A risk ratio (RR), also called relative risk, compares the risk of a health event (disease, injury, risk factor, or death) among one group with the risk among another group It does so by dividing the risk (incidence proportion, attack rate) in group 1 by the risk (incidence proportion, attack rate) in group 2Odds ratio and relative riskRef=reference category Table A PORs are reciprocals of each other and pvalues are the same regardless of which outcome (yes or no) is modelled
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Odd ratio and relative risk calculation-USE OF ODDS RATIO odds ratio gives an indication of the strength of association between groups commonly used in metaanalysis;コレクション odds ratio vs relative risk formula Odd ratio and relative risk calculation • risk and relative risk or • odds and odds ratio Risks and odds Risks and odds Risks A proportion Numerator / Denominator Odds A ratio Numerator / (Denominator Numerator) 2 Two by two table Outcome event Total Yes No Experimental group a b
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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 confidence intervals 26 , 32 ,The probability of PONV with no Drug X is 40/100 or 040 Therefore, the relative risk for PONV with Drug X vs PONV without Drug X is 0/040 = 05 Odds ratios are used instead of relative risk for casecontrol studies To be able to calculate relative risk, we compare the risks of outcome in different groupsOR 1 − risk ratio In the first formula, the numerator (risk among unvaccinated − risk among vaccinated) is sometimes called the risk difference or excess risk Vaccine efficacy/effectiveness is interpreted as the proportionate reduction in disease among the vaccinated group
Odds ratios work the same An odds ratio of 108 will give you an 8% increase in the odds at any value of X Likewise, the difference in the probability (or the odds) depends on the value of X So if you do decide to report the increase in probability at different values of X, you'll have to do it at low, medium, and high values of XWhere RR is the relative risk, OR is the odds ratio, and p is the control event rate, which leads to the following OR = ((1 p) * RR) / (1 RR * p) Thus, for instance, a RR of with a p of 01 would lead to an OR of 225, whereas if p increases to 02 it would lead to an OR of 267If the relative risk equals 1, then factor is not associated with the outcome Another statistic similar to relative risk and often used by epidemiologists is the odds ratio a/b c/d When the difference in incidence or prevalence rate of an outcome is very small, the odds ratio and the relative risk yield similar results, but when the
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 nonLet us now look at the relation between the relative risk and the odds ratio (Zhang and Yu, 1998) OR= ˇ 1 1 1ˇ 1 ˇ 2 1 ˇ 2 = ˇ ˇ 2 1 2 1 1 = RR 2 1 (21) From this we see that OR is always further away from 1 than RR But, more importantly, we see that the odds ratio is close to the relative risk if probabilities of the outcome are small (Davies et al, 1998) Relative measures of effect are risk ratio (ie the ratio between two incidence proportions), incidence rate ratio (the ratio between two incidence rates), and OR (the ratio between two odds) The risk difference is an absolute measure of effect (ie the risk of the outcome in exposed individuals minus the risk of the same outcome in unexposed)
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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 riskIn a control group The odds ratio (OR) is the odds of an event in an experimental group relative to that in a control group An RR or OR of 100 indicates that the risk is comparable in the two groups A value greater than 100 indicates increased risk;Relative Risk (RR) is a ratio of probabilities or put another way it is one probability divided by another Odds Ratio (OR) is a ratio or proportion of odds I just remember that odds ratio is a ratio of odds and probability isn't a ratio of odds (AKA it is the other option) Relative Risk = Probability / Probability
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The homemade video abstract on the BMJ website shows you the difference between odds and risk, and how one odds ratio can mean several different relative risks (RRs), depending on the risk in one of the groups Unfortunately, in some situations, you just have to get an OR, notably logistic regression and retrospective casecontrol studies If the relative risk is 1, the tutoring made no difference at all If it's above 1, then the tutored group actually had a higher risk of failing than the controls Odds Ratio The odds ratio is the ratio of the odds of an event in the Treatment group to the odds of an event in the control groupRelative Risk and Odds Ratio The relative risk (RR) is the probability that a member of an exposed group will develop a disease relative to the probability that a member of an unexposed group will develop that same disease RR = P(diseasejexposed) P(diseasejunexposed) If an event takes place with probability p, the odds in favor of the event
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Must be used in casecontrol studies rather than relative risk (RR) as there is no information on the numbers of all exposed and nonexposed;As 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% = 01% x 10), more than 10 times higher Risk ratios, odds ratios, and hazard ratios are three ubiquitous statistical measures in clinical research, yet are often misused or misunderstood in their interpretation of a study's results A 01 paper looking at the use of odds ratios in obstetrics and gynecology research reported 26% of studies (N = 151) misinterpreted odds ratios as risk ratios , while a
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The odds ratio is the ratio of two odds ODDS RATIO Odds Ratio = Odds of Event A / Odds of Event B For example, we could calculate the odds ratio between picking a red ball and a green ball The probability of picking a red ball is 4/5 = 08 The odds of picking a red ball are (08) / 1(08) = 08 / 02 = 4 The odds ratio for picking a redThe quote surely just means to say that the odds ratio is a relative risk measure rather than an estimate of the relative risk, which as already point out is only approximately the case in cohort studies/randomized trials for very low proportions By relative risk measure I mean something that is given relative to some comparison group in a way that the absolute difference depends on theThe odds ratio ((a/c)/(b/d)) looks at the likelihood of an outcome in relation to a characteristic factor In epidemiological terms, the odds ratio is used as a point estimate of the relative risk in retrospective studies Odds ratio is the key statistic for most casecontrol studies
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