Odds ratio and relative risk

Odds ratio and relative risk

In statistics, at times we want to evaluate the association between variables. This topic which evaluates the association between variables, is referred to as the measures of association. It refers to a wide array of coefficients that gauges the strength or weakness of an association. Even though the measures of association is a statistical term, it finds applications in fields such as epidemiology where they are used to quantify the relationship between various groups. The measure of association can be determined by statistical analyses such as correlation and regression coefficient, but the data available for analysis determines the method used to measure association. There are different methods, but there are two, which are easily confused by students, which we will address in this article. They are the odds ratio and relative risk.  After understanding what each of the two mean, we will show you how to get the odds ratio relative risk assignment help or measures of association assignment help.

Relative risk

We first start with the relative risk ratio; then we shall proceed to the odds ratio. Relative risk is a measure of association normally used for categorical data in epidemiology. It normally quantifies the association between two groups in the study, I.e. the one exposed and the unexposed.  In calculating the relative risk ratio, we divide the ratio of the exposed group in the study by the ratio of the unexposed group in the study. Let us take an example of a study that was studying the likelihood of developing lung cancer between two groups, i.e. smokers and nonsmokers. Assuming the research found that 4 out of 100 smokers developed lung cancer while 1 out of 100 nonsmokers developed lung cancer. Therefore the relative risk ratio is calculated as (4/100)/ (1/100) = 4

From the above analogy, it is evident calculating the relative risk requires us to know the level of the exposure of the individuals who were exposed and unexposed. Simply, it compares the risk of an event in two groups. Here is the relative risk formula.

RR= the ratio of the exposed/ the ratio of the unexposed

Odds ratio.

The odds ratio measures the association between variables and is commonly applied in epidemiology studies.  What makes it easy to confuse the two?   The odds ratio gives the odds of the likelihood of occurrence of a particular outcome in an exposure.

The formula for calculating the odds ratio is somehow akin to the relative risk formula and is given by

Exposed individuals= number exposed in category A/ number exposed in category B

Unexposed individuals= number unexposed in category A/number unexposed in category B

Odds ratio = exposed individuals / unexposed individuals.

For the above example, we calculate the odds ratio as follows

Odds ratio = (4/1)/(100/100) =4

As can be seen even from the formula itself, the two look somewhat similar. They even yield the same result.


Depending on the results given by the two, we can determine the association of the cohorts under study.

The interpretations of the two are equal. If the result from the two cases is equal to one, we infer that the exposure to smoke does not affect the outcome. For values greater or less than one, we conclude that the exposure increases or decreases the probability of the event under study occurring

Confidence interval.

The confidence interval is a statistical measure that reflects the level of certainty or uncertainty we have with the odds or relative ratio. However, it does not indicate the statistical significance of the study. A higher confidence interval indicates that we have a low level of confidence in the accuracy of the two association measures. On the other hand, a lower confidence interval implies a higher level of confidence in the accuracy of the odds ratio or relative ratio.  The 95% confidence interval is preferred in most studies. However, in case it’s not indicated, the general assumption is to use the 95% confidence interval.

If we are using the 95% confidence interval for both analyses, a value of one indicates a lack of association.

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