Decoding Relative Risk: A Step-by-Step Guide to Calculation and Interpretation

Understanding the potential impact of risk factors on health outcomes is crucial in various fields, from medical research to public health policy. One key statistical measure used to quantify this impact is Relative Risk (RR). Relative risk compares the likelihood of an event occurring in one group (exposed) to the likelihood of it occurring in another group (unexposed). This article provides a detailed, step-by-step guide on how to calculate relative risk, its interpretation, and its limitations.

What is Relative Risk?

Relative risk, also known as the risk ratio, is a statistical measure used to compare the probability of an event occurring in two different groups. It essentially tells you how much more likely an event is to occur in the exposed group compared to the unexposed group. A relative risk of 1 indicates no difference in risk between the groups, whereas values greater than 1 suggest an increased risk, and values less than 1 suggest a decreased risk in the exposed group.

For instance, let’s say we’re looking at the risk of developing lung cancer between smokers (exposed group) and non-smokers (unexposed group). A relative risk of 10 would suggest that smokers are 10 times more likely to develop lung cancer than non-smokers.

When to Use Relative Risk

Relative risk is commonly used in:

• Cohort Studies: Studies that follow groups of individuals over time to see if exposure leads to an outcome.
• Randomized Controlled Trials (RCTs): Studies that randomly assign participants to different treatment groups.
• Epidemiology: The study of disease patterns in populations.
• Public Health: To assess the impact of public health interventions.

It’s important to note that relative risk is most appropriate when assessing the impact of an exposure on a relatively common outcome. When the outcome is rare, other measures like the odds ratio may be more appropriate.

Key Terms

Before diving into the calculation, let’s clarify some key terms:

• Exposed Group: The group that has been exposed to the factor under investigation (e.g., smokers, individuals taking a particular medication).
• Unexposed Group: The group that has not been exposed to the factor under investigation (e.g., non-smokers, individuals not taking the medication).
• Outcome: The event or condition of interest (e.g., lung cancer, heart attack).
• Incidence: The number of new cases of a disease or event occurring in a given time period.
• ‘a’: The number of exposed individuals who experienced the outcome.
• ‘b’: The number of exposed individuals who did not experience the outcome.
• ‘c’: The number of unexposed individuals who experienced the outcome.
• ‘d’: The number of unexposed individuals who did not experience the outcome.
• Total exposed group: a+b
• Total unexposed group: c+d

How to Calculate Relative Risk: A Step-by-Step Guide

Let’s walk through the calculation process with a practical example. Imagine we are conducting a study to investigate whether a new diet plan increases the risk of developing type 2 diabetes. Here are the steps:

Step 1: Organize Your Data into a 2×2 Contingency Table

First, we need to organize the data into a 2×2 contingency table. This table will show the number of people who experienced the outcome (type 2 diabetes) and who did not, in both the exposed group (diet plan group) and unexposed group (control group).

Here’s how the table is structured:

Let’s say, after conducting our study, we get the following numbers:

• a: 50 people in the diet plan group developed type 2 diabetes.
• b: 450 people in the diet plan group did not develop type 2 diabetes.
• c: 20 people in the control group developed type 2 diabetes.
• d: 480 people in the control group did not develop type 2 diabetes.

Now, let’s populate the table with these values:

Step 2: Calculate the Incidence in the Exposed Group

The incidence in the exposed group is the proportion of exposed individuals who developed the outcome. This is calculated as:

Incidence (Exposed) = a / (a + b)

In our example:

Incidence (Exposed) = 50 / (50 + 450) = 50 / 500 = 0.1

This means that 10% of people in the diet plan group developed type 2 diabetes.

Step 3: Calculate the Incidence in the Unexposed Group

Similarly, the incidence in the unexposed group is the proportion of unexposed individuals who developed the outcome. This is calculated as:

Incidence (Unexposed) = c / (c + d)

In our example:

Incidence (Unexposed) = 20 / (20 + 480) = 20 / 500 = 0.04

This means that 4% of people in the control group developed type 2 diabetes.

Step 4: Calculate the Relative Risk

Finally, the relative risk is calculated by dividing the incidence in the exposed group by the incidence in the unexposed group:

Relative Risk (RR) = Incidence (Exposed) / Incidence (Unexposed)

In our example:

RR = 0.1 / 0.04 = 2.5

Therefore, the relative risk of developing type 2 diabetes is 2.5 for individuals following the new diet plan compared to the control group.

Interpreting Relative Risk

The interpretation of relative risk is straightforward:

• RR = 1: There is no association between the exposure and the outcome. The risk is the same in both groups.
• RR > 1: There is an increased risk in the exposed group. The higher the value, the greater the increased risk. In our example (RR = 2.5), individuals on the new diet plan are 2.5 times more likely to develop type 2 diabetes than those in the control group.
• RR < 1: There is a decreased risk in the exposed group. The lower the value, the greater the decreased risk. For example, an RR of 0.5 means that the risk is halved in the exposed group.

