I’ve been thinking a lot lately about relative risk in the context of health research. Relative risk is used to describe the chance of an event occurring with respect to the chance of the event not occurring, or occurring in a different group, etc. It often accompanies general media reports of health research e.g. the risk of getting scurvy is 10 times higher for people not taking vitamin C vs. those who do (completely fictional example!). Indeed, it almost always accompanies the written results in the original research paper, and it should. However, what is often lacking in media reports is the context of the risk, and/or an interpretation of its impact.
Using the vitamin C example above, we might be concerned that we’ll get scurvy if we don’t take vitamin C supplements. Ten times higher seems like a lot! Although I’m sure the vitamin C manufacturers would like this assessment, let’s see if it really holds water. Imagine in our fictional universe that the researchers followed 100,000 people for 10 years. After 10 years they counted that 55 people had gotten scurvy over that time. They also recorded that half of the people were taking vitamin C supplements regularly, while half were not. Of the 55 scurvy sufferers, 50 were not taking vitamin C, while 5 were. In probability terms then, non-vitamin C takers had a probability of getting scurvy equal to 50/50,000 = 0.001, or 0.1%, while the probability for vitamin C takers was 5/50,000 = 0.00001 or 0.01%. Therefore, the risk of getting scurvy was 10 fold higher (0.0001 x 10 = 0.001), for non-vitamin C takers. Which still sounds bad! However, you might not actually be super concerned about a 0.1% chance of acquiring scurvy, especially as the researchers in our fictional example did not factor in other possible causes of scurvy e.g. socioeconomic status, and other illnesses that may influence the absorption of vitamin C.
I think it’s pretty clear from this example that without information about sample size, it’s difficult to assess the size of the actual risk. Indeed, to be really thorough we would also need to know the numbers of people in each group, not just the total. Next time you’re reading a news article that reports relative risk, see if it also reports total sample size and group sizes. You may be surprised at how often it gets left out of the discussion.
Arianne Albert – WHRI Biostatistician