Sometimes, we see the log odds ratio instead of the odds ratio The log OR comparing women to men is log(144) = 036 The log OR comparing men to women is log(069) = 036 log OR > 0 increased risk log OR = 0 no difference in risk log OR < 0 decreased risk Odds Ratio 0 5 10 15 More on the Odds Ratio Log Odds Ratio4 2 0 2 4OR = odds ratio; The odds ratio is reported as 1 with a confidence interval of (144, 234) Like we did with relative risk, we could look at the lower boundary and make a statement such as "the odds of MI are at least 44% higher for subjects taking placebo than for subjects taking aspirin"
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When to use odds ratio versus risk ratio-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 groupA nonmemorization method of dealing with RR and OR*USMLE is a registered trademark of its respective holder I am in no way affiliated with itDisclaimer
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An odds ratio of 05 would mean that the exposed group has half, or 50%, of the odds of developing disease as the unexposed group In other words, the exposure is protective against disease Is odds ratio a measure of risk? An Odds Ratio (OR) then is simply the comparison of two odds, OR=Odds (A)/Odds (B) The Relative Risk (RR) is simply the comparison of two risks or probabilities, RR=Probability (A)/Probability (B) This is made more clear when the term is referred to as the Risk Ratio Let's look at this graphically Odds ratio vs relative risk 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
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 calculated on the same data and may come as a surprise to some readers who are accustomed of thinking of odds ratio as of relative risk (Greenland, 1987)People often (I think quite understandably) findCollapsibility Odds Ratios versus Risk Ratios It is known that odds ratios enjoy a certain symmetry For example, the odds ratio of outcome Y is the inverse of the odds ratio of outcome ¬ Y Risk ratios, on the other hand, do not enjoy this symmetry However, risk ratios have the property of collapsibility Odds ratio vs risk ratio You know the difference between risk and odds A risk is the proportion of subjects with an event in a total group of susceptible subjects Thus, we can calculate the risk of having a heart attack among smokers (infarcted smokers divided by the total number of smokers) and among nonsmokers (the same, but with nonsmokers)
Cases 1 and 4 have the same absolute risk reduction, NNT, and odds ratios, but very different relative risk, relative risk reduction, and risk at baseline Real Example The following example 18 is a prospective study, which compares the incidences of dyskinesia after ropinirole (ROP) or levodopa (LD) in patients with early Parkinson's disease The odds ratio comparing the new treatment to the old treatment is then simply the correspond ratio of odds (01/09) / (02/08) = 0111 / 025 = 0444 (recurring) This means that the odds of a bad outcome if a patient takes the new treatment are 0444 that of the odds of a bad outcome if they take the existing treatment Relative Risk, Odds, and Fisher's exact test I) Relative Risk A) Simply, relative risk is the ratio of p 1/p 2 For instance, suppose we wanted to take another look at our Seat belt safety data from Florida Safety equipment Injury in use Fatal Nonfatal Total None 1,601 165,527 167,128 Seat belt 510 412,368 412,878Odds Ratio versus Relative Risk Odds ratio can be calculated in
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Odds Ratio Vs Relative Risk When two groups are under study or observation, you can use two measures to describe the comparative likelihood of an event happening These two measures are the odds ratio and relative risk Both are two different statistical concepts, although so much related to each otherWhen 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;Pute either the odds ratio or the relative risk to answer this question The odds ratio compares the relative odds of death in each group For women, the odds were exactly 2 to 1 against dying (154/308 05) For men, the odds were almost 5 to 1 in favor of death (709/142 4993) The odds ratio is 9986 (4993/05) There is a 10fold greater
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INTRODUCTION 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 calculatedRather the odds is threefold greater Interpretation of an OR must be in terms of odds, notAs an extreme example of the difference between risk ratio and odds ratio, if action A carries a risk of a negative outcome of 999% while action B has a risk of 990% the relative risk is approximately 1 while the odds ratio between A and B is 10 (1% =
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The 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,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 riskThe odds ratio should be used as an approximation to the relative risk of the event of interest when both of the following conditions are met The probability of the event of interest is small (
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Second, if you happen across these terms odds, Odds Ratio, risk, Relative Risk, probability, or terms that are based on them such as prevented fraction, then before you start comparing numbers or getting into the indepth discussion, do a quick review 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 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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And a risk of 095 is equivalent to odds of 19Odds Ratio versus Relative Risk Since it is a ratio of ratios, the odds ratio is very difficult to interpret The relative risk is easier to interpret, so the odds ratio alone is not very helpful However, there are certain commonly occurring situations in which the estimate of the relative risk is not very good, and the odds ratio can be usedThis video demonstrates how to calculate odds ratio and relative risk values using the statistical software program SPSSSPSS can be used to determine odds r
