Absoluteness, Estimation and Absurdity – Part 2 (Final)

Another day passed and another milestone exceeded.  I’m going to include an image again today, from Worldometers, showing the latest global COVID-19 figures, as of this writing.

Now more than three quarters of a million diagnosed cases of COVID-19 have been registered; deaths are on the way to 38,000 and the death rate has risen to 19%. See the Worldometers Coronavirus web page for the latest updated figures.

That’s a good point for me to continue my discussion on the widely variant reporting of death statistics.

Let me start by saying that all statistical calculations related to any ongoing real life event or sequence of events or continuous processes, can only be estimates.  Only at the conclusion of such events or processes, if such is possible (many such processes are never-ending as long as the world keeps turning), can the true account of any feature of interest be told.  That is as true for COVID-19 or any other microbial or viral outbreak of illness as for anything else.

We accept the usefulness of such estimates, recognising their inherent weaknesses, for many purposes, such as planning.  Yet all too often, when a statistical figure is declared, it is taken as somehow possessing an air of  acceptable and actionable ‘realness’ which is quite unjustified.  Estimates are just that, estimates.  And that is why the science of statistics was born – to provide, using mathematical constructs, a degree of confidence through the measurement of probabilities of the accuracy or otherwise of any calculated measure.
And yet we simple humans much prefer to see simple measures, measures that we can understand, even vaguely, to provide the guidelines we seek in order to gain some understanding of life processes.

We want to know about death rates.  It is something in which we all have a vested interest.  And so we look for the simplest ways of calculating those measures.  But we must always remember that simple is not always safe, and can be misleading.

There are two basic methods of calculating death rates from illnesses such as COVID-19.  Neither of them is accurate until the day after the last case is closed, and both have been described as ‘naive’ and ‘misleading’.  See the second image – an article abstract from the American Journal of Epidemiology – click on it for source.

Abstract from: American Journal of Epidemiology, Volume 162, Issue 5, 1 September 2005, Pages 479–486

There are several basic metrics we can use to calculate estimates of death rate from an illness.  They are Total Confirmed Cases, Death Count, Recoveries(or Hospital Discharges) – from which can also be derived Total Active Cases and Total Closed Cases.  

I should say that no other metric – such as undiagnosed cases or cases with other co-morbidities – can be recognised as having any bearing on the death rate estimate.  Also that any other inaccuracies inherent in the collection of the data must also be ignored.  The data is what it is, and can be the only criteria for the calculations – always recognising however, that those other factors may also play a role.  Never forget that we are dealing with ‘estimates’ here. 

There is one other measure to take into account. This is the CFR or Case Fatality Rate – which is the result of the calculation. 

Method 1.   The Most Naive Method

CFR = Deaths / Total Confirmed Cases

This, the most crude and naive method, totally ignores all future case outcomes on the assumption that none of them will result in a death.  In other words the current death count is assumed to be the final death count = no more deaths.  This method, still the most widely used, is illogical, unscientific, and is not recommended by epidemiologists.  It does however tend to downplay the real effect of the illness and thus dispense calmness instead of panic.

Method 2.   The Closed Outcomes Based Method 

CFR = Deaths / (Deaths + Recoveries)

which can also be expressed as:

CFR = Deaths / Total Closed Cases

This method ignores the inherent time lag between resolution of the separate outcomes (deaths usually occur more quickly than recoveries) but can be adjusted to compensate for that by the introduction of a time factor.  It is however, based on the logical premise that the only cases to be included in the calculation are those that have already been resolved one way or the other.  A more sophisticated statistical method based on this premise has been advocated by epidemiologists: https://academic.oup.com/aje/article/162/5/479/82647 (this is in fact a different link to the same article behind the image above)

I prefer the simple but more logical version of the closed outcomes based method, since I don’t know of any source that is regularly calculating death rates using the Kaplan-Meier based method, and that is what I will continue to report.  But your choice of estimating method is entirely up to you.

I think I have run out of steam now.  The fact remains that if you are not convinced, you will probably remain unconvinced no matter what I may say.  So, I will leave it there.

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