## What is an Odds Ratio?

Posted by ryanlindsay on June 3, 2008

Reliable data and correct interpretations thereof will help move global health interventions in the right direction. Interventions need to be evidence-based. Hunches, gut feelings, premonitions, and even guesses about health issues need to be proven before we make incorrect conclusions resulting in wasted time, effort and money on techniques that are not scientifically sound. **Odds ratios are a surprisingly simple, yet powerful way to show statistical associations in health.**

I have tried to share in simple words, how to calculate and use odds ratio. This is a stab at something I just learned about as a first year MPH student, and not something I profess to be an expert at. This post is undeniably more *practical *than entertaining…

2×2 contingency tables are helpful in organizing binary (a.k.a categorical, nominal, or “yes or no”) data so that statistical associations like chi-square tests and odds ratios can be calculated.

Contingency tables have exposures for the rows and outcomes (usually disease conditions) for the columns.

###### Source: Principles of Epidemiology by Ray Merrill and Thomas Timmreck.

A basic and *hypothetical *situation in global health might be to find out if the village well is the source of a cholera outbreak throughout a village. The first row would represent those exposed (those who didn’t drink the water) and the second row would be those unexposed (those who didn’t drink the well water). The first column would be those that had a disease outcome (in this case cholera). The second column would be those that didn’t have a disease outcome (no cholera).

This is visually summed up in the following table:

For our *hypothetical* example the numbers might be:

or

Now we can calculate and odds ratio. Calculating an odds ratio is simply multiplying box A by box D and then dividing by box B times box C.

For our example:

**Odds ratio’s measure association between exposures** (i.e. well water) **and outcomes** (i.e. cholera). Since odds ratio is the odds of disease among exposed individuals divided by the odds of disease among unexposed individuals, odds ratios allow us to speak about probability.

Odd ratio’s are commonly reported in peer-reviewed journals, so it is important that we know how to calculate and interpret them. An odds ratio of 1 equals no association between exposure and outcome. **Odds ratios measure the direction of an association, be it positive, negative or no association.** In our example, our calculation yielded on odds ratio of 2.84. This can be interpreted as “there is a positive relationship between drinking the well water and contracting cholera.” In different terms, you can say that drinking well water acts as a *significant* risk to getting cholera.

Odds ratios can be strengthened in measuring association through calculation of 95% confidence intervals (CI). Intervals that do not contain 1 indicate association. Without including the equation in this post, here is the CI for our well-cholera example 1.59 to 5.09. With this confidence interval we can say that we are 95% confident that the true odds ratio is between 1.59 and 5.09. This would indicate that there is a positive statistical association between drinking well water and getting cholera (because the interval doesn’t overlap 1). There is a site that allows you to calculate odds ratios and odds ratio confidence intervals online. You can also read more about odds ratios here. Chi-square tests are very important as well and as soon as I figure out how to post googledocs, I can share a spreadsheet that makes calculating chi-square values and corresponding p-values *easy*.

To further suggest examples of when odds ratios would be helpful in global health to measure statistical association, one could look at the relationship between the following topics (taken from the blog):

- How effective vaccination is against measles
- Gatorade and recovery from diarrhea
- Efficacy of male circumcision as a protection from HIV/AIDS

## Kirk Dearden said

Great post on odds ratios, Ryan. I find them very helpful in international health and use them all the time. If you didn’t mention it in the body of your post, readers should know odds ratios are for cross-sectional case/control studies (data collected at one point in time). Relative risks are the appropriate measure for longitudinal data. Folks interested in odds ratios and other epidemiological measures (and how to calculate them) may also want to look at a recent book by Lisa Sullivan: Essentials of Biostatistics in Public Health. You can find it on Amazon: http://www.amazon.com/Essentials-Biostatistics-Public-Health-Sullivan/dp/0763756202/ref=sr_1_1?ie=UTF8&s=books&qid=1212529248&sr=8-1.

## chads said

Timely post for me, Ryan. Thanks. I’ll be taking biostatistics this fall. I’ve always had a tough time clearly articulating the difference between OR and RR. Any thoughts?

## Joseph A Banken said

Very nice post Ryan. You conciseness, clarity and parsimony is much appreciated. I look forward to additional reading from you.

## swarna venugopal said

hey ryan.. thank you sooo much for the explanation on odds ratio. i’m having my thesis exam tomorrow and after reading your write-out i have a much clearer picture of what i am doing with my data.. thanks again buddy!!

## Kelvin said

Very clear explanation! However, how can I use this method in SPSS? Can you show the step for me with the above example? Thanks

## Hanem said

Thank you for great effort for simplifying the concepts for us

could you please let me know how can I calculate the confecence interval and how can I enter such data to excel or SPSS, I am facing a problem as i enter the data to spss, I know how do the test in spss as it is explained in a book but I it did not explained how to enter the data of yes know question

best wishes

Hanem

## Mark said

This is extremely helpful! Thank you for such a great walk-through.

## archana said

hey….thanks a lot for making this so simple…..i am havin my stat exam tomorrow…thank u again

## Nyaaba said

I have my end of semester next week and this has helped me understand the concept of odds ratio

## lin said

Hi all,

is odd ratio the same as incidence?

Thank you

## Ryan said

No, odds ratios are different then incidence. This site has a good equation for calculating incidence.

http://www.hcoa.org/hcoacme/chf-cme/chf00014.htm

## delores said

Thanks for the explanation and I think I got it. However, in your example the total is 522, shouldn’t the total = 261

Please reply – I want to truly make sure I have this…

## Ryan said

Delores, you are absolutely right, good job. The total should be 261 not 522.

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## vandana said

very simply and clearly explained ……….thank you

## fadhil said

Thank about this subject and I now write about dependent categorical data and I need to use odds ratio

Dr. Fadhil Abidy

Iraq

## Mondal said

How can I calculate lower and upper limits of OR (95% CI) from the coefficient of binary logistic regression model?

## Ella said

Very well explained. Thanks Ryan.

## Ella said

hey folks, I will be starting my MSc. dissertation in few months from now. Am just a little bit confused about what topic to choose and write on. i will be glad if any one could send me suggested topic(s)

## Kim said

Ryan, this is very helpful. However, I think you were correct the first time. The total should be 261 not 522. Each person is in one of the 4 cells, so that adds up to 261.

## Syeda Aleena Fazal said

the description you gave is really helpful. Thanks

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what if i have the data like

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how can i calculate its allele frequency, odd ratio and from odd ratio its confidence interval?

## Azeb said

How can I get CI given odds ratio?Thank you

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