Risk Ratios and Rate Ratios (Relative Risk) Measures of disease frequency can be compared by calculating their ratio Common terms to describe these ratios are risk ratio rate ratio relative risk relative rate Frequently, the term "relative risk" is used to encompass all of these These relative measures give an indication of the "strength RELATIVE RISK AND ODDS RATIO Risk and Odds just seemed the same to me for a long time Since then, I have come to understand to important difference Lets start with Relative Risk Relative Risk can be addressed by asking the following question How many times more likely is an "exposed" group to develop aFor 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

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Odds versus relative risk
Odds versus 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 B 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 audience



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Relative 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 riskOdds ratio and relative riskA rate ratio, ;
Subsequently, the term relative risk commonly refers to either the risk ratio or the odds ratio However, only under certain conditions does the odds ratio approximate the risk ratio Figure 1 shows that when the incidence of an outcome of interest in the study population is low (In the general medical literature, rate is often incorrectly used for prevalence measuresThe relative risk and the odds ratio are measures of association between exposure status and disease outcome in a population
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 programRelative 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 510 412,368 412,878The odds ratio and the relative risk will not always disagree by this much Large effects on groups with high initial risk seem to cause the most problems See Davies et al (1998) for some useful guidelines for when the odds ratio and relative risk are likely to differ When they do differ, the relative risk represents the typical interpretation



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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 Instead of reporting how many times the risk one group bears relative to the other, it reports how many times the odds one group bears to the other For most, this is a more difficult statistic to understand Risk is often a more intuitive concept than odds, and thus understanding relative risks is often preferred to understanding relative odds RELATIVE RISK AND ODDS RATIO An RR (or OR) more than 10 indicates an increase in risk (or odds) among the exposed compared to the unexposed, whereas a RR (or OR)




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A smaller proportion of the probiotic group developed diarrhoea associated with antibiotic use compared with the placebo group (7 (12%) v 19 (34%); A 1 to 4 odds means there are five possible outcomes If you are interested in the blue card, it happens once among those five outcomes, or % of the time Likewise, relative risk makes a lot of sense The relative risk of picking a blue card in group A compared to group B is 1/3 or 033 We can understand that by looking at the pictureEven an odds ratio;



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The relative risk is confused by some with the odds ratio and absolute risk Relative risk is the ratio of the probability of an event occurring with an exposure versus the probability of the event occurring without the exposure Thus to calculate the relative risk, we must know the exposure status of all individuals (either exposed or notCancer by % (ie the relative risk is 12) Lung cancer has a baseline incidence of 3% per year (in the nonexposed group) Suppose as well that baseline incidence in obese individuals is 1/3 less (ie 1%/yr), and the relative risk associated with the exposure is also 12 You follow up 1000 nonobese and 1000 obese subjects with the exposure,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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RR Relative risk or RR is very common in the literature, but may represent a 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 groupThe odds ratio (OR) is a ratio of 2 numbers, like the relative risk we have 3 options OR = 1 The odds in the first group are the same as those in the second So no evidence that drinking wine can either OR > 1 The odds of having the disease in the exposed group are




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Research Statistics Basics Contents 1 Basic Concepts 2 References Basic Concepts Null Hypothesis The Hypothesis That The Independent Variable Has No Effect On The Dependent Variable For Example Steroids Do Not Improve Outcomes In Ards Would Be
For example, a relative risk of 15 would suggest a 50% increase in risk, whereas a relative risk of 05 would suggest a 50% decrease in risk Odds ratios The main difference between this and the other two measures is that there is no way of including aOdds 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 helpful9222 Measures of relative effect the risk ratio and odds ratio Measures of relative effect express the outcome in one group relative to that in the other The risk ratio (or relative risk) is the ratio of the risk of an event in the two groups, whereas the odds ratio is the ratio of the odds of an event (see Box 92a)For both measures a value of 1 indicates that the estimated effects




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Risk vs odds The terms 'risk' and 'odds' are often used interchangeably but they actually have quite different implications and are calculated in different ways Odds is a concept that is very familiar to gamblers It is a ratio of probability that a particular event will occur and can be any number between zero and infinity 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 calculated The odds ratio (OR) is the ratio of the odds of cancer in smokers to the odds of cancer in nonsmokers OR = (a/b)/ (c/d) = (ad)/ (bc) The risk ratio (RR), also called the relative risk, is the ratio of the probability of cancer in smokers to the probability of cancer in nonsmokers Given that you know a, b, c, and d, you can compute either of




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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 distinctionRelative risk 036, 95% confidence interval 017 to 079) When adjusted using logistic regression to control for other factors, the effects of the probiotic drink in reducing antibiotic associated diarrhoea remained (oddsA prevalence ratio, or ;




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The relative risk is best estimated using a population sample, but if the rare disease assumption holds, the odds ratio is a good approximation to the relative risk — the odds is p / (1 − p), so when p moves towards zero, 1 − p moves towards 1, meaning that the odds approaches the risk, and the odds ratio approaches the relative risk A 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 confidenceBoth 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



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We are 95% confident that the true odds ratio is between 185 and 2394 The null value is 1, and because this confidence interval does not include 1, the result indicates a statistically significant difference in the odds of breast cancer women with versus low DDT exposure Note that an odds ratio is a good estimate of the risk ratio when the 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 aAbout Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How works Test new features Press Copyright Contact us Creators




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Portantly, 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 outcomeThe 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 variableOdds 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 used




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There can be substantial difference in the association of a risk factor with prevalent disease versus ; Relative Risk Ratio and Odds Ratio , 500 pm The 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



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