In 2010, two research teams separately analyzed data from the same U.K. patient database to see if widely prescribed osteoporosis drugs increased the risk of esophageal cancer. They came to surprisingly different conclusions.

One study, published in the Journal of the American Medical Association, found no increase in patients' cancer risk. The second study, which ran three weeks later in the British Medical Journal, found the risk for developing cancer to be low, but doubled. Which conclusion was correct?

It...