Risk is the number of those having the outcome of interest (death, infection, illness, etc) divided by the total number exposed to the treatment Odds is the number having the outcome divided by the number not having the outcome Risk and risk ratios are more commonly used than odds and odds ratios in medicine as these are much more intuitive Risk describes the probability of an event occurring In medicine this is often an undesirable health outcome or adverse event Odds ratio = (A*D) / (B*C) The relative risk tells us the ratio of the probability of an event occurring in a treatment group to the probability of an event occurring in a control group It is calculated as Relative risk = A/ (AB) / C/ (CD) In short, here's the difference An odds ratio is a ratio of two odds
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Odds versus risk
Odds versus risk-Odds 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) 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 occur (p/ (1p))
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An odds ratio greater than 1 indicates that the disease more likely to occur in the group than the group Similarly, an odds ratio less than 1 indicates that the disease is less likely to occur in the group For example an odds ratio of 2 indicates that people from the group had twice the risk of having the disease as people from the groupRISK AND ODDS DEFINITIONS "Risk" refers to the probability of occurrence of an event or outcome Statistically, risk = chance of the outcome of interest/all possible outcomes The term "odds" is often used instead of risk "Odds" refers to the probability of occurrence of an event/probability of the event not occurring then the odds ratio is computed by taking the ratio of odds, where the odds in each group is computed as follows OR = (a/b) / (c/d) As with a risk ratio, the convention is to place the odds in the unexposed group in the denominator
That is one of the attractive features of the odds ratio — when the health outcome is uncommon, the odds ratio provides a reasonable approximation of the risk ratio Another attractive feature is that the odds ratio can be calculated with data from a casecontrol study, whereas neither a risk ratio nor a rate ratio can be calculated 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 programAnd a risk of 095 is equivalent to odds of 19
For instance, odds are a symmetric measure, meaning that while risk only examines outcomes given interventions, odds can also examine interventions given outcomes Thus, a study can be constructed where, rather than choosing trial groups and measuring outcomes, outcomes can be chosen, and other factors can be analyzedRather the odds is threefold greater Interpretation of an OR must be in terms of odds, not The odds ratio is a common measure of risk but its interpretation may be hazardous The risk ratio is a ratio of probabilities, which are themselves ratios The numerator of a probability is the number of cases with the outcome, and the denominator is the total number of cases
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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 In this article, which is the fourth in the series of common pitfalls in statistical analysis, we explain the meaning of risk and odds and the difference between the twoBMJ 14;348g1407 doi /bmjg1407 (Published 7 February 14) Page 1 of 2 Endgames ENDGAMES STATISTICAL QUESTION Relative risks versus odds ratios Philip Sedgwick reader in medical statistics and medical education Centre for Medical and Healthcare Education, St George's, University of London, London, UK Researchers investigated the effectiveness of a probiotic drink Risk Ratio vs Odds Ratio Whereas RR can be interpreted in a straightforward way, OR can not A RR of 3 means the risk of an outcome is increased threefold A RR of 05 means the risk is cut in half But an OR of 3 doesn't mean the risk is threefold;
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It turns out that odds ratio can be an approximation of the relative risk when the latter cannot be calculated For example In casecontrol studies when the risk of a disease cannot be knownWhen 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; For instance, odds are a symmetric measure, meaning that while risk only examines outcomes given interventions, odds can also examine interventions given outcomes Thus, a study can be constructed where, rather than choosing trial groups and measuring outcomes, outcomes can be chosen, and other factors can be analyzed
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