My old friend, mentor and former manager Joe Marasco has devised a very cool way to present information on the estimated true mortality rate, using a technique I’d expect very few people under 60 years of age will ever have encountered – the NOMOGRAM.
If you’ve ever used a slide rule (“slipstick”) then a Nomogram is not that difficult to understand, but I suspect there’s nowadays very few of us left who’ve actually used slide rules for calculations, so I’ll take a stab at explaning how to read the Nomogram below.
Basically, what we are trying to achieve here is to present the estimated likely ranges for he true mortality rate for the Corona virus, in a very compact way.
The official numbers for mortality rate suffer from a selection bias, in that they are obtained by dividing the number of deceased by the number of confirmed cases. And as we now know, far from all infected by the virus are tested, meaning that they will never enter the statistics on confirmed cases.
Therefore, both Joe and I use different computational/numerical/probabilistic methods to come up with estimates on the true mortality rate (‘R’) and the factor (‘F’) between true infected and confirmed infected. (More details on how the variables R and F can be estimated can be found here).
What Joe has done is to come up with a very compact way to present these estimates, using Nomograms, for a number of countries – in the Nomogram below, 4 countries + Worldwide.
In the Nomogram, the left side axis (y) represents the official mortality rate, and the right side axis represents F, that is, the factor to multiply Confirmed with to get an estimate for the true number of infected. The diagonal z-axis represents what we really are after, the estimated true mortality rate. The values for x and y axes are obtained from the computational/numerical/probabilistic methods mentioned above, e.g. Grid Approximation or, in my case, Markov Chain Monte Carlo simulation.
To see how to read this Nomogram, let’s use China as an example: start by locating the (yellow) marker for China on the left side y-axis. From that yellow marker goes two lines to two similar yellow markers on the right hand side x-axis. These two latter points represents the estimated lower and upper range for the factor F.
Now, to find out the number – or more correctly, the most likely range for – the parameter we are interested in, the estimated true mortality rate, ‘R’, just follow the lines from the left hand side yellow marker, and read the estimated mortality rate values (lower, upper) on the diagonal z-axis. In case of China, what we obtain by doing so is a lower value of about 0.9% and an upper value of just about 1.6%.
I find this way to present the information very attractive – not only does the Nomogram allow us to present lot’s of information in a very compact format, but furthermore, I find high esthetic value in this way to present the information !
In case the graphics don’t come out very well on this WordPress-site, here’s a link to the actual .png for the Nomogram graphic.