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Relative Risk and Vioxx
Rebecca Goldin Ph.D, December 10, 2007
How a statistical slight of hand that went unnoticed by a prestigious medical journal, many doctors, and the media hide a glaring risk.

Here at STATS, we often counsel readers about the importance of understanding the concept of relative risk, when bombarded with frightening stories in the media about the risks from drugs. Unfortunately, when it comes to numbers and the “bottom line” for companies, the accusation of “Lies, Damn Lies, and Statistics” is sometimes justified. A case in point is Merck, which seems to have taken the public and doctors alike for a statistical ride over Vioxx. But had doctors read this article and understood what relative risk really means, they may have concluded that Merck was skewing the numbers in favor of the drug; and we could have avoided the disastrous side effect of a medication that has become a byword for undisclosed risk.

In an analysis of the effects of the drug rofecoxib (marketed as Vioxx), Merck published data in 2000 in the New England Journal of Medicine showing that this drug had some benefits, compared to naproxen (a drug many know by the brand name Aleve). While both drugs had the same positive effect for those with arthritis, Vioxx had fewer gastrointestinal side-effects than naproxen. Merck showed this by randomly assigning one group of patients naproxen and another rofecoxib, and then comparing the incidence of gastrointestinal side (GI) effects in each group.

Specifically, Merck calculated the relative risk for those taking rofecoxib compared to those taking naproxen. This is the ratio of the rate of “gastrointestinal events” for those on Vioxx, to the rate of gastrointestinal events for those on naproxen. In other words, the relative risk is given by the ratio:

A number less than one indicated that rofecoxib was less likely than naproxen to cause these problems. Merck also calculated the relative risk of severe gastrointestinal incidents and, again, the relative risk was below one, suggesting that Vioxx was safer than Aleve.

Now came the trick: for the risk of heart attack (myocardial infarction, MI), Merck calculated the relative risk of naproxen to rofecoxib, and got 0.2. This number may seem good for the cursory reader, since it’s still less than one. But notice that this ratio is given the inverse of the one used for GI events, i.e. the relative risk is:

If Merck had calculated instead the risk of rofecoxib compared to naproxen (as it did for gastrointestinal events), the relative risk would have been one over that number:

In other words, those patients on rofecoxib were five times more  likely to get a heart attack than those on naproxen.

The typical reader may not have absorbed that information, as we often assume that information is presented in a parallel way. To be fair, the report did note that “the incidence of myocardial infarction was lower among patients in the naproxen group than among those in the rofecoxib group.” But if Merck compared rofecoxib to naproxen for the benefits, they should have also compared them the same way for the detriments.

As Nick Horton, a professor at Smith college put it in his commentary “What Your Doctor Should Know about Statistics (but Perhaps Doesn’t...)”:

“While doctors judge risks based on their severity and how often they occur, a five-fold risk for heart attack typically attracts notice. Was this result understood to be an acceptable risk, justifiable given the benefit of decreased gastrointestinal events? Would readers have made a different judgment if the relative risk had been reported as 5.0 (comparing Vioxx to naproxen), as opposed to 0.2 (comparing naproxen to Vioxx)?”

No doubt Merck is using its “full disclosure” of information beforehand to defend itself against the ensuing lawsuits. But why else invert the relative risk if not to deceive those who read them quickly?

The peer review process should have insisted that the Merck authors state their results in clearer language, rather than hiding behind a clever inversion of numbers to make problematic results opaque. Instead, The New England Journal of Medicine inadvertently contributed to widespread Vioxx use over four years and a concomitant increase in heart attack before Merck pulled this drug from the shelves due to inescapable safety concerns.

All of which reminds us (but doctors and reporters in particular), why understanding what the numbers really say is crucial to public health.

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