Hi Ahmad,

As Michele puts it, an odds ratio is a way of quantifying the relationship between two variables.

My background being in psychology, I’ll give you an answer that is very simple and sets things straight with my students :)

Imagine you want to know whether left-handedness is associated with gender in humans (or apes, lizards, etc.). It’s a simple example because left-handedness and gender are dichotomous variables. Indeed one is either left-handed or not left-handed (i.e., right-handed), and either male or not male (i.e., female).

Let’s see this with a simple example, with some (fake) data. Suppose you have a sample of 66 men and 95 women, and 8 of the 66 men are left-handed while 6 of the 95 women are left-handed.

First thing you may want to do is to compute the odds of being left-handed for a man:

o(M) = n(ML)/n(M) = 8/66 (=0.1212121212)

Then the odds of being left-handed for a woman:

o(notM) = n(notML)/n(notM) = 6/95 (=0.06315789)

IF the two odds are exactly the same, then this means one have the same “chance” of being left-handed, no matter that (s)he is a man or a woman. This means that the odds of being left-handed are the same in men and woman, that is, that left-handedness is independent of gender. Note that in this case if you take the ratio of the two odds, i.e., the odds ratio, it will be exactly of 1.

Now, if the odds ratio is not of 1, the further the ratio from 1, the more important the relationshiop/link/dependence between the two variables.

Note that the value of the ratio can be smaller than 1 or bigger than one for the same set of data, depending on the question you ask. For instance if you ask the question “are men more prone to left-handedness” then the odds ratio to answer this question would be:

R(M/notM) = o(M) / o(notM) = 0.1212121212/0.06315789 =1.919192

This value, because it is bigger than 1, means that yes, men are indeed more prone to left-handedness than women (actually, about 1.92 times so).

If you ask the question “are women more prone to left-handedness” then the odds ratio to answer this question would be:

R(notM/M) = o(notM) / o(M) = 0.06315789/0.1212121212 =0.521052

and the answer, since the result is less than 1, would be “no, to the contrary, women are actually less prone to left-handedness than men (actually, woman are “0.52 time more prone to left-handedness”, which means they are 1/0.52 =1.92 times less prone to left-handedness).

Hope this gives you a feeling of what odds ratio is.

An odds ratio is defined as a measure of association between an exposure and an outcome. For instance, in the case of pharmacogenomics, it is the association between the presence of a specific genotype (exposure) and the response (outcome) to a specific drug, either in terms of efficacy, or toxicity.

A genotype that associates to a drug response with an OR=0.3 means that that genotype provides a 3.3-fold protection against that drug response (inversed association).

Hi Ahmad,

As Michele puts it, an odds ratio is a way of quantifying the relationship between two variables.

My background being in psychology, I’ll give you an answer that is very simple and sets things straight with my students :)

Imagine you want to know whether left-handedness is associated with gender in humans (or apes, lizards, etc.). It’s a simple example because left-handedness and gender are dichotomous variables. Indeed one is either left-handed or not left-handed (i.e., right-handed), and either male or not male (i.e., female).

Let’s see this with a simple example, with some (fake) data. Suppose you have a sample of 66 men and 95 women, and 8 of the 66 men are left-handed while 6 of the 95 women are left-handed.

First thing you may want to do is to compute the odds of being left-handed for a man:

o(M) = n(ML)/n(M) = 8/66 (=0.1212121212)

Then the odds of being left-handed for a woman:

o(notM) = n(notML)/n(notM) = 6/95 (=0.06315789)

IF the two odds are exactly the same, then this means one have the same “chance” of being left-handed, no matter that (s)he is a man or a woman. This means that the odds of being left-handed are the same in men and woman, that is, that left-handedness is independent of gender. Note that in this case if you take the ratio of the two odds, i.e., the odds ratio, it will be exactly of 1.

Now, if the odds ratio is not of 1, the further the ratio from 1, the more important the relationshiop/link/dependence between the two variables.

Note that the value of the ratio can be smaller than 1 or bigger than one for the same set of data, depending on the question you ask. For instance if you ask the question “are men more prone to left-handedness” then the odds ratio to answer this question would be:

R(M/notM) = o(M) / o(notM) = 0.1212121212/0.06315789 =1.919192

This value, because it is bigger than 1, means that yes, men are indeed more prone to left-handedness than women (actually, about 1.92 times so).

If you ask the question “are women more prone to left-handedness” then the odds ratio to answer this question would be:

R(notM/M) = o(notM) / o(M) = 0.06315789/0.1212121212 =0.521052

and the answer, since the result is less than 1, would be “no, to the contrary, women are actually less prone to left-handedness than men (actually, woman are “0.52 time more prone to left-handedness”, which means they are 1/0.52 =1.92 times less prone to left-handedness).

Hope this gives you a feeling of what odds ratio is.

Thank you. I really appreciate your marvelous answers.

That's a wonderful and very effective example, Serban. I appreciate it so much, and I'll use it when teaching my students.

Thanks a lot, Michele, you are welcome to do so, I have no copyright on it :p

Cheers,

SCM

Just passing by. I'll keep that simple and effective example from Serban in my wallet. Thanks.