From WHO Basic Epidemiology:
http://whqlibdoc.who.int/publications/2006/9241547073_eng.pdf
"The odds ratio is very similar to the risk ratio, particularly if a disease is rare. For the odds ratio to be a good approximation, the cases and controls must be representative of the general population with respect to exposure.
However, because the incidence of disease is unknown, the absolute risk can not be calculated. An odds ratio should be accompanied by the confidence interval observed around the point estimate".
A relative risk is much easier to interpret and makes much more sense to the layman - e.g. a relative risk of 7.0 means that the affected group has seven times the risk of a non-affected group. Most people can grasp this concept fairly easily.
An odds ratio (the ratio of the relative odds of the disease occurring in Group A compared to it occurring in Group B) is more complex conceptually, but has some statistical advantages over the relative risk - essentially it's more versatile.
The general rule though is that if the prevalence of the disease is <10% or so, the relative risk and the odds ratio will be approximately the same. The rarer the disease, the closer the approximation.
If it is statistically sound to do so, it's generally safer, easier and less open to misinterpretation if you use the relative risk, especially if dealing with a less prevalent disease outcome.
This is the simple answer anyway.

An odds ratio is simply an association. That is to say what are the "odds" of having one condition or exposure if you have another. There is no implication of temporality that one condition came before another, just that the two conditions are statistically significantly related. Odds ratios can be calculated from cross-sectional and case-control study designs. Relative risk is generally considered as the risk of developing one condition if you have the exposure as compared (relative to) another group of differing exposure. Commonly relative risk demonstrates temporality and therefore fulfills the required A.B. Hill criteria for causation. Relative risks can be calculated from prospective and retrospective cohort studies, as well as randomized controlled trials. Therefore relative risk calculations often carry stronger implications for causation than odds ratios.

When two groups are under study or observation, you can use two measures to describe the comparative likelihood of an event happening. These two measures are the odds ratio and relative risk. Both are two different statistical concepts, although so much related to each other.
1. Odds Ratio It is defined as the ratio of the odds of an event occurring in one group to the odds of it occurring in another group or to a sample-based estimate of that ratio= [A/(1-A)]/[B/(1-B)].
2. Relative risk (RR) is the risk of an event (or of developing a disease) relative to exposure=A/B

From WHO Basic Epidemiology:
http://whqlibdoc.who.int/publications/2006/9241547073_eng.pdf
"The odds ratio is very similar to the risk ratio, particularly if a disease is rare. For the odds ratio to be a good approximation, the cases and controls must be representative of the general population with respect to exposure.
However, because the incidence of disease is unknown, the absolute risk can not be calculated. An odds ratio should be accompanied by the confidence interval observed around the point estimate".
A relative risk is much easier to interpret and makes much more sense to the layman - e.g. a relative risk of 7.0 means that the affected group has seven times the risk of a non-affected group. Most people can grasp this concept fairly easily.
An odds ratio (the ratio of the relative odds of the disease occurring in Group A compared to it occurring in Group B) is more complex conceptually, but has some statistical advantages over the relative risk - essentially it's more versatile.
The general rule though is that if the prevalence of the disease is <10% or so, the relative risk and the odds ratio will be approximately the same. The rarer the disease, the closer the approximation.
If it is statistically sound to do so, it's generally safer, easier and less open to misinterpretation if you use the relative risk, especially if dealing with a less prevalent disease outcome.
This is the simple answer anyway.

I do agree with the answers provided by Matthew, Fahmi and Simon. They have very well explained the difference between Odds ratio and Relative risk. To my understanding about these factors of association, i would like to add one thing also that is TIME. Consideration of time in conceptual framework for study design and estimation of factor of association is also needed. For example in case of OR, estimated for Case-control study, we do not know which one of either factor (risk or exposure factor/variable)or event (disease/outcome/death) preceded the another. Time remain silent as far as the occurrence of either exposure or event is considered. So OR becomes a mere estimate of Odds of occurrence of event among exposed group compared to unexposed group.
Where as in case of Relative-Risk, estimated under Cohort study, Time is considered in conceptual framework of study design. For example in Prospective Cohort study a cohort is followed over a period of TIME for occurrence of event and risk of occurrence of event is considered among exposed in comparison to those unexposed in same cohort. In other study design, retrospective cohort, Cohort is traced back in TIME and occurrence of event is analyzed in prospective time. Advantage of the retrospective cohort study is that we do not need to follow up the cohort in prospective time, but the retrospective data is required to estimate RR. In both design of cohort studies for estimating the RR, a cohort is followed up in time for occurrence of event and risk of occurrence of such event is compared between exposed and unexposed. In such design we ensure exposure precede the event, that's why ratio of occurrence becomes relative risk of occurrence of event among exposed.

