Numerators, Denominators, and COVID-19

Numerators, Denominators, and COVID-19

After a seven-year absence, this blog is returning, just in time to tackle what will surely become one of the most discussed debates in public health for years to come—how best to manage the COVID-19 infection pandemic currently gripping the world’s attention. A recent provocative article in STAT by widely respected expert in evidence-based medicine John Ioannidis suggests that sweeping and consequential public policy decisions are being made “without reliable data.” The result, he suggests, may be “a fiasco in the making.” The article is well worth reading for an evidence-based perspective on the data we have—and the critically important data that we do not have—on  COVID-19. Surprisingly, the question Ioannidis is raising may be described as one of numerators and denominators.

At JMCP, the most common mathematical errors we identified in submitted work were not made in sophisticated models or multivariate analyses; they were made in calculating and describing simple percentages. The main problem was—and seems to be today—confusion over numerators and denominators used to estimate risks. The fundamental question raised by Ioannidis isn’t whether COVID-19 is a pandemic, as it has been named as such by the World Health Organization. The question is how medically serious the pandemic is, and to know that, one requires the data needed for an empirically accurate calculation of infection-associated risk. Ioannidis argues convincingly that we do not have the data to make such a calculation.

When I teach analytics, I make three key points about percentages:

(1)    The most important word in describing a percentage is “of,” which identifies the group you are describing—who is at risk? This is the denominator. Ioannidis observes that the only known denominator today is the count of people who are both symptomatic and test positive. As Ioannidis points out, this is the well-known methodological problem of selection bias. The people selected for testing are those with symptoms; they do not represent the total infected population. So, the correct statement to describe most of the percentages cited for COVID-19 today should be: “Of those who are so sick that they seek health care and test positive for COVID-19, what percentage experience an adverse outcome?”

(2)    For a percentage to be accurate, the numerator must be an accurately described subset of the denominator. Estimates of the effects of the COVID-19 pandemic may be flawed by numerators mismatched to the denominators they are intended to represent. The 16% rate of serious illness cited by the CDC means that 16% of those who became so sick that they were tested in a hospital experienced serious illness (in China). Unfortunately, the State of Ohio, among the first to impose widespread closures, increased that number to 20% and applied it to all infected people, not just those who get sick. The result of this mathematical error is likely a substantial overestimate of the total number of persons who will require hospitalization.  

(3)    For a percentage to be accurate, both the numerator and denominator must be known and measured accurately. Neither is true of the numbers used to represent the effects of COVID-19 in the United States. Numbers reported to date reflect health systems and environments that differ greatly from those of the United States:

-The rate of health care-associated infection in Italy is nearly double that of the United States.
-The rate of daily smoking is 25% in China, 20% in Italy, and 11% in the United States.
-The death rate from air pollution (per 100,000 population) is 140 in China, 49 in Italy, and 24 in the United States.

I will leave it to others to draw your own opinions about the effects and merits of the policies in place now. While we await data, the members of my family and I are adhering to the CDC guidelines. Time—and accurate information, I hope—will provide us all with the empirical evidence we need.