Risk is the chance that an event will occur. Risk can be expressed in various ways, usually either as probability or as odds. Probability is normally expressed as 1 in n where n is the total number of events e.g. 1 in 10 (or 10%). Odds is normally expressed as the ratio of the number of times an event occurs to the number of times it does not occur, e.g. 1 to 10. A probability of 1 in 10 is not the same as an odds of 1 to 10; 1 in 10 is equivalent to an odds of 1:9. Or an odds of 1:10 is equivalent to a probability of 1 in 11. There are several advantages to using odds, namely
- Presentational symmetry with odds
As odds become higher, say from 1:10 to 1:1 to 10:1 the scale risk is uniform and symmetrical about 1:1 so that 1:10 is as far "below" 1:1 as 10:1 is "above" it. This is not the case with the equivalent probabilities, namely 1 in 11 (for 1:10), 1 in 2 (for 1:1) and 10 in 11 (for 10:1).
- Simple calculation of OAPR using odds
In screening the result of a screening test can be expressed in terms of the Likelihood Ratio.