Calculating and interpreting the odds ratio

Understanding the odds ratio aids implementation of nursing practices and policies based on correct interpretation of the evidence.

Note from the editor: This is the second article in our “Spotlight on statistics” series, which aims to clarify statistical practices used in research articles.

As a nurse, you’re expected to use evidence-based practice to make clinical decisions. To do this, you need to understand basic statistical concepts so you can critically evaluate statistical analyses and draw conclusions about the accuracy and meaning of the results. In this article, we define the concept of the odds ratio and show how it’s calculated and interpreted.

Much of the clinical research relevant to nursing practice focuses on this question: Which of two groups of individuals, each characteristically different, has a higher risk of suffering an adverse outcome? Calculating the odds ratio can answer this question. Here’s another question that can be answered by calculating the odds ratio: Will an intervention change the amount of risk for an individual or a group of individuals experiencing a poor health outcome?

Within each group, some proportion of individuals (who vary either by personal characteristics or intervention) will suffer an adverse outcome (known as risk). The metric most commonly used to compare risks is the relative risk. As discussed in the January issue (“Grasping the all-important concept of risk”), relative risk is the ratio of the proportion of individuals who experienced the undesirable outcome and were exposed to a risk-increasing factor, divided by the proportion of individuals who experienced the undesirable outcome but weren’t exposed to that factor.

But relative risk isn’t used universally. Many investigators report odds ratios instead. To understand the odds ratio, you must understand how odds differ from risks.

Simplest calculation

The simplest calculation of the odds ratio is used when only two choices for a characteristic exist—for example, men compared to women. Suppose we wish to compare the odds ratio of men and women for the risk of an adverse drug event. Table 1 below, which uses hypothetical data, shows the calculation of risk, relative risk, odds, and the odds ratio. The risk of the adverse event is the proportion of individuals in a group who experienced the adverse event. The odds of the adverse event is the ratio of the number of people in the group who experienced the event to the number of people in the group who didn’t experience it. Thus, the risk of the adverse event for men is 23.81% (25 ÷ 105), as shown below.

The odds ratio reflects the relative odds for the two groups—in this case, 6.56 (0.3125 ÷ 0.047619). This contrasts with the relative risk ratio, which is 5.24 (23.81 ÷ 4.55). In some cases, the odds ratio and relative risk ratio are closer together, although the two ratios are calculated using different equations.

When more than two categories exist

When more than two categories exist for the characteristic used to compare the odds of the adverse event, the most common approach is to construct a table with one column for each value of the characteristic and two rows, as in Table 1. Then each category can be compared separately with the first category.

Alternatively, any two categories can be compared. In this case, be aware that the ratio implies a calculation using only two measures of odds. This is no different from a relative risk ratio that allows comparison of two risks at a time. Table 2 below shows this type of calculation, using hypothetical data pertaining to the risk of adverse drug events in older adult Medi­care enrollees.

Controlling for other differences

When comparing the odds of an adverse event for men and women, gender may not be the only difference between the two groups. The groups also may differ in insurance status, income, age, and other variables that can influence the odds of the adverse event. When we read about a study in which a logistic regression was performed to obtain an estimate of an adjusted odds ratio, the result can be interpreted the same way as the odds ratios in Tables 1 and 2. However, the analysis controls for other confounders.

Different values of the odds ratio

To interpret the importance of an odds ratio, you need to understand the meaning of the values. When the odds ratio is near 1, the odds are similar for people who have or who don’t have a particular characteristic (such as gender). For instance, an odds ratio of 1 for the risk of a certain type of cancer by gender means men and women have the same odds and no relationship exists between gender and the odds of getting that cancer.

If, on the other hand, the odds ratio is much higher than 1, the odds are greatly increased for men (assuming women are the reference group). If the odds ratio is much lower than 1, the odds are much lower for men.

Can the odds ratio be used to infer a benefit?

Suppose a researcher conducts a randomized trial to study an intervention aimed at preventing influenza. Assuming this investigator compares the odds of getting influenza for those who received the intervention versus the odds for those who didn’t receive it, we’d expect an odds ratio lower than 1. This value indicates the intervention confers a benefit rather than an additional risk. Many intervention studies have this expected outcome.

Why odd ratios are important

To review, the odds ratio compares those who experience an event with those who don’t experience it. The risk ratio, on the other hand, compares those who experience the event with the entire exposed population. If the group experiencing the event is very small, the risk and odds ratios won’t differ much. However, as the risk increases, the gap between the two ratios grows.

One reason to focus on the odds ratio is that the underlying mathematics of logistic regression analysis (commonly reported in studies measuring an intervention’s effectiveness) lead directly to an estimate of the odds ratio. The key is to understand how the odds ratio differs from the risk ratio.

Analysis of odds ratios helps you interpret statistical analyses. In your search for best practices, the ability to critique statistics enables you to use research results more appropriately and implement programs and interventions based on the evidence. The next article in this series discusses correlational analysis, a method used to measure the association between two variables.

Selected references

Newhouse R, Dearholt S, Poe S, Pugh LC, White K. Johns Hopkins Nursing Evidence-Based Practice Model and Guidelines. Indianapolis, IN: Sigma Theta Tau International; 2007.

Polit DF. Statistics and Data Analysis for Nursing Research. 2nd ed. Boston, MA: Pearson; 2010.

Kevin D. Frick is a professor of health policy and management at Johns Hopkins Bloomberg School of Public Health in Baltimore, Maryland. Renee A. Milligan is a professor of nursing at George Mason University School of Nursing in Fairfax, Virginia. Linda C. Pugh is a professor of nursing at York College of Pennsylvania in York.

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