Clinical Trials

❘❙❚■ Chapter 20 | Comparison of ProportionsOdds ratioA third measure of treatment effect is the odds ratio (OR). The odds of anoutcome event are calculated as the number of events divided by the number ofnonevents. For example, in the active treatment arm in the MI trial, the numberof deaths is 110 and the number of survivals is 1,935, so the odds of death are110 / 1935 = 0.057. If the odds of an event are >1, the event is more likely tohappen than not. In particular, the odds of an event that is certain to happen areinfinite, and the odds of an impossible event are zero. The OR is calculated bydividing the odds in the active treatment group (a / c) by the odds in the placebogroup (b / d):OR = a/cb/d= adbcFor the MI trial data, the OR is calculated as (110 × 1857) / (1936 × 165) = 0.64,meaning that the odds of deaths after MI in the drug group are 64% of the oddsin the placebo group. Clinical trials typically look at treatments that reduce theproportion of patients with an event or, equivalently, have an OR of