You might have noticed that, particularly in the medical field, a result from a randomised controlled trial (RCT) is frequently presented as an "Odds Ratio". Sentences such as "With an odds ratio of 2.67 we recommend that all neonates with breathing difficulties are prescribed (insert drug name here)". But what the hell does 2.67 actually mean (and I’m not turning all postmodern on you here)? In other words, what are "Odds Ratios"?
In simple terms, the odds ratio is the likelihood of getting better in the experimental group, compared to the odds of getting better in the control group. Probably the best way of explaining this is with an example. Let’s go with an experiment where we have just two possible outcomes – alive or dead:
Suppose that you run a RCT where you give 100 heart attack sufferers a new active pill (treatment group) and another 100 are given a similarly coloured sugar pill (control group). At 1 year follow-up you see how many in each group are still alive and how many are dead. Forgetting the ethics (which some find surprisingly easy to do with political forces and money behind you), you might then use an odds ratio when writing up your results. Let’s say that 80 people in the treatment group are still alive, compared to only 60 in the control group. The odds of still being alive at the end of the study are 80 out of 100 in the treatment group and only 60 out of 100 in the control group. This is best described as the ‘event rate ’ and in this example the event rate for the treatment group is 0.8 and for the control group is 0.6. The event rate is exactly what it sounds like – it’s the likelihood of an event occurring given the results of the study (in this case - still being alive one year later while the experimenters presents their results during a drug company funded conference in Tahiti).
As is explained under the event rate heading, these figures are only referent within their own condition. To compare the event rate of the treatment group with the event rate of the control group leads to a statistic known as a ‘relative risk ’. This is the degree to which one is more likely to survive (or get better, not change, or get worse – whichever you want to look at) in the treatment condition compared to the control condition. It is derived by dividing the event rate for the treatment group by the event rate of the control group. In this example, the relative risk for surviving in the treatment group compared to the control group is 0.8 divided by 0.6, deriving a relative risk of 1.33. In this particular case, there is a relative risk increase of 33.33% of still being alive if one were in the treatment group compared to the control group.
However, another way of representing the results is to look at the survival rate compared with the non-survival rate within each condition. In this example, the experimental group were four times more likely to survive than to die (80 divided by 20). The control group, however, were only 1.5 times more likely to survive than die (60 divided by 40). Therefore, in this example, the odds of surviving the event (i.e., the ‘event odds ’) in the experimental condition is 4, while the event odds of surviving in the control group was a dismal 1.5.
But, how do the experimental group and control group compare to each other in their survival rates? This is where an odds ratio comes in. One looks at the event odds of surviving in the experimental group (in this case 4.00) and divide it by the event odds of surviving in the control group (in this case 1.5). The result (2.67) is what is meant by "an odds ratio of 2.67". It is the odds of a particular event compared to the odds of the same event under another condition.
This programme is unique in that it will compute the event and odds ratios for improvement, no change, and deterioration. A short explanation of what to do if you only know two of the conditions (e.g., improvement Vs no change or deteriorated) is provided in the related section on event & odds ratio data entry.
For more on the positives and negatives of different event or odds ratios a good first start is Cook & Sackett (1995).