Some thoughts about denominators

Let's face it: denominators keep numbers (and people reporting them) honest. Imagine if I said that there were 3,352 cases of a never-before-seen strain of flu in the US. To be sure, 3,352 cases is a large enough number to send us rushing to buy a respirator mask! But what if I put it slightly differently and said that out of the population of roughly 300,000,000 individuals, 3,352 have contracted this strain of flu. I think this makes things a little different, since it means that the risk of contracting this flu to date is about 1 in 100,000, a fairly low number as risks go. Now, I am going to give you another number -- 86. This represents the number of the novel H1N1 flu-related deaths in Mexico reported on April 25, 2009, by the health minister of Mexico, and at that time this flu had been thought to have sickened 1,400 people. This gives us the risk of death with the flu of roughly 6%, a very high risk indeed! Well, that was then. Now that we have all steadied our pulses, and the health authorities have gone back and done some testing, as of yesterday Mexico had confirmed 2,059, cases with 56 fatalities, equating to a 2.7% risk of dying with the disease. Still a high number, to be sure, but lower than what was though before.

In the US, we have had 3 fatalities among 3,352 cases reported as of yesterday, yielding the risk of death from H1N1 in this country of about 1 in 1,000. But, of course, the denominator of 3,352 persons represent only those who sought medical attention and got tested, so probably it is an underestimate of the true burden of this strain of flu, and necessarily also an over-estimate of its attendant mortality. Now, apply this to the situation in Mexico, and it's likely that the risk of death from H1N1 is also lower than what we have observed precisely due to the under-estimation of the denominator. 

So how could we get a true estimate of the numbers of people afflicted with the H1N1 influenza? Well, we could screen absolutely everyone (or more likely a large and representative group of individuals). Then what? Do we treat them all with anti-virals? Do we observe them? Since the Centers for Disease Control and Prevention recommends testing only severe cases and treating only persons at a high risk for complications, universal testing does not seem like a practical approach. So, the bottom line is that we are not likely ever to get at the correct denominator for the risk of dying with this disease, and any number that we get is likely to be an over-estimate of the true risk.

So, what are the lessons here? First, don't let anyone get away with only giving you the numerator, as that is not even a half of the story. Second, even when the denominator appears known, be skeptical -- does it really represent the entire pool of cases that are at risk for the event that the numerator describes? The likely answer will most of the time be "no". Clearly, it is the denominator that is the key to being an educated consumer of health information.