What is an Odds Ratio?

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):

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