Odds and Odds RatiosOdds and Odds Ratios

By Lawrence Axten (here in spirit!)By Lawrence Axten (here in spirit!)

OddsOdds

• The odds of something happening The odds of something happening can be referred to as the probability can be referred to as the probability of an event happening.of an event happening.

• The odds of an event occurring are The odds of an event occurring are found by dividing the numbers of found by dividing the numbers of events by the number of non-events.events by the number of non-events.

For example…For example…

• 51 boys are born out of every 100 births.51 boys are born out of every 100 births.

• Therefore…Therefore…

Number of boys 51/number of girls 49=1.04Number of boys 51/number of girls 49=1.04

• Your odds of having a boy are 1.04.Your odds of having a boy are 1.04.

• If the number (in this case 1.04) is greater If the number (in this case 1.04) is greater than one an event is more likely to happen.than one an event is more likely to happen.

• If it is less than one it is less likely to If it is less than one it is less likely to happen.happen.

• The odds of an impossible event are zero.The odds of an impossible event are zero.

Odds RatioOdds Ratio

• The odds ratio is found by dividing the The odds ratio is found by dividing the number in the exposed or treated group by number in the exposed or treated group by that of the control group.that of the control group.

• Epidemiological studies generally try to Epidemiological studies generally try to identify factors that cause harm - those with identify factors that cause harm - those with odds ratios greater than one (event more odds ratios greater than one (event more likely).likely).

• Clinical trials look for treatments which Clinical trials look for treatments which reduce adverse events-so look for a odds ratio reduce adverse events-so look for a odds ratio of less than one (less likely).of less than one (less likely).

A point to note…A point to note…

• Trials often quote the percentage Trials often quote the percentage reduction in odds ratio.reduction in odds ratio.

• For example-the ISIS-4 trial reported For example-the ISIS-4 trial reported a 7% reduction in the odds of a 7% reduction in the odds of mortality related to captopril. Not mortality related to captopril. Not that the ratio was 0.93. that the ratio was 0.93.

References.References.

• http://www.medicine.ox.ac.uk/bandolhttp://www.medicine.ox.ac.uk/bandolier/band25/b25-6.htmlier/band25/b25-6.html

• The Odds Ratio. J Bland. BMJ 2000 The Odds Ratio. J Bland. BMJ 2000 May; 320:1468.May; 320:1468.