Relative Risk


Article Author:
Steven Tenny


Article Editor:
Mary Hoffman


Editors In Chief:
Iryna Filippava
Lance Wilcox


Managing Editors:
Avais Raja
Orawan Chaigasame
Carrie Smith
Abdul Waheed
Khalid Alsayouri
Frank Smeeks
Kristina Soman-Faulkner
Trevor Nezwek
Radia Jamil
Patrick Le
Sobhan Daneshfar
Anoosh Zafar Gondal
Saad Nazir
William Gossman
Pritesh Sheth
Hassam Zulfiqar
Navid Mahabadi
Steve Bhimji
John Shell
Matthew Varacallo
Heba Mahdy
Ahmad Malik
Mark Pellegrini
James Hughes
Beata Beatty
Nazia Sadiq
Hajira Basit
Phillip Hynes
Tehmina Warsi


Updated:
3/26/2019 10:57:57 PM

Introduction

Relative risk is a ratio of the probability of an event occurring in the exposed group versus the probability of the event occurring in the non-exposed group.  An example is a relative risk of developing lung cancer (event) in smokers (exposed group) versus non-smokers (non-exposed group).  Relative risk does not provide any information about the absolute risk of the event occurring but rather the higher or lower likelihood of the event in the exposure versus the non-exposure group.[1][2]

Function

Relative Risk = (Probability of event in exposed group) / (Probability of event in not exposed group)[1]

An example will help clarify this formula.

If we hypothetically find that 17% of smokers develop lung cancer and 1% of non-smokers develop lung cancer, then we can calculate the relative risk of lung cancer in smokers versus non-smokers as:

Relative Risk = 17% / 1% = 17

Thus, smokers are 17 times more likely to develop lung cancer than non-smokers.

A second example involves a study of a new medicine. Fourteen of the volunteers who were given the new medicine have an upset stomach, and 42 of the volunteers who were given the new medicine do not have an upset stomach. The not exposed group included a survey of individuals on the street and resulted in finding two people who have never taken the new medicine have an upset stomach and 83 people on the street who have never taken the new medicine do not have an upset stomach.

First, calculate the probability of having an upset stomach with the exposure to the new medication. Fourteen people have an upset stomach who were exposed, and 42 people do not have an upset stomach who were exposed. Thus, the probability of having an upset stomach in the exposed group is as follows:

Probability in exposure group = 14 / (14+42) = 14 / 56 = 0.25

Note the probability is the probability of having an upset stomach in all individuals in the exposure group, both those with and without an upset stomach which took the new medicine. Next, we calculate the probability of an upset stomach in the non-exposure group.

Probability in non-exposure group = 2 / (2 + 83) = 2 / 85 = 0.024

Now we can calculate the relative risk of having an upset stomach (event) after taking the new medicine (exposure).

Relative Risk = 0.25 / 0.024 = 10.4

Thus, it is 10.4 times more likely to have an upset stomach after taking the new medicine in this study than if you did not take the new medicine in the study.

Exposure can also provide benefit and decrease the risk of the event.  A survey of a group of people finds that 40% of those who perform moderate exercise are overweight or obese and 70% of those do not perform moderate exercise are overweight or obese.  In this example the event is "overweight or obese, " and the exposure is "moderate exercise."  Then relative risk is calculated as:

Relative risk = 40% / 70% = 0.57

Thus, the group looked is 0.57 times as likely to be overweight or obese if an individual performs moderate exercise. Stated another way one is 43% less likely (0.43 = 1 – 0.57) to be overweight or obese in the surveyed population if moderate exercise is performed. When the event is an improvement in health due to a health exposure, then the relative benefit is usually reported rather than the relative risk.  The relative benefit is  1 – relative risk.

A relative risk of one implies there is no difference of the event if the exposure has or has not occurred.  If the relative risk is greater than 1, then the event is more likely to occur if there was an exposure. If the relative risk is less than 1, then the event is less likely to occur if there was an exposure.

