Odds Ratio vs Relative Risk What's the Difference?Both the odds ratio and the relative risk compare the relative likelihood of an event occurring between two groups The relative risk is easier to interpret and is consistent with general intuition Some designs, however, allow only for the calculation of the odds ration Covariate adjustment is easier for an odds ratio The odds ratio will be greater than the relative risk if the relative risk is greater than one and less than the relative risk otherwise In the example above, if the adjusted odds ratio were interpreted as a relative risk, it would suggest that the risk of antibiotic associated diarrhoea is reduced by 75% for the intervention relative to the placebo group
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Odds vs relative risk-Since relative risk is a more intuitive measure of effectiveness, the distinction is important especially in cases of medium to high probabilities If action A carries a risk of 999% and action B a risk of 990% then the relative risk is just over 1, while the odds associated with action A are more than 10 times higher than the odds with BThe relative risk (RR) and the odds ratio (OR) are the two most widely used measures of association in epidemiology The direct computation of relative risks is
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Odds ratio relative risk Relative risk An odds ratio is a ratio of two odds Relative risk isThe absolute risk is the probability of an event in a sample or population of interest The relative risk (RR) is the risk of the event in an experimental group relative to that in a control group The odds ratio (OR) is the odds of an event in an experimental group relative to that in a control groupThe difference between odds ration and relative risk is that the relative risk is a ration of two ideal properties while the odds ratio is mainly concerned about the specific ratio of two different odds This is because, the relative risk is often used to refer the proportion of people with a particular risk factor who have that risk factor
When the disease is rare, the odds ratio will be a very good approximation of the relative risk The more common the disease, the larger is the gap between odds ratio and relative risk In our example above, p wine and p no_wine were 0009 and 0012 respectively, so the odds ratio was a good approximation of the relative risk OR = 0752 and RR = 075The Relative Risk Ratio and Odds Ratio are both used to measure the medical effect of a treatment or variable to which people are exposed The effect could be beneficial (from a therapy) or harmful (from a hazard) Risk is the number of those having the outcome of interest (death, infection, illness, etc) divided by the total number exposed to the treatmentRelative Risk Relative risk is a ratio of the risks of two groups In the example described above, it would be the risk of heart attack for a person in their current condition compared to the risk of heart attack if that person were in the normal ranges However, to truly interpret the severity of a relative risk we have to know the baseline risk
Risk is often a more intuitive concept than odds, and thus understanding relative risks is often preferred to understanding relative odds However, OR does not suffer from the same causal assumption limitations as RR, making it more widely applicablePortantly, we see that the odds ratio is close to the relative risk if probabilities of the outcome are small (Davies et al, 1998) And it is this fact that enables us, most of the time, to approximate the relative risk with the odds ratio Table 5 below illustrates the relationship between RR and OR for some probabilities of the outcomeRelative risk is the ratio of the risks for an event for the exposure group to the risks for the nonexposure group
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You may have noticed that the odds ratio and relative risk are very similar in this case This happens when the proportions being compared are both close to 0 Which one you decide to use is a matter of personal preference and perhaps your audienceThe relative risk (also known as risk ratio RR) is the ratio of risk of an event in one group (eg, exposed group) versus the risk of the event in the other group (eg, nonexposed group) The odds ratio (OR) is the ratio of odds of an event in one group The basic difference is that the odds ratio is a ratio of two odds (yep, it's that obvious) whereas the relative risk is a ratio of two probabilities (The relative risk is also called the risk ratio) Let's look at an example Relative Risk/Risk Ratio Suppose you have a school that wants to test out a new tutoring program
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Odds ratios and relative risks are interpreted in much the same way and if and are much less than and then the odds ratio will be almost the same as the relative risk In some sense the relative risk is a more intuitive measure of effect sizeOdds ratios (OR) are commonly reported in the medical literature as the measure of association between exposure and outcome However, it is relative risk that people more intuitively understand as a measure of association Relative risk can be directly determined in a cohort study by calculating a risk ratio (RR) Attack Rate (Risk) Attack rate for exposed = a ⁄ ab Attack rate for unexposed = c ⁄ cd For this example Risk of tuberculosis among East wing residents = 28 ⁄ 157 = 0178 = 178% Risk of tuberculosis among West wing residents = 4 ⁄ 137 = 0029 = 29% The risk ratio is simply the ratio of these two risks Risk ratio = 178 ⁄ 29 = 61
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If odds are stated as an A to B chance of winning then the probability of winning is given as P W = A / (A B) while the probability of losing is given as P L = B / (A B) What does Relative Risk tell you?2) Relative Risk and Odds Ratio for the nonobese Relative Risk and Odds Ratio for the obese 3) Overall, you can see that decreasing the baseline incidence will decrease the odds ratio (300 in those who are nonobese versus 129 in those who are obese) Obviously, these results run counter
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