Others have provided very nice replies. Nothing to add.
I attach a simple article from the journal Biochemia Medica (http://www.biochemia-medica.com/) on risk reduction statistics. I believe this might help you and other researchers who have similar dilemmas.
Biochemia Medica publishes short educational articles on some very simple topics in biostatistics in every journal issue, within the section Lessons in biostatistics. Lessons are intended for laboratory medicine professionals (and other scientists in biomedicine) with little or almost no basic knowledge in biostatsitcs.
Journal is indexed in Medline, IF (for 2012) is 1.873
Hope this helps!
Kind regards, Ana-Maria Simundic
Biochemia Medica, Editor-in-chief

Has anyone ever heard (read) the sentence " statisticaal analysis was by cond log regression which accounted for the matched design and gave odds ratio estimates of relative risks", ?? Now try making me make sense of this !! ( Stuck in a labyrinth of mind numbing articles for a systematic review :(

Oct 18, 2013

Krzysztof Lach · Fundació Clínic per a la Recerca Biomèdica

Sometimes only a contact with the author may help dispel doubts...

Oct 21, 2013

Azubuike Victor Chukwuka · National Environmental Standards and Regulations Enforcement Agency (NESREA)

More crucial to the interpretation of logistic regression is the value of the odds ratio which is an indicator of the change in odds resulting from a unit change in the predictor. As such, it is similar to the b coefficient in logistic regression but easier to understand (because it doesn’t require a logarithmic transformation). When the predictor variable is categorical the odds ratio is easier to explain, so imagine we had a simple example in which we were trying to predict whether or not someone got pregnant from whether or not they used a condom last time they made love. Thus the odds of an event occurring are defined as the probability of an event occurring divided by the probability of that event not occurring.

Oct 24, 2013

Azubuike Victor Chukwuka · National Environmental Standards and Regulations Enforcement Agency (NESREA)

...Relative risk on the other hand can be described as a measure of the association between exposure to a particular factor and risk of a certain outcome, calculated as
relative risk =incidence rate among exposed/ incidence rate among non-exposed Thus a relative risk of 5, for example, means that an exposed person is 5 times as likely to have the disease than one who is not exposed. Relative risk does not measurethe probability that someone with the factor will develop the disease.

Oct 24, 2013

Monah Zealia · University of the West of England, Bristol

If odds ratio is used in case control studies and relative risk in cohort; generally it means odds ratio assesses effect based on the disease whereas relative risk does based on exposure ???

Chapter 5 in Joe Hilbe's book Logistic Regression Models provides one of the best explanations on this topic.

Apr 24, 2015

Seyi Ajao · The Federal Polytechnic, Ado-Ekiti, Nigeria.

odd ratio (OR) which is a measure of the strength of the association between risk factor (e.g. smoking) and outcome (e.g cancer). Odds ratio is closely related to relative risk.

Risk Ratio is the same as Relative Risk

Risk - Risk is the probability that an event will happen latter

therefore Relative risk = no of events happened / Total no of risk

Jul 29, 2015

Ritul Kamal · Indian Institute of Toxicology Research

Another point to add to this is that relative risk has a tendency to underestimate in case of common outcomes.

Odds Ratio approximates Risk Ratio only if incidence is low in both the exposed and the unexposed group … If risk of incidence is high in either or both exposed and unexposed, then Risk Ratio and Odds Ratio differ.

## Popular Answers

Simon John Wheeler· University of CambridgeAna-Maria Simundic· Klinička bolnica "Sveti Duh"## All Answers (21)

Matthew S Thiese· University of UtahFahmi Khan· Hamad Medical Corporation1. Odds Ratio It is defined as the ratio of the odds of an event occurring in one group to the odds of it occurring in another group or to a sample-based estimate of that ratio= [A/(1-A)]/[B/(1-B)].

