Every day when I watch the news they show graphs of which states have an increasing number of cases. Guess what? That information doesn’t tell you much if anything at all. They are to be blunt essentially useless graphs and innumeracy writ large. It makes me angry and to paraphrase a friend: “when I get angry, I do a quick blog” – so you’ll have to wait to see if you were better at understanding testing than the average Harvard medical school person for another day or so.
Yes, show the graphs of states where the number of cases is decreasing, that’s great news. Alas, showing graph of cases in states where cases are increasing, when testing is increasing constantly, not so much. Certainly a better graph to show is the daily increase in the number of hospital admissions alongside the increasing number of cases. When the number of admissions is decreasing you obviously know that the most serious cases of Covid-19 are decreasing. But we need to tell people not only whether there are more or fewer hospitalizations but whether the increase in cases is a result of increased testing.
Let me reiterate: what you (and the people making decisions about whether to reopen) need to know is if the increase in cases is only coming from an increased number of tests! And it may very well be that. Think of it this way: if you had a 100 cases a week ago and then this week you test twice as many people and you find 200 cases, do you really have a disease whose prevalence is increasing? It isn’t clear if you have really gotten an increase in cases at all, it’s more likely just an artifact of testing more.
As you might expect, to know what is really going on in less obvious situations than the one I just mentioned, requires computing a fraction expressed as a percentage. It is:
(Number of positive tests)/(Total number of tests)
This is the test positivity ratio that I talked about in an earlier blog. Recall that this is the clever idea of putting the number of tests done in the bottom of the fraction (the denominator) and the number of positive tests you found in the top (the numerator) and looking at the result. It is the easiest way to know if an increase in positive tests is just an artifact of more testing. For example, if you went from 100 cases last week to 200 cases this week but you tripled the number of tests, that’s good news. Your test positivity ratio went down. When you combine this information with just looking at the absolute number of infections found, then you have real information.
The moral of the story: when you show graphs of the test positivity ratio along with one of total hospital admissions – and both are increasing – things are getting worse. When the two graphs are straight lines, you aren’t moving the needle. When the graphs of both of these numbers are going down, that’s when you can start thinking about reopening.
While it is hard to find the test positivity ratio graphs on news programs, luckily it’s easy with google: https://coronavirus.jhu.edu/testing/individual-states