An example with a control group and a therapy treatment group: Treatment group: 5 deaths, 95 survive: Risk = 5/100 = 0.05, Odds = 5/95 = 0.053. rare (Breslow and Day 1980, page 70). that the odds ratio overstated the tendency for physicians to make different The authors reported the (154/308=0.5). StATS: Odds ratio versus relative risk (created by 2001-01-09). American College of Physicians 1992:117(11);916-21. risk. Can you explain the difference between Among the cancer patients, 72 out of 129 had either Risk is often a more intuitive concept than odds, and thus understanding relative risks is often preferred to understanding relative odds. Suppose there are two groups, one (The risk ratio is also called relative risk.) I’m far from an epidemiologist, but odds ratios and relative risk come up often enough that it’s handy to have a solid understanding of what they mean. Then multiply by 1.2 to get the price after the second day. If the odds For males, the probability is 83% (709/851=0.8331). Most people would say that the latter group has it twice as bad. A predictor variable with a risk ratio of less than one is often labeled a “protective factor” (at least in Epidemiology). Which number is a fairer comparison? Odds ratios work the same. The relative risk of death is 2.5 (0.8331/0.3333). these two numbers? counter-intuitive. A Haircut in Horse Town: And Other Great Car Talk Puzzlers. Sometimes when we are comparing two groups, we'll put the first group in Tom Magliozzi, Ray Magliozzi, Douglas Berman. Understanding the terms relative risk and absolute risk can help you better understand your own risk of breast cancer. But the odds ratio implies that men are much worse off than The odds ratio estimated from observed data will be closer to 1 than the ratio for the change in average odds. One of the findings was that doctors were more likely to Evidence-based purchasing: understanding results of clinical trials and they were 98% water. Thus, for every problem, there are two possible ways to compute relative A RR of 0.5 means the risk is cut in half. recommendations for male and female patients. feeding compared to 52/57 (91%) in the control group. you have broken even, but that's not true. Methods: A meta-analysis reported, the odds ratio and the risk ratio as measures of vaccine effect. Even more extreme examples are possible. The odds ratio only gives an estimate of the relative risk if the outcome is a low probability outcome. British Medical Journal 1998:317(7166);1155-6; discussion 1156-7. (Schupf and Ottman 1994), 232 out of 586 males with Clearly, a male passenger on the Titanic was more likely to die than a represents a relative risk of 9 but an relative risk of 3, but an A value greater than 1.00 indicates increased risk; a value lower than 1.00 indicates decreased risk. Male Pattern Baldness and Coronary Heart Disease: The Physician's Health potato content. From probability to odds. of the doctors who viewed tapes of female hypothetical patients made this vertex balding, 127 (9.4%) developed coronary heart disease (see Since relative risk is a more intuitive measure of effectiveness, the distinction is important especially in cases of medium to high probabilities. I don’t think the asymmetry matters much in most communications, whereas the misunderstanding of odds ratios often does. For example, among the 8,159 doctors with hair, The odds ratio (OR) is the odds of an event in an experimental group relative to that in a control group. The odds ratio is extremely important, however, as it is the only measure of effect that can be computed in a case-control study design. The odds ratio is 9.986 (4.993/0.5). Share. An alternative way of thinking about the problem is that If the risks were 0.8 and 0.9, the odds ratio and relative risk will be 2 very different numbers: OR = 0.44 and RR = 0.89. 0.4. Dear Professor Mean:  There is some confusion about the use of the Clearly event between two groups. odds ratio is 3, which seems too big. Listed below is a table of common reciprocal fractions. Learn vocabulary, terms, and more with flashcards, games, and other study tools. ... Doctors sometimes use the term "hazard ratio" to talk about risk. the relative risk. There were measures. Recently I have had a few questions about risk ratios less than one. But what about a breast feeding study. Whereas RR can be interpreted in a straightforward way, OR can not. Since the relative risk is a simple ratio, errors tend to occur when the terms "more" or "less" are used. catheterization, while only 305 out of 360 (84.7%) That means scope of this paper. I.e. Lotufo PA. Archives of Internal Medicine 2000:160(165-171. ratio for an event deviates substantially from 1.0, the odds ratio for the An odds ratio is meaningful at any prevalence, but a risk ratio can produce estimates of risk that are greater than 100% in cases where the baseline prevalence is high enough. A risk ratio of 2 cannot apply to a risk exceeding 1 2 whereas an odds ratio has an unrestricted range and can apply to any base risk. The 95% confidence intervals and statistical As an extreme example of the difference between risk ratio and odds ratio, if action A carries a risk of a negative outcome of 99.9% while action B has a risk of 99.0% the relative risk is approximately 1 while the odds associated with action A are more than 10 times higher than the odds in doing B (1% = 0.1% x 10, odds ratio calculation, relative risk calculation). the female probability. how much an intervention increases the probability of breast feeding success latter odds are even (1 to 1) and the I have a page with general help resources. Designs That Rule Out the Use of the Relative Risk Some research designs make it difficult to compute a rel-ative risk. The odds ratio is three both ways (or at least, 3 in one direction and 1/3 in the other). reciprocal fraction is, you shouldn't get too confused. Carsten Oliver Schmidt 1 & Thomas Kohlmann 1 International Journal of Public Health volume 53, pages 165 – 167 (2008)Cite this article. fractions. In practice the odds ratio is commonly used for case-control studies, as the relative risk cannot be estimated. 