Amateur epidemiology (interpretation)

From a strategy perspective, epidemiology is irritating because it is: controversial, beyond my competence to assess, and yet extremely important.

My initial instinct was clearly to defer to the epidemiologists, on the grounds that they would know much more about this than me, or Elon Musk or Jamie Dimon.  Away from myself, people who are successful at business or corporate bureaucracy often overstate their ability to weigh in on issues outside their core competence.  You don’t want to be that person.

But about three weeks ago I began to notice that epidemiologists are a lot like macroeconomists, sensitive to their field’s underdevelopment and extremely prone to insecurity and covering up for that with assertions of credential.

My favorite example of this involves Harvard.  There is a poorly credentialed “nutrition” epidemiologist there who has radically overstated the threat from coronavirus, and continues to do so.  There is also a far better credentialed real epidemiologist who happens to have overstated the likely body count who now spends seemingly half his time slagging the pleb, who is apparently sullying Harvard’s reputation in epidemiology.  Rather than admitting his own mistake, he deflects by kicking down.  My god, does that ever remind me of economists.

That makes me a bit less shy to weigh in – very tentatively – with my own idea.  So, here is that.

A few weeks ago, the economist Tyler Cowen wrote a really interesting article for Bloomberg in which he made a distinction between the “growther’” and “base rater” interpretations of the path of the coronavirus.

Cowen had been struck by Bill Gates’ insistence that this was the scariest thing in his lifetime, and tried to explain why a guy like Gates might be outside the then-complacent consensus on this issue.

Cowen’s hypothesis was that tech folk are just much more comfortable with the notion of exponential growth, intuitively. So, they are less inclined to dismiss something with a three-day doubling time as “still minor.”  In contrast, the base raters were inclined to ask, how often does a global pandemic wreck my investment strategy?  Round I to Gates. Maybe Gates also got network effects. In the old days, going viral was good.

The way this links back to formal epidemiology is through the differential logistic. The simplest way to think about a novel contagion ripping through a “naïve” population is that it generates new infections at a rate that is proportional with those already infected but also proportional with the share of the population not yet infected, on the grounds that one cannot be infected twice.  The integral of that looks like the cumulative normal distribution, flat then steep, then steepest half way through, then flat again. In the early stages, it resembles an exponential. That’s why all the charts you now see are plotted on a log scale.

So far, none of this involves any thinking by me, which is nice.  But I suspect that the epidemiology bulls (who really do exist) have maybe overlearned the lesson of exponentials, and the need to depict an epidemic’s progress on a log scale.  And here is why.

The risk of you getting infected by the coronavirus is not actually proportional with the log of the population already infected.  It is, rather, quite a bit more complex, such that the reduced functional form varies with where we are in the pandemic.

Near herd immunity, presuming that exists in this case, the risk might actually be inversely related with the (share of the) population already infected. At herd immunity, a big share of the population has been infected. Hence that late stage flat section.

It would follow from this that innocently reacting to the log of the population already infected would actually overstate the risk of your getting infected. But at least that would be less misleading that looking at the raw value, i.e. before taking the log.

Conversely, though, if we are still a long way from herd immunity, then the risk of any individual, including say you, getting infected in any given week would be more a function of the absolute level of infections than the log level.

The reason is that, still distant from herd immunity, the count of total infections and the count of still contagious infections would be fairly tightly correlated.  And, key point here, it would follow from this that efforts to relax social distancing would generate public health costs that are related linearly, rather than log-linearly, with the prevalence of the contagion.

I am not sure people instinctively get that.  But I can tell you one thing: I am not jumping on a train to come visit you simply because the log level of infections in NY has inflected, i.e. experienced a change of the second derivative. Nor do I expect you to invite me.  And generalizing, the pace of social un-distancing will be slow, especially if it begins soon.

So, this is me doing what the credentialed epidemiologists say should never be done, weighing in with college or AP level math and nothing more. In my own defense, I comment here on how know nothings like us interpret the charts, not actual epidemiology.

There is a minor irony here.  The fact that some of the credentialed epidemiologists have been caught out overstating the risk inclines me to think for myself.  But when I do that, I actually come away thinking that the convention of looking at log levels is itself a source of complacency in the current context.