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The odds ratio supports clinical decisions by providing information on the odds of a particular outcome relative to the odds of another outcome In the endocarditis example, the risk (or odds) of dying if treated with the new drug is relative to the risk (odds) of dying if treated with the standard treatment antibiotic protocolA crude odds ratio can be converted to a crude risk ratio risk ratio = odds ratio/(1 − p0) (p0 × odds ratio), in which p0 is the outcome prevalence (risk) among the unexposed Some have applied this formula to an adjusted odds ratio to obtain an adjusted risk ratio 49 This method can produce biased risk ratios and incorrect confidenceRelative 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 ratio
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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 When adjusted using logistic regression to control for other factors, the effects of the probiotic drink in reducing antibiotic associated diarrhoea remained (odds ratio 025, 95% CI 007 to 085) The researchers concluded that consumption of the probiotic drink reduced the incidence of antibiotic associated diarrhoeaThe simple relative risk is 055 and the simple odds ratio is 025Clearly the probability of fathering a child is strongly dependent on a variety of demographic variables, especially age (the issue of marital status was dealt with by a separate analysis) The control group was 84 years older on average (435 years versus 351), showing the need to adjust for this variable
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R C = absolute risk in the unexposed group, given as a fraction (for example fill in 10% risk as 01) Confusion and exaggeration Odds ratios have often been confused with relative risk in medical literature For nonstatisticians, the odds ratio is a difficult concept to comprehend, and it gives a more impressive figure for The ratio of these is the risk ratio, a relative measure of association Risk Ratio = CI e /CI u = 090/058 = 155 Interpretation Smokers had 155 times the risk of respiratory disease compared to nonsmokers over an 18 year period of observation Using the same cumulative incidences we can calculate the risk difference, an absolute measure Odds and odds ratios rather than risk ratios are used in casecontrol studies because risks cannot be calculated However, odds and odds ratios can also used to display the results of cross sectional studies, cohort studies and randomized controlled trials The reason for this is that a commonly used regression model for binary (dichotomous) outcomes called logistic regression only allows the calculation of the odds ratio and not the risk ratio
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Odds ratios While risk reports the number of events of interest in relation to the total number of trials, odds report the number of events of interest in relation to the number of events not of interest Stated differently, it reports the number of events to noneventsOdds versus risk ratio Risk Ratio is often expressed as a factor and a whole positive number, such as " is times more likely" The difference between odds ratio and risk ratio While Risk Ratio is the probability of one thing divided by the probability of another (usually in a separated group), Odds Ratio is the odds of one event happeningA 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 calculated on the same data and may come as a surprise to some readers who are accustomed of thinking of odds ratio as of relative risk (Greenland, 1987)
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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 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 (TheOdds Ratio (OR) measures the association between an outcome and a treatment/exposure Or in other words, a comparison of an outcome given two different groups (exposure vs absence of exposure) OR is a comparison of two odds the odds of an outcome occurring given a treatment compared to the odds of the outcome occurring without the treatmentDecimal odds represent
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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 Note that an odds ratio is a good estimate of the risk ratio when the outcome occurs relatively infrequently (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)
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Odds ratio is similar to relative risk In the sheepskin trial the relative risk was 058 and the odds ratio was 054 For most clinical trials where the event rate is low, that is less than 10% of all participants have an event, the odds ratio and relative risk can be considered interchangeableThe odds ratio is a common measure of risk but its interpretation may be hazardous Odds is the number having the outcome divided by the number not having the outcome The risk or odds ratio is the risk or odds in the exposed group divided by the risk or odds in the control group A risk or odds ratio = 1 indicates no difference between the groups
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