Issues of Concern

The relative risk is mistaken by some with the odds ratio and absolute risk. Relative risk is the ratio of the probability of an event occurring with an exposure versus the probability of the event occurring without the exposure. Thus to calculate the relative risk, we must know the exposure status of all individuals (either exposed or not exposed). This implies that relative risk is only appropriate for cases where the exposure status and incidence of disease can be accurately determined such as prospective cohort studies.[1][3][2]

The odds ratio compares the odds of some event in an exposed group versus the odds in a non-exposed group and is calculated as the number of events / the number of non-events. Stated another way, if the probability of an event is P, then the odds ratio would be P / (1 – P).  In a two-by-two table with cells a, b, c, and d then the odds ratio is odds of the event in the exposure group (a/b) divided by the odds of the event in the control or non-exposure group (c/d). Thus the odds ratio is (a/b) / (c/d) which simplifies to ad/bc. This is compared to the relative risk which is (a / (a+b)) / (c / (c+d)). If the disease condition (event) is rare, then the odds ratio and relative risk may be comparable, but the odds ratio will overestimate the risk if the disease is more common.  In such cases, the odds ratio should be avoided, and the relative risk will be a more accurate estimation of risk.

Absolute risk is the actual risk of some event happening given the current exposure. For example, if 1 in 10 individuals with exposure develops the disease then the absolute risk of developing the disease with exposure is 10% or 1:10. If only 1 in 100 individuals without exposure develop the disease, then the absolute risk for developing the disease without exposure would be 1% or 1:100. Thus the relative risk of developing the disease would be 0.1 / 0.01 = 10. Therefore, an individual has a 10% chance of developing the disease with exposure (absolute risk), 1% chance of developing the disease without exposure (absolute risk), and they are 10 times more likely to develop the disease if they have exposure (relative risk).[4][5]

Finally, very small numbers can create large changes in relative risk but small changes absolute risk. The annual risk for seizure (event) in the general population (non-exposure) is around 0.057%. Certain medications can lower the seizure threshold and increase the likelihood of a seizure. Taking one specific medication (exposure) increases the annual risk of seizure (event) to 0.16%. Thus the relative risk of seizure when taking the specific medication is 2.8 (2.8 = 0.16 / 0.057).  A person is 2.8 times more likely to have a seizure when taking the specific medication, but that is only a 0.103% increase in absolute risk (1 in 1000 increase in absolute risk).

Clinical Significance

Relative risk is the ratio of the risks for an event for the exposure group to the risks for the non-exposure group. Thus relative risk provides an increase or decrease in the likelihood of an event based on some exposure. Relative risk has the benefit of being a ratio of risks which means it can be applied to populations with differing disease prevalence. Relative risk does not specify the absolute risk of the event occurring.


  • Image 5593 Not availableImage 5593 Not available
    Contributed by Steven Tenny, MD, MPH, MBA
Attributed To: Contributed by Steven Tenny, MD, MPH, MBA

Interested in Participating?

We are looking for contributors to author, edit, and peer review our vast library of review articles and multiple choice questions. In as little as 2-3 hours you can make a significant contribution to your specialty. In return for a small amount of your time, you will receive free access to all content and you will be published as an author or editor in eBooks, apps, online CME/CE activities, and an online Learning Management System for students, teachers, and program directors that allows access to review materials in over 500 specialties.

Improve Content - Become an Author or Editor

This is an academic project designed to provide inexpensive peer-reviewed Apps, eBooks, and very soon an online CME/CE system to help students identify weaknesses and improve knowledge. We would like you to consider being an author or editor. Please click here to learn more. Thank you for you for your interest, the StatPearls Publishing Editorial Team.

Relative Risk - Questions

Take a quiz of the questions on this article.

Take Quiz
What is defined as the incidence rate among the exposed divided by the incidence rate among the non-exposed?



Click Your Answer Below


Would you like to access teaching points and more information on this topic?

Improve Content - Become an Author or Editor and get free access to the entire database, free eBooks, as well as free CME/CE as it becomes available. If interested, please click on "Sign Up" to register.

Purchase- Want immediate access to questions, answers, and teaching points? They can be purchased above at Apps and eBooks.


Sign Up
The relative risk (RR) of an experimental study is 1. What does this mean?



Click Your Answer Below


Would you like to access teaching points and more information on this topic?

Improve Content - Become an Author or Editor and get free access to the entire database, free eBooks, as well as free CME/CE as it becomes available. If interested, please click on "Sign Up" to register.

Purchase- Want immediate access to questions, answers, and teaching points? They can be purchased above at Apps and eBooks.


Sign Up
Which is most closely related to "risky shift" phenomenon?



Click Your Answer Below


Would you like to access teaching points and more information on this topic?

