Predicting the Past
Any fool can predict the future; politicians and investment counselors do it all the time. Modeling past medical and financial events accurately remains a major challenge. Percent change is commonly used in these and other fields of measurement. Quantities in the form of a “percent” are used every day; they are familiar, useful, and generally harmless. But not always.
Proportions as a percent, no problem. “Sixty percent of medical students are female.”
Percent as a measure of change: “My tax load has increased by 8% in the past year.” No problem so far, but begs the question: 8% of what?
Percent as a measure of relative change: “The group given “NewDrug™” increased bone density by 5%; 50% more than the group given “OldDrug™.” This is a gross misrepresentation. “Despite recommendations that bone mineral density precision and followup assessment be based upon absolute measurements (in g/cm2), the use of relative change (in percent) is still frequently encountered.”1
Two decades ago, I was 60 and my son 30, half my age. Thirty years later he will be 60, having aged 100%. If I survive, I will age only 33%. Clearly, he is aging 300% faster than I. A grandson, who will be 33 years of age at that time, will age 1000% during that same interval. In time I shall stop aging altogether, so they can catch up.
Are things better in Boston? In the May 6, 2010, issue of the New England Journal of Medicine, a group from the Brigham and Women’s Hospital report on the use of a technology to reduce medication errors. “...units that did not use [the new technology] reported an 11.5% error rate ...versus [a 6.8% error rate] in those that did... — a 41.4% relative reduction”2. (Why not a 4.7% reduction? …
Address correspondence to Dr. H.A. Smythe, 2 Heathbridge Park, Toronto, Canada M4G 2Y6. E-mail: hasmythe{at}rogers.com