Questions On Statistics In The Epidemic

I have had some questions about how to get numbers for modeling the course of the SARS-CoV-2 infections and buildup of immunity in the population. Today others were asking those questions on Twitter.

I am definitely not a statistician. The only things I know about statistics come from having a team of very capable statisticians working with me on environmental cleanups to tell me how to sample to determine how much needed to be cleaned up, and then how we could tell if things were properly cleaned up.

But I think I learned enough to ask reasonable questions and to suggest what might be priorities. I would greatly appreciate it if knowledgeable people would comment.

One of the great unknowns about Covid-19 is whether and how long an infected person is asymptomatic but may be spreading the virus. Some people may spread the virus for several days before symptoms appear. Some people may be infected and recover without ever showing symptoms. A further question is whether recovered people may spread the virus.

Most of the testing, however, is of people already showing symptoms, for good clinical reasons. Questions: Are there ways to use these results to project back to numbers of asymptomatic infected people? Is there a testing regime that would add to the available data that could give the numbers of asymptomatic infected people? Or are the two pretty much separate questions?

My sense is that the sampling doesn’t have to be totally random across the population. That’s in analogy to my experience in environmental cleanups: it was more important to sample where we knew contamination was likely to exist than broadly across an entire area. Iceland may be doing some work along these lines, as is the Seattle Flu Study and possibly South Korea and towns in Colorado and Italy.

It would also be extremely helpful to know, as the epidemic proceeds, the number of people who have become immune to the virus. There’s an additional unknown here: whether recovered people are immune and, if so, for how long. Many people become ill with something that has similar symptoms to Covid-19 but stay home, recover, and are not tested. Are they immune? If so, how many are there?

Finally, what I hope is a clarification. Once we know the numbers of asymptomatic infections, we would have a total number of infections. From that, an overall death rate could be calculated. To my mind, that’s an interesting number for an epidemiological overview maybe ten years from now. For now, it could even be dangerous in allowing Donald Trump to minimize the epidemic. The most relevant death rates now are the rate for symptomatic people and the rate for hospitalized people. Both of those can be used to estimate hospital needs.

I hope this helps some of those asking the questions and maybe attracts statisticians who can better frame the questions or even answer them.

Cross-posted to Balloon Juice


  1. Andy Dawson · March 25, 2020

    Not a statistician, but a fair understanding of the m mechanics

    There’s no reliable way to project back to numbers infected (particularly those infected but asymptomatic).

    However, since we’ve no reason to assume that the ratio of symptomatic to asymptomatic will change, growth in detected case numbers remains a good enough proxy for the RATE of spread, unless there’s a sudden change in testing pactice.

    Understanding the proportion of those infected, asymptomatic and now presumably immune is key to understanding where we stand on herd immunity. That will only be done by large scale antibody testing.

    The UK has just ordered 3.5 million antibody test kits for m just that purpose.


    • Cheryl Rofer · March 25, 2020

      The reason I’m asking statisticians is that they have ways to do things. My own suspicion is that there is no way to back out the numbers of asymptomatic carriers from what we’ve got, but I wanted a statistician’s take on it.

      So thanks for your speculations, but I was already there.


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