Dear Mahmoud,

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)].

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

Applying Concept of Odds

 So, the odds of having the disease is the ratio of the probability that the disease will occur to the probability that the disease will not occur

Or, the odds of having the disease can be calculated as the number of people with the disease divided by the number of people without the disease

[Note: in the exposure-disease 2x2 table, the odds of having a disease in the exposed group is the same as the odds that an exposed person develops the disease]

Odds ratio is the ratio of the odds of disease in the exposed to the odds of disease in the non-exposed

OR = odds that an exposed person develops the disease / odds that a non - exposed person develops the disease

Odds ratio can be calculated in a cohort study and in a case control study

− The exposure odds ratio is equal to the disease odds ratio

Relative risk can only be calculated in a cohort study

When Is Odds Ratio a Good Estimate of Relative Risk?

When the “cases” studied are representative of all people with the disease in the population from which the cases were drawn, with regards to history of the exposure

When the “controls” studied are representative of all people without the disease in the population from which the cases were drawn, with regards to history of  exposure

When the disease being studied is not a frequent one

Interpreting Odds Ratio of a Disease

If OR = 1

− Exposure is not related to disease

− No association; independent

If OR > 1

− Exposure is positively related to disease

− Positive association; ? causal

If OR < 1

− Exposure is negatively related to disease

− Negative association; ? protective

Relative Risk or Risk Ratio

Relative risk (RR) = Risk in exposed / Risk in non-exposed

Interpreting Relative Risk of a Disease

If RR = 1

− Risk in exposed = Risk in non-exposed

− No association

If RR > 1

− Risk in exposed > Risk in non-exposed

− Positive association; ? causal

If RR < 1

− Risk in exposed < Risk in non-exposed

− Negative association; ? protective

n medical literature, the relative risk of an outcome is often described as a risk ratio (the probability of an event occurring in an exposed group divided by the probability in a non-exposed group). Certain types of trial designs, however, report risk as an odds ratio. This format is commonly expressed in cohort studies using logistic regression. When the incidence of an outcome is low (

Please find the following link 

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2938757/

Dear Mohy,

An odds ratio (OR) is a measure of association between an exposure and an outcome. The OR represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure. Odds ratios are most commonly used in case-control studies, however they can also be used in cross-sectional and cohort study designs as well.

I fully agree with both answers. i just want to stress one point. For odds ratios computed from case-control studies a "rare disease condition" is often said to be a condition. "When the disease being studied is not a frequent one" says Rafik. In fact, the mathematical condition (easy to demonstrate) is that the prevalence has to be roughly under 10%. This is too stated by Rafik "When the incidence of an outcome is low (

Great and scholarly answers have already been given now we must learn.

Thank for all, all data that has been written are interesting

Hi everyone,

I am an epidemiologist now and I work with ratios a lot - but there was a point when had not worked with them much, and I had a lot of trouble getting the feel for them. When I teach, I give an example. I say let's say that student A and student B take a test, and they get different scores, but they don't tell me the scores. Instead, they only tell me 1) the result of dividing one score by the other score, and 2) whose score was divided by whose.

Then I tell them to imagine the students tell me the result of the division is 1.5, and student A's score is divided by student B's score. I tell them I immediately know that student A did better just because it is above 1. If it was 2, it means A did twice as better. 

Then I ask them what would happen if the result of the division was 1. They usually realize it means the two have the same score - but the problem is, we don't know if they both scored low, or they both scored high. We just know they did the same.

Then I point out that if the answer is less than 1, it means the person whose score is on the bottom had a bigger score. I explain that in epidemiology, we don't really know what the right score is a lot of the time, we just want to figure out who is worse off than who else. Hence, we take an indicator of bad health for population A and put it on top of a ratio, the same metric for population B and put it on the bottom, and if we get a number greater than 1, we intervene on A, if it's less than 1, we intervene on B, and if it is 1, we don;t target anyone for intervention.

I hope this helps with the interpretation.

-Monika

yes very good interpretations.

One more point to specify is odds is used over a sample statistics, ie when we donot know or are perhalps not knowing the baseline population. Odds have also popularized because of ease of calculation like in regression and in chi sqaure , the point of significance is often judged from odds, which is a ratio.

Risk is an estimate when the baseline population is under consideration .RR calls for more complicated statistics.

Thanks to every body, very intresting. I would like just to add somethings

1- As in descriptive statistique, when we work with sample, we have to express the confidence interval at 95%. So for both OR or RR, we have to calculate 95%CI. If this interval doesn't contain "1" then we can argue that the difference between case and control is significant. Otherwise it's not possible even if OR is different from 1.

2- Be carefull to the interpretation after OR and RR calculation. Statistic is good, but the relation between risk and event (outcome) should be logical and reasonnable (biologically possible). Think about confounding factors is important and valuable to avoid misunderstanding of phenomens. 

Mediha - you add *GREAT POINTS* about the interpretation.

Your second point is especially important - you are talking about "biologic plausibility" as a criterion for interpreting causality. I will link here to an online posting of the rest of Bradford Hills Criteria of Causation that I use with my students. This is a nice laundry list of considerations when trying to determine cause, or as you put it, the "relation between risk and event".

http://www.drabruzzi.com/hills_criteria_of_causation.htm

If in a study (cross sectional or prospective studies), among those exposed the number of those having the disease is a, the number of those without the disease is b, the total number of the "sample" of exposed is a+b. This total is an unknown fraction of the exposed population (sample fraction F1) if it is a representative saample. The same thing among the unexposed gives c,d (c+d) and a sample fraction F2. Then the proportion of diseased among the exposed is a/a+b), c/(c+d) among the unexposed. The Relative Risk is then the ratio of these 2 values [a/(a+b)]/[c/c+d)]. This might look complicated but is at the level of secondary school...

Now comes the "miracle". If a is mathematically small compared to b and c compared to d, then a+b is closed to b, c+d closed to d. Then the former formula is simplified as [a/b]/[c/d] which is ac/bd which is... the odds ratio.

If you make a 2x2 table, things will look easy (or easier).

I remind that the true measure of risk is the incidence density (case/person x time), and so, the proportion being used above are already approximates.

Good explanation

Hi, 

The explanation of the colleagues were so much detailed and complete. I want just to add, that in addition to calculation of OR or RR value, we have to validate with calculation of their Confidence interval (CI) or standard error (SE) and also with Chi square test. And we could argue if a result is significant or not, only if also chi square value is significant and SE > 1.

To say things simpler : OR is to estimate if a suspicious factor enhances the occurrence of a given disease  (ex., cigarettes enhance breast cancer). This risk estimator is always calculated in case control studies. It's the fraction= Exposition to the factor in case/Exposition to the factor in controls

RR is to estimate if the occurrence of a given disease is much important in exposed group to a given factor. It's = Incidence in exposed group/Incidence in non exposed group. (ex., the incidence of cervical cancer is higher in woman taking contraceptive pill).

Please, don't hesitate to ask more if it's unclear.

Best

The odds ratio is actually used when the outcome is categorical and it is obtained from a logistic regression not a linear. The RR is very straightforward to interpret. The odds are a bit more challenging to interpret.