2. Relative risk (RR) is the risk of an event (or of developing a disease) relative to exposure=A/B

Simon John Wheeler· University of CambridgePraveen Anand· Indian Council of Medical ResearchWhere as in case of Relative-Risk, estimated under Cohort study, Time is considered in conceptual framework of study design. For example in Prospective Cohort study a cohort is followed over a period of TIME for occurrence of event and risk of occurrence of event is considered among exposed in comparison to those unexposed in same cohort. In other study design, retrospective cohort, Cohort is traced back in TIME and occurrence of event is analyzed in prospective time. Advantage of the retrospective cohort study is that we do not need to follow up the cohort in prospective time, but the retrospective data is required to estimate RR. In both design of cohort studies for estimating the RR, a cohort is followed up in time for occurrence of event and risk of occurrence of such event is compared between exposed and unexposed. In such design we ensure exposure precede the event, that's why ratio of occurrence becomes relative risk of occurrence of event among exposed.

Ana-Maria Simundic· Klinička bolnica "Sveti Duh"I attach a simple article from the journal Biochemia Medica (http://www.biochemia-medica.com/) on risk reduction statistics. I believe this might help you and other researchers who have similar dilemmas.

Biochemia Medica publishes short educational articles on some very simple topics in biostatistics in every journal issue, within the section Lessons in biostatistics. Lessons are intended for laboratory medicine professionals (and other scientists in biomedicine) with little or almost no basic knowledge in biostatsitcs.

Journal is indexed in Medline, IF (for 2012) is 1.873

Hope this helps!

Kind regards, Ana-Maria Simundic

Biochemia Medica, Editor-in-chief

Ana-Maria Simundic· Klinička bolnica "Sveti Duh"Ricardo de Almeida Albuquerque· Centro Universitário Jorge AmadoKrzysztof Lach· Fundació Clínic per a la Recerca BiomèdicaZohaib Khan· Universität BremenKrzysztof Lach· Fundació Clínic per a la Recerca BiomèdicaAzubuike Victor Chukwuka· National Environmental Standards and Regulations Enforcement Agency (NESREA)Azubuike Victor Chukwuka· National Environmental Standards and Regulations Enforcement Agency (NESREA)relative risk =incidence rate among exposed/ incidence rate among non-exposed Thus a relative risk of 5, for example, means that an exposed person is 5 times as likely to have the disease than one who is not exposed. Relative risk does not measurethe probability that someone with the factor will develop the disease.

Monah Zealia· University of the West of England, BristolMadkour Aicha· University Mohammed V AgdalRR is for the higher probabilities and OR is for the smaller one to show an association between events

Krzysztof Lach· Fundació Clínic per a la Recerca BiomèdicaAlso according to Cochrane´s Handbook, when dealing with very rare frequencies of events in at least one of the groups (n=0) it is recommended to calculate odds ratio with Peto method http://handbook.cochrane.org/chapter_9/9_4_4_2_peto_odds_ratio_method.htm

James A. DiGabriele· Montclair State UniversityChapter 5 in Joe Hilbe's book Logistic Regression Models provides one of the best explanations on this topic.

Seyi Ajao· The Federal Polytechnic, Ado-Ekiti, Nigeria.odd ratio (OR) which is a measure of the strength of the association between risk factor (e.g. smoking) and outcome (e.g cancer). Odds ratio is closely related to relative risk.

Risk Ratio is the same as Relative Risk

Risk - Risk is the probability that an event will happen latter

therefore Relative risk = no of events happened / Total no of risk

Ritul Kamal· Indian Institute of Toxicology ResearchAnother point to add to this is that relative risk has a tendency to underestimate in case of common outcomes.

James A. DiGabriele· Montclair State UniversityOdds Ratio approximates Risk Ratio only if incidence is low in both the exposed and the unexposed group … If risk of incidence is high in either or both exposed and unexposed, then Risk Ratio and Odds Ratio differ.

Georgina Martin· Trinity College DublinWhat determines if incidence is high or low enough for RR or OR, is there a cut off point?

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