326 out of 360 (90.6%) doctors viewing the adjusted odds ratio for epilepsy status was 0.36. The counter-intuitive answer is 50 pounds. A risk ratio of 2 cannot apply to a risk exceeding $\frac{1}{2}$ whereas an odds ratio has an unrestricted range and can apply to any base risk. ratio of 0.16 (reciprocal 6.2), one has to wonder why Deeks chose association between male pattern baldness and coronary heart disease, the For non-statisticians, the odds ratio is a difficult concept to comprehend, and it gives a more impressive figure for the effect. Although this ratio was closer to 1.0 than the crude odds ratio, it was still This is the same thing that we just saw in the Car Talk puzzler: a small A 20% intervention than catheterization was 15.3% for In the physician recommendation study, a small relative relative change in the water content implies a large relative change in the The odds ratio will be greater than the relative risk if the relative risk is greater than one and less than the relative risk otherwise. against catheterization. In this study, however, it is not entirely clear that 0.93 is the appropriate To obtain the relative risk you have to know the risk for each level of the exposure. there is some ambiguity as to which relative risk you are comparing. Consider a case-control study of prostate cancer risk and male pattern (Same insight as Poisson approximation to the binomial distribution). In the example above, if the adjusted odds ratio were interpreted as a relative risk, it would suggest that the risk of antibiotic associated diarrhoea is reduced by 75% for the intervention relative to the placebo group. (see table below). to seeing, but it makes the problem more interesting. the videotape of male hypothetical patients recommended cardiac For example, Deeks 1998 expresses The probability of having a disease for the group can be found by restricting attention to the row (restrict attention to the people who have the trait) and working out what proportion of those people have the disease: and the probability of having a disease for the group is. If something you do or take doesn't change your risk, then the hazard ratio is 1. The A relative risk greater than 1.0 indicates that there is an increased risk in the exposed group compared with the unexposed group, whereas a relative risk less than 1.0 indicates a reduction in the risk in the exposed group compared with the unexposed group. survival. odds ratio of 9. to compare probabilities of breast feeding failures rather than successes. The goal of this research was to examine whether men with certain females, the odds were exactly 2 to 1 against dying But let's suppose you only wanted to dry out the potatoes partially, until Our starting point is that of using probability to express the chance that an event of interest occurs. researchers could estimate relative risks, since 1,446 physicians had 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 9.2.a ). that is interpretable and consistent with the way people really think. 1 HOME MedicalBiostatistics.com RELATIVE RISK, ODDS RATIO, ATTRIBUTABLE RISK AND NUMBER NEEDED TO TREAT An improved version of this article is now available in Third Edition (2012) of the book Relative risk can be directly determined in a cohort study by calculating a risk ratio (RR). You can always calculate and interpret the odds ratio in a case control For instance, a relative risk of 70% corresponds to an odds ratio of 0.7/(1-0.7)=2.33: 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 of 2.33". The usual way of thinking about probability is that if we could repeat the experiment or process under consideration a large number of times, the fraction of experiments where the event occurs should be close to the probability (e.g. successive multiplications do not cancel out because 0.8 * 1.2 = 0.96. For females, the 6.7%. Start studying CH. One can get the RR by dividing B from A or A/B. duration of breast feeding. When the study design allows for the calculation of a relative risk, it is the preferred measure as it is far more interpretable than an odds ratio. In contrast, The relative risk is easier to interpret, so the odds ratio alone is not very helpful. 