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The
odds ratio is a measure of
effect size particularly important in
Bayesian statistics and logistic regression.
It is defined as the ratio of the odds of an event occurring in one group to the odds of it occurring in another group, or to a sample-based estimate of that ratio. These groups might be men and women, an experimental group and a control group, or any other dichotomy classification. If the probabilities of the event in each of the groups are
p (first group) and
q (second group), then the odds ratio is:
{ p/(1-p) \over q/(1-q)}=\frac{\;p(1-q)\;}{\;q(1-p)\;}.
An odds ratio of 1 indicates that the condition or event under study is equally likely in both groups. An odds ratio greater than 1 indicates that the condition or event is more likely in the first group. And an odds ratio less than 1 indicates that the condition or event is less likely in the first group. The odds ratio must be greater than or equal to zero. As the odds of the first group approaches zero, the odds ratio approaches zero. As the odds of the second group approaches zero, the odds ratio approaches positive infinity.
For example, suppose that in a sample of 100 men, 90 have drunk wine in the previous week, while in a sample of 100 women only 20 have drunk wine in the same period. The odds of a man drinking wine are 90 to 10, or 9:1, while the odds of a woman drinking wine are only 20 to 80, or 1:4 = 0.25:1. Now, 9/0.25 = 36, so the odds ratio is 36, showing that men are much more likely to drink wine than women. Using the above formula for the calculation yields:
{ 0.9/0.1 \over 0.2/0.8}=\frac{\;0.9\times 0.8\;}{\;0.1\times 0.2\;} ={0.72 \over 0.02} = 36.
This example also shows how odds ratios can sometimes seem to overstate relative positions: in this sample men are 4.5 times more likely to have drunk wine than women, but have 36 times the odds.
Taking the
logarithm of the odds ratio ameliorates this effect, and also improves symmetry. For example, using natural logarithms, an odds ratio of 36 maps to 3.584, an odds ratio of one maps to zero, and an odds ratio of 1/36 maps to -3.584.
The logarithm of the odds ratio is the difference of the
logits of the probability.
The increased use of
logistic regression in medical and social science research means that the odds ratio is commonly used as a means of expressing the results in some forms of clinical trials, in survey research, and in
epidemiology, such as in
case-control studies. It is often abbreviated "OR" in reports. When data from multiple surveys is combined, it will often be expressed as "Pooled OR".
See also
External links
- The Odds Ratio Generator - Freeware
- Odds Ratio Calculator - website
- Odds ratio definition and examples
The
odds ratio is a measure of effect size particularly important in
Bayesian statistics and
logistic regression.
It is defined as the ratio of the
odds of an event occurring in one group to the odds of it occurring in another group, or to a sample-based estimate of that ratio. These groups might be men and women, an experimental group and a control group, or any other dichotomy classification. If the probabilities of the event in each of the groups are
p (first group) and
q (second group), then the odds ratio is:
{ p/(1-p) \over q/(1-q)}=\frac{\;p(1-q)\;}{\;q(1-p)\;}.
An odds ratio of 1 indicates that the condition or event under study is equally likely in both groups. An odds ratio greater than 1 indicates that the condition or event is more likely in the first group. And an odds ratio less than 1 indicates that the condition or event is less likely in the first group. The odds ratio must be greater than or equal to zero. As the odds of the first group approaches zero, the odds ratio approaches zero. As the odds of the second group approaches zero, the odds ratio approaches positive infinity.
For example, suppose that in a sample of 100 men, 90 have drunk wine in the previous week, while in a sample of 100 women only 20 have drunk wine in the same period. The odds of a man drinking wine are 90 to 10, or 9:1, while the odds of a woman drinking wine are only 20 to 80, or 1:4 = 0.25:1. Now, 9/0.25 = 36, so the odds ratio is 36, showing that men are much more likely to drink wine than women. Using the above formula for the calculation yields:
{ 0.9/0.1 \over 0.2/0.8}=\frac{\;0.9\times 0.8\;}{\;0.1\times 0.2\;} ={0.72 \over 0.02} = 36.
This example also shows how odds ratios can sometimes seem to overstate relative positions: in this sample men are 4.5 times more likely to have drunk wine than women, but have 36 times the odds.
Taking the logarithm of the odds ratio ameliorates this effect, and also improves
symmetry. For example, using natural logarithms, an odds ratio of 36 maps to 3.584, an odds ratio of one maps to zero, and an odds ratio of 1/36 maps to -3.584.
The logarithm of the odds ratio is the difference of the
logits of the
probability.
The increased use of logistic regression in medical and social science research means that the odds ratio is commonly used as a means of expressing the results in some forms of clinical trials, in
survey research, and in epidemiology, such as in
case-control studies. It is often abbreviated "OR" in reports. When data from multiple surveys is combined, it will often be expressed as "Pooled OR".
See also
External links
- The Odds Ratio Generator - Freeware
- Odds Ratio Calculator - website
- Odds ratio definition and examples
Odds and odds ratio
Odds and odds ratio ... Odds and odds ratio Odds. A ratio of the number of people incurring an event to the number of people who have non-events.
Swots corner: What is an odds ratio? [Mar 1996; 25-6]
A monthly newsletter about evidence-based health care; top source for such information on the net
Odds ratio - Wikipedia, the free encyclopedia
The odds ratio is a measure of effect size particularly important in Bayesian statistics and logistic regression. It is defined as the ratio of the odds of an event occurring in ...
Definition: odds ratio from Online Medical Dictionary
The Online Medical Dictionary is a searchable dictionary of definitions from medicine, science and technology.
BMJ Clinical Evidence: The international source of the best available ...
If the 95% confidence interval for a relative risk (RR) or an odds ratio (OR) crosses 1, then this is taken as no evidence of an effect. The practical advantages of a confidence ...
Calculator for confidence intervals for odds ratio unmatched case ...
OR confidence interval calculator. Calculator for confidence intervals of odds ratio in an unmatched case control study.
Stats: What is an odds ratio?
What is an odds ratio? The odds ratio is a way of comparing whether the probability of a certain event is the same for two groups. An odds ratio of 1 implies that the event is ...
Odds Ratio — Medical Sciences Division Website
What and odds ratio is, why it is used and what it means. ... Odds Ratio. What and odds ratio is, why it is used and what it means.
How do Relative Risk and Odds Ratio compare
How do Relative Risk and Odds Ratio compare? In the FAQ on Relative Risk, there was advice against the use of Odds Ratio, given without explanation.
Peto odds ratio meta-analysis
C opyright © 1990-2008 StatsDirect Limited, all rights reserved. Download a free trail of StatsDirect. Peto odds ratio meta-analysis . Menu location: Analysis_Meta-Analysis_Peto ...
