A terminology problem odds ratio versus odds Author William Gould, StataCorp James Hardin, StataCorp Unfortunately, the language used to describe statistical terms is not used uniformly across fields One example of this is odds and odds ratio Economists especially refer to what others call the odds as the odds ratio Below, we will be careful to define our terms Proof thatWhen 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 riskFor instance, a relative risk of 70% corresponds to an odds ratio of 07/(107)=233 however, it is clearer to say to the layman that a certain risk factor "increases the probability of a disease by 70%" (relative risk) rather than that it "increases the probability of the disease by an odds ratio

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Odds ratio versus relative risk interpretation
Odds ratio versus relative risk interpretation- · L'Odds Ratio (OR) est le rapport des cotes d'exposition Cette notion de cote est semblable à celle utilisée pour les paris sportifs Dans notre exemple la cote chez les personnes exposées est de 30 contre 70 Chez les non exposés, cette cote est de 10 pour 90 Ainsi l'OR est égal à (30/70)/(10/90) = 39 · 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 At the start of the school year they impose the new



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Common pitfalls in statistical analysis Odds versus risk In biomedical research, we are often interested in quantifying the relationship between an exposure and an outcome "Odds" and "Risk" are the most common terms which are used as measures of association between variables · 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 size Note that the choice is only for prospective studies were the distinction becomes important in cases of medium to highAs an example, an odds ratio of 11 would suggest a 10% increase in
· After converting the odds ratio to a risk ratio, the actual risk is 14 (mortality is 14 times more likely in patients with ICU delirium compared to those without ICU delirium) Because the incidence rate in the nondelirium group is high, the odds ratio exaggerates the true risk demonstrated in the study · Odds Ratios Versus Relative Risk Published on December 14, 15 by Howard Herrell, MD Many great things have been written about the difference between Odds Ratios (OR) and Relative Risks (RR) Every medical student at some point has been taught the difference Yet these statistical terms are confused and misused every day in both the writing of and the · Risk ratio = ratio of 2 cumulative incidence estimates = relative risk Since all of the measures are ratios, either of probabilities or of odds, it is clearer and simpler to use the word ratio in describing each type
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 to expected results, putting the onus on the researcher to justify them Similarly, you should find that increasing the incidence will increase the odds ratioWhen events are common, as is often the case in clinical trials, the differences between odds and risks are large For example, a risk of 05 is equivalent to an odds of 1;If risk was the same in both groups, the odds would be equal A comparison of odds, the odds ratio, might then make sense OR= ˇ 1 1 ˇ 1 ˇ 2 1 ˇ 2 Odds ratio for the Titanic example is OR= 376 037 = 1016 This is very different from the relative risk


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Neither the risk ratio nor the odds ratio can be calculated for a study if there are no events in the control group This is because, as can be seen from the formulae in Box 92a, we would be trying to divide by zero The odds ratio also cannot be calculated if everybody in the intervention group experiences an event In these situations, and others where standard errors cannot be computedAnd a risk of 095 is equivalent to odds of 19StATS Odds ratio versus relative risk (created by ) Dear Professor Mean There is some confusion about the use of the odds ratio versus the relative risk Can you explain the difference between these two numbers?



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OR = odds ratio;In fact, the odds ratio has much more common use in statistics, since logistic regression, often associated with clinical trials, works with the log of the odds ratio, not relative risk Because the (natural log of the) odds of a record is estimated as a linear function of the explanatory variables, the estimated odds ratio for 70yearolds and 60yearolds associated with the type of · Before we look at odds and risk ratios, let's be clear on what odds and probabilities are (this couple of paragraphs added on August 18) Using binomial versus quasibinomial does make a difference to confidence intervals, but in our current case it's not material The confidence intervals at least contain the correct values;



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This implausible scenario is shown in Table 5, where collapsed counts for low (or high) risk subjects only produce a 2 × 2 table with an odds ratios of 400The relative risk and the odds ratio are measures of association between exposure status and disease outcome in a population Relative risk In epidemiology, relative risk (RR) can give us insights in how much more likely an exposed group is to develop a certain disease in comparison to a nonexposed group Once we know the exposure and disease status of a research population,Although the point estimate is biased



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The 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 group · Odds ratio (OR) and risk ratio (RR) are two commonly used measures of association reported in research studies In crosssectional studies, the odds ratio is also referred to as the prevalence odds ratio (POR) when prevalent cases are included, and, instead of the RR, the prevalence ratio (PR) is calculated However, it should be noted that, although, mathematical · If we go a step further, we can calculate the ratio between the two risks, called relative risk or risk ratio (RR), which indicates how much more likely is the occurrence of the event in one group compared with the other group Meanwhile, the odds represents a quite different concept The odds indicates how much more likely is an event to occur than not to



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