Improve Content - Become an Author or Editor and get free access to the entire database, free eBooks, as well as free CME/CE as it becomes available. If interested, please click on "Sign Up" to register.

Purchase- Want immediate access to questions, answers, and teaching points? They can be purchased above at Apps and eBooks.


Sign Up
A researcher found that 20% of mice exposed to compound FC420 developed cancer and only 1% of mice not exposed to compound FC420 developed cancer. Which of the following is the best interpretation of these results?



Click Your Answer Below


Would you like to access teaching points and more information on this topic?

Improve Content - Become an Author or Editor and get free access to the entire database, free eBooks, as well as free CME/CE as it becomes available. If interested, please click on "Sign Up" to register.

Purchase- Want immediate access to questions, answers, and teaching points? They can be purchased above at Apps and eBooks.


Sign Up
A researcher recruits 200 people for a study. The first 100 people get a new medication. Sixty of these people report they have a runny nose after taking the medication. The next 100 people do not get any medication. Thirty of these people report they have a runny nose. What is the relative risk of having a runny nose after taking the medication?



Click Your Answer Below


Would you like to access teaching points and more information on this topic?

Improve Content - Become an Author or Editor and get free access to the entire database, free eBooks, as well as free CME/CE as it becomes available. If interested, please click on "Sign Up" to register.

Purchase- Want immediate access to questions, answers, and teaching points? They can be purchased above at Apps and eBooks.


Sign Up
A physician finds that 5% of her patients who had the influenza vaccination report having influenza symptoms during the year; whereas, 10% of her patients who did not have the influenza vaccination report suffering from influenza symptoms during the year. For this physician's patients, what is the relative risk of having influenza symptoms after receiving the influenza vaccination?



Click Your Answer Below


Would you like to access teaching points and more information on this topic?

Improve Content - Become an Author or Editor and get free access to the entire database, free eBooks, as well as free CME/CE as it becomes available. If interested, please click on "Sign Up" to register.

Purchase- Want immediate access to questions, answers, and teaching points? They can be purchased above at Apps and eBooks.


Sign Up

Relative Risk - References

References

Understanding relative risk, odds ratio, and related terms: as simple as it can get., Andrade C,, The Journal of clinical psychiatry, 2015 Jul     [PubMed]
Bodemer N,Meder B,Gigerenzer G, Communicating Relative Risk Changes with Baseline Risk: Presentation Format and Numeracy Matter. Medical decision making : an international journal of the Society for Medical Decision Making. 2014 Jul;     [PubMed]
Simon SD, Understanding the odds ratio and the relative risk. Journal of andrology. 2001 Jul-Aug;     [PubMed]
Dupont WD,Plummer WD Jr, Understanding the relationship between relative and absolute risk. Cancer. 1996 Jun 1;     [PubMed]
Ranganathan P,Pramesh CS,Aggarwal R, Common pitfalls in statistical analysis: Absolute risk reduction, relative risk reduction, and number needed to treat. Perspectives in clinical research. 2016 Jan-Mar;     [PubMed]

Disclaimer

The intent of StatPearls is to provide practice questions and explanations to assist you in identifying and resolving knowledge deficits. These questions and explanations are not intended to be a source of the knowledge base of all of medicine, nor is it intended to be a board or certification review of Nurse-Calculations. The authors or editors do not warrant the information is complete or accurate. The reader is encouraged to verify each answer and explanation in several references. All drug indications and dosages should be verified before administration.

StatPearls offers the most comprehensive database of free multiple-choice questions with explanations and short review chapters ever developed. This system helps physicians, medical students, dentists, nurses, pharmacists, and allied health professionals identify education deficits and learn new concepts. StatPearls is not a board or certification review system for Nurse-Calculations, it is a learning system that you can use to help improve your knowledge base of medicine for life-long learning. StatPearls will help you identify your weaknesses so that when you are ready to study for a board or certification exam in Nurse-Calculations, you will already be prepared.

Our content is updated continuously through a multi-step peer review process that will help you be prepared and review for a thorough knowledge of Nurse-Calculations. When it is time for the Nurse-Calculations board and certification exam, you will already be ready. Besides online study quizzes, we also publish our peer-reviewed content in eBooks and mobile Apps. We also offer inexpensive CME/CE, so our content can be used to attain education credits while you study Nurse-Calculations.