What are the ways of expressing risk?

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

  1. 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).
  2. Simple calculation of OAPR using odds
    In screening the result of a screening test can be expressed in terms of the Likelihood Ratio.