It’s crucial to always interpret the relative risk in the context of the study being conducted. A statistically significant relative risk might not always be clinically significant. The magnitude of the effect should also be considered, alongside other factors such as absolute risk and the severity of the outcome.

Practical Example Using Different Scenarios

Let’s explore a few more scenarios to further clarify the use of relative risk.

Scenario 1: Vaccination and Flu

A study investigates the effectiveness of a new flu vaccine. Here are the results:

• a: 100 people who were vaccinated got the flu.
• b: 900 people who were vaccinated did not get the flu.
• c: 300 people who were not vaccinated got the flu.
• d: 700 people who were not vaccinated did not get the flu.

Let’s calculate the relative risk:

Incidence (Vaccinated) = 100 / (100 + 900) = 0.1

Incidence (Unvaccinated) = 300 / (300 + 700) = 0.3

RR = 0.1 / 0.3 = 0.33

Interpretation: The relative risk of getting the flu for vaccinated people is 0.33, or approximately 1/3rd, compared to unvaccinated people. This means that vaccinated people are significantly less likely to get the flu (roughly 67% less likely).

Scenario 2: Exercise and Heart Disease

A study examines the relationship between regular exercise and heart disease:

• a: 20 people who exercise regularly developed heart disease.
• b: 480 people who exercise regularly did not develop heart disease.
• c: 80 people who do not exercise regularly developed heart disease.
• d: 420 people who do not exercise regularly did not develop heart disease.

Let’s calculate the relative risk:

Incidence (Exercise) = 20 / (20 + 480) = 0.04

Incidence (No Exercise) = 80 / (80 + 420) = 0.16

RR = 0.04 / 0.16 = 0.25

Interpretation: The relative risk of developing heart disease for regular exercisers is 0.25, or 1/4th compared to people who don’t exercise regularly. This means people who exercise regularly have much lower (75% less) risk of heart disease compared to those who don’t exercise regularly.

Scenario 3: Smoking and Cancer

Consider this hypothetical study on smoking and the development of a certain type of cancer:

• a: 150 smokers developed cancer.
• b: 350 smokers did not develop cancer.
• c: 20 non-smokers developed cancer.
• d: 480 non-smokers did not develop cancer.

Let’s calculate the relative risk:

Incidence (Smokers) = 150 / (150 + 350) = 0.3

Incidence (Non-Smokers) = 20 / (20 + 480) = 0.04

RR = 0.3 / 0.04 = 7.5

Interpretation: The relative risk of developing this particular type of cancer for smokers is 7.5 compared to non-smokers. Thus smokers have a 7.5 times higher risk of developing the cancer than non smokers.

Limitations of Relative Risk

While relative risk is a valuable tool, it has limitations:

• Does not indicate absolute risk: Relative risk only shows how much the risk changes, not the actual probability of the outcome occurring. A high relative risk can be misleading if the absolute risk is low. For instance, a treatment with a relative risk of 2 for a rare disease would only be clinically meaningful if the base risk for the disease was reasonably high.
• Can be misinterpreted: People often confuse relative risk with absolute risk, leading to incorrect interpretations of study results. It’s important to clearly communicate the base rate of the disease for proper understanding.
• Sensitive to base rates: In rare events, a small change in absolute risk can translate into a large relative risk. For example, an increase in risk from 1 in 10,000 to 2 in 10,000 will have a relative risk of 2 but the increase in actual number is very small (one additional case).
• Cannot be used in case-control studies: Relative risk is used for cohorts where the number of participants in both exposed and unexposed group are fixed. In case control studies, we do not fix the exposed and unexposed groups, rather we choose cases first. For case control studies, odds ratios are more appropriate.

Distinction Between Relative Risk and Odds Ratio

It’s important to distinguish between relative risk (RR) and the odds ratio (OR), another commonly used measure of association. While both compare the likelihood of an event between groups, they are calculated differently and interpreted differently.

• Relative Risk (RR): Calculates the ratio of incidences (probabilities) of an outcome in two groups as explained above. It measures how much more likely a particular outcome is to occur in the exposed group compared to the unexposed group. It is primarily used in prospective studies where we can calculate incidences.
• Odds Ratio (OR): Compares the odds of an outcome in the exposed group to the odds of the outcome in the unexposed group. Odds are the ratio of the number of times an outcome occurs to the number of times it doesn’t. Unlike relative risk, odds ratios are often used in case-control studies where we don’t calculate incidences.

For rare diseases or events, the odds ratio and relative risk will be similar. However, for common diseases and outcomes, they can differ significantly, and relative risk is preferred as it directly reflects a change in probability.

Conclusion

Relative risk is an essential statistical tool for assessing the impact of risk factors on health outcomes. By following the steps outlined in this guide, you can accurately calculate and interpret relative risk. Remember to always interpret the results in the context of the study, consider both relative and absolute risks, and be mindful of its limitations. A sound understanding of relative risk will enable you to better understand risk in various scenarios. By being able to accurately calculate and interpret it, you can gain important insights for research, clinical practice, and policy development.

This guide gives you the tools to calculate RR. Understanding it is the first step to interpreting complex health data and making informed decisions.