# Explaining Odds Ratios to non-statisticians

Often as a biostatistician I am asked to explain Odds Ratios to people who do not know anything about statistics. And it is not an easy undertaking. There are many colleagues who do not master this measure themselves.

Below I will try to explain step by step how I respond to people who ask me “What does Odds Ratio
mean”?

My little speech, sitting at the desk, begins like this:

“The Odds Ratio is a measure of the strength of the association between an exposure and an event. For example: is candy consumption (exposure) associated with the evolution of dental caries (event)?
Another example: is there an association between being a woman (exposure) and a bowel cancer (event)?

This measure of association is called “Odds Ratio” because it is exactly a relationship between the Odds!”

Here the trouble begins: “Odds, Gianfranco? What the hell do the Odds mean?”;

I handle it usually like this: “For example, the odds of bowel cancer in women are the ratio between the number of diseased women and the number of healthy women. The same applies to the odds of cancer in men. The relationship between two relationships is the Odds Ratio”.

At this point the look of my interlocutor becomes impassive and a question mark is printed on his forehead.

I wait a moment and then cut through the wind increasing the dose.

The Odds Ratio takes values from zero to positive infinity. If it equals 1, it means that the exposure and the event are not associated, if it is less than 1, it means that the exposure prevents the event, and if it is bigger than 1, it means that the exposure is the cause of the event.

At this point the customer wants to go further.

In other cases, however, the customer insists: “So, let me understand: if the odds ratio is less than 1 …?”

At this point I do not let him finish and proceed with a practical example:

“Yes, if the odds ratio of illness between females and males is, for example, 0.4, it means that your exposure is protective for females, because the value of 0.4 is less than 1. For example, the odds ratio of 0.4 could mean, in numerical terms it means that for every 10 females without bowel cancer there are 20 who does, while in males, for every 10 individuals who do not have the tumor there are 50 who does”

“For example, if the Odds Ratio was, for example, 1.25, it would mean that the fact of being a woman is a risk factor for cancer because for every 10 women without a tumor there would be 50 with it, while for every 10 healthy men there would be only 40 diseased”.

Many non-statisticians, from my experience, understand the Odds Ratio in this way.

Obviously the explanation is simplified and incomplete. I would need to talk about the relationship between the Relative Risk and Odds Ratio, or the fact that it is mainly used in a case-control context, and for this reason it is more and more appropriate to talk about “Odds of an exposure” and not about “Odds of a disease”.

But for non-statisticians it can be sufficient.