# How to Calculate an Adjusted Odds Ratio

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Your physician has given you the choice between two medications for the treatment of asthma. When you compare emergency department visits, you notice that 10 patients on medication A reported a trip to the hospital versus the five patients on medication B. At first glance, it would appear that medication B is the obvious best choice. In order to make an informed decision, however, you'll need to examine the data a little more closely. To determine which of these two asthma medications will better serve you, you can use statistics to calculate the adjusted odds ratio.

#### TL;DR (Too Long; Didn't Read)

An odds ratio is a statistical measure of association, used to determine the relationship between different sets of exposures and outcomes. Found by dividing the results of one outcome by the results of a second, an odds ratio can provide insight into the effectiveness of experimental treatments and more. However, determining the adjusted odds ratio of two data sets requires you to factor in confounding variables -- making adjusted odds ratios difficult to determine in many situations.

## What is an Odds Ratio?

An odds ratio is the statistical measure of association between an exposure and an outcome. In other words, the odds ratio is the statistical chance than an outcome will occur under a specific condition: in the case of our example, the odds ratio represents the chance that taking one of two asthma medications may still lead to a hospital visit. Odds ratios are easy to calculate. If you divide the reported hospital visits for medication B by those for medication A, you'll come up with the odds ratio. In this example, the odds ratio is 0.5. The ratio means that you have roughly a 50% greater chance of going to the hospital when taking medication A over medication B. However, this doesn't necessarily mean that medication B is better: this 0.5 ratio is known as an unadjusted, or crude odds ratio, because it doesn't take anything into account except the reported number of hospital visits.

## Exposures and Outcomes

The numeric value of an odds ratio gives you some idea of what will happen when a patient is exposed to something -- in this case, asthma medication. An odds ratio of 1 means that exposure does not affect the outcome: In other words, the medication doesn't work. An odds ratio greater than 1 indicates higher odds of the outcome while a ratio less than 1 indicates lower odds of the outcome.

## Life and Confounding Variables

The trouble with a crude odds ratio is that it is entirely one-dimensional. It doesn't reflect the influence of confounding factors such as age, other medical conditions or even something as simple as access to a clinic versus an emergency department. Your odds ratio interpretation of the medications might change if you learned that all of the patients on medication A were also receiving treatment for lung cancer and all of the patients on medication B were in otherwise good health, or if you found out that patients on medication A lived five miles away from the hospital and 60 miles away from the nearest clinic.

## Seeking the Adjusted Odds Ratio

Very few things in life have a clear cause and effect relationship. In statistics, the "other" factors which affect the relationship between two things are known as confounding variables. If just one variable affects the relationship, mathematicians will do a statistical adjustment to give a more accurate ratio. When all variables have been taken into account, the ratio is said to be fully adjusted. Because adjusting an odds ratio is very complex, researchers try to control as many variables as possible to ensure accurate results. In pharmaceutical trials, for instance, researchers will look for participants of the same age and gender with similar medical histories.