In 1995 the results of the West of Scotland Coronary prevention study were presented in the following press release: “People with high cholesterol can rapidly reduce…their risk of death by 22% by taking a widely prescribed drug called pravastatin sodium. This is the conclusion of a landmark study presented today at the annual meeting of the American Heart Association.” 1 One cannot interpret this statistic correctly without knowing what is divided by what. The percentage presented was one of relative risk reduction. It was based on the number of deaths per 1,000 people with high cholesterol. Thirty-two of these people taking pravastatin died. In the placebo, or control or comparison, condition 41 died. The computation was for relative risk reduction, so the difference between the pravastatin and placebo groups, 9, was divided by the number of people who died in the placebo group, 41, to get the 22% figure. Usually when you hear a percentage reported, particularly in the news or in advertising, it is for relative change (for example, the inflation rate has increased by 50%, which could mean that it had gone from 1% to 1.5%) because that is more impressive.
There are other means of reporting this result that might not be as impressive, but might be more revealing of the truth. Absolute risk reduction is the proportion of patients who die without treatment (the placebo group) minus those who die with treatment. In this case, pravastatin reduced the number of people who died from 41 to 32. So the absolute risk reduction is nine in 1,000, which is 0.9%.
Perhaps an even less impressive means of presenting these results would have been is the number needed to treat (NNT). This is the number needed to treat to save one life. Here the NNT to save one life in a thousand is 111 (1,000 divided by 9 (41 in the placebo group minus 32 in the pravastin group).
So when you hear a percentage, be sure you know how it is computed. It might also be useful to compute other types of statistics, absolute risk reduction, NNT, to get a more accurate feel of the result.
1This example is taken from Gerd Gigerenzer’s book, Calculated Risks: How to Know When Numbers Deceive You. 2002. New York: Simon & Schuster. I highly recommend this book.