the underreporting of deaths.

My initial estimate of the mortality rate was around 1% which is confirmed by this test.  This makes all the projections for future waves of infection more likely to be ones we should be confident about.

Is this a surprise?

To me, no.  It is very much in the range of where medical expert consensus had it beforehand.  I do not think I have been proposing a model any different from mainstream medical thought, but I have found it useful to be able to make my own projections and explain the implications.

However, looking at media reports and my Bloomberg inbox, I have only read people saying that this data shows that the mortality rate is lower than expected. Some are very excitedly saying is a “game changer” and “most of our clients think this is a potentially important development”.  If this reaction is common, then it shows that while the news is virtually only about COVID, very little of it is genuinely informative and people’s understanding of the data is extremely poor.

One of the persistent misrepresentations of the data is that the reported case fatality rate is an estimate.  It is not.  It is a statistic.  It is simply confirmed deaths divided by confirmed cases.  Given the low levels of testing, we know that reported cases are a small fraction of actual infections.  Hence it may be used as an estimate, but it is a truly terrible estimate if you simply take the headline number.  Did anyone really think that mortality was “estimated” to be 13% in the UK for people who got infected?   Only if you thought this was an estimate would this “new” estimate of 1% seem lower to you.

Policy implications

The debate on deaths vs economic costs of reopening will continue, but I hope that so many pseudo-experts will now refrain from saying that COVID has a mortality rate close to flu.

Using the estimate of mortality rate from the NY data to imply infection rates in other countries, suggests that herd immunity is a very long way off.  The UK would have infection levels of just 4%.

PS Treatment news

Yesterday the S&P dropped 1.5% on news that Gilead’s drug which they touted as a treatment for COVID-19 had failed its first clinical trial.  It was a major positive news story a week ago, which tells us how people struggle to interpret news and statistics and the media struggles to provide sensible coverage.  As I mentioned on April 20^th “It is overwhelmingly likely that it is not true … Until we have some proper testing, I will assume this is a nonsense story”

Similarly, please do not inject or drink disinfectant.  Killing a virus outside your body is not the same as killing it inside your body.  On the bright side, this was a Trump theory that was so bad even Fox News has not been pushing it.