When can odds ratios mislead?

Abstract

Odds and risk There is a problem with odds: unlike risks, they are difficult to understand. The risk of an event happening is simply the number of those who experience the event divided by the total number of people at risk of having that event. It is usually expressed as a proportion or as a percentage. In either case the meaning is usually clear. In contrast, the odds of an event is the number of those who experience the event divided by the number of those who do not. It is expressed as a number from zero (event will never happen) to infinity (event is certain to happen). Odds are fairly easy to visualise when they are greater than one, but are less easily grasped when the value is less than one. Thus odds of six (that is, six to one) mean that six people will experience the event for every one that does not (a risk of six out of seven or 86%). An odds of 0.2 however seems less intuitive: 0.2 people will experience the event for every one that does not. This translates to one event for every five non-events (a risk of one in six or 17%). A second problem with odds is that, although they are related to risk, the relation is not straightforward. The table shows the odds for various risks. For risks of less than about 20% the odds are not greatly dissimilar to the risk, but as the risk climbs above 50% the odds start to look very different.