All Answers (17)
 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 crosssectional and casecontrol 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 samplebased estimate of that ratio= [A/(1A)]/[B/(1B)].
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 nonaffected 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 Casecontrol 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 RelativeRisk, 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.biochemiamedica.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, AnaMaria Simundic
Biochemia Medica, Editorinchief  And another very nice article on odds ratio... (from the same author)
 What`s the formula for the odds ratio to do with the rarity of the outcome studied?
 Do you mean Peto odds ratio? http://www.mrcbsu.cam.ac.uk/cochrane/handbook/chapter_9/9_4_4_2_peto_odds_ratio_method.htm
 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 :(
 Sometimes only a contact with the author may help dispel doubts...
 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.
 ...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 nonexposed 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.  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 ???

RR is for the higher probabilities and OR is for the smaller one to show an association between events

Also 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

Chapter 5 in Joe Hilbe's book Logistic Regression Models provides one of the best explanations on this topic.
 Views 115639
 Followers 50
 Answers 17
Popular Answers