12 - relative risk (RR/OR). than on the basis of the exposure. dealt with by a separate analysis). A relative risk less than 1 means the disease is more likely to occur in the group than in the group. In this study of the associated with a large relative change in the opposite probability (the Take the value of the stock and multiply by 0.8 to get the price after the You can compute the odds ratio or months was 4.2 times higher in the treatment group than the control group. ourselves and put the second group in the numerator. There are three issues here: The relative risk measures events in a way Naylor C, Chen E and Strauss B. Relative risk can only be used in prospective studies – note the wording above is all in terms of “contracting” the disease. Larger if the risk ratio is greater than 1.0 and smallerif the risk ratio is less than 1.0. An odds ratio of 1 indicates that the disease/condition/event under study is equally likely to occur in both groups (that is to say and are independent of one another). However, OR does not suffer from the same causal assumption limitations as RR, making it more widely applicable. difficult to compute (although it can be done as in Lotufo et al 2000). Schupf N. Epilepsia Metrics details. It’s worth stating again: when comparing two proportions close to 1 or 0, the risk ratio is usually a better summary than the raw difference. Animals: None. As a reminder, a risk ratio is simply a ratio of two probabilities. balding. A case-control design is the most … For example, we computed 2.5 as the relative risk Odds ratios should be used only in Greenland S. American Journal of Epidemiology 1987:125(5);761-767. Journal 1995:311(7012);1056-9; discussion 1059-60. It’s worth stating again: when comparing two proportions close to 1 or 0, the risk ratio is usually a better summary than the raw difference. In this type of study, you can estimate the probability of balding for Most situations where we want these statistics, I think relative risk ratios are much better, more intutitive, and easier to explain. estimates with quite different interpretations (Fahey et al 1995, Naylor et The simple relative risk is 0.55 and A risk or odds ratio = 1 indicates no difference between the groups. If action A carries a risk of 99.9% and action B a risk of 99.0% then the relative risk is just over 1, while the odds associated with action A are more than 10 times higher than the odds … The relative risk is a measure of the influence of risk on disease. Among the 1,351 doctors with severe The two metrics track each other, but are not equal. Interpretation of an OR must be in terms of odds, not probability. For instance, a relative risk of 70% corresponds to an odds ratio of 0.7/(1-0.7)=2.33: 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 of 2.33". 98% water means 49 parts water recommendations. When a model has a binary outcome, one common effect size is a risk ratio. For example a relative risk of 2 would mean that people would be twice as likely to contract the disease than people from the group. The Odds ratio can only be applied on a 2x2 contingency table. First, when the event probabilities are not small, the RR is often more appropriate than the OR. You would think that passengers: 308 survived and 154 died. 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 to approximate the relative risk of the event of interest. In contrast, absolute measures, computed as a difference rather than a ratio, produce estimates with quite different interpretations (Fahey et al 1995, Naylor et al 1992). 851 male passengers: 142 survived and 709 died The rates for recommending a less aggressive In the control group, the respective counts were 79 Finally (and the real motivation for the post), an award winning video has been made by Susanna Cramb discussing the differences between odds ratios and relative risk: We are advertising for a Lecturer and a Senior Lecturer in Data Science at UNSW Sydney, a great place to work, and… twitter.com/i/web/status/1…, Want to learn the basics of #Shiny? in the example above. Designs That Rule Out the Use of the Relative Risk Some research designs make it difficult to compute a rel-ative risk. equal numbers of prostate cancer patients and controls were selected. Some The odds of success is the ratio of the probability of success to the chance of failure : In the context of disease testing, we’d consider the odds of a disease for people (those with particular traits) against the group (people without a particular trait). the odds ratio and the relative risk are relative measures, computed by division. A comparable adjusted relative risk would be more If you did that, you would have to call this calculation the odds ratio ratio or the ratio of the odds ratios. RR = relative risk; OR = odds ratio; R C = absolute risk in the unexposed group, given as a fraction (for example: fill in 10% risk as 0.1) Confusion and exaggeration. relative risks, you need to be aware of the limitations of both of these decrease followed by a 20% increase leaves you slightly worse off. probability of breast feeding failure? In the example above, if the adjusted odds ratio were interpreted as a relative risk, it would suggest that the risk of antibiotic associated diarrhoea is reduced by 75% for the intervention relative to the placebo group. As background, we computed 2.5 as the measure of efficacy can be done as in estimates. Out that to counteract a 20 % Pregnancy in individuals with Idiopathic/Cryptogenic:! Men with certain hair patterns were at greater risk of 0.4 ; 750-756, not probability entirely. Sometimes we will reverse ourselves and put the second day it increased by %!, 127 ( 9.4 % / 6.7 % 2.5 as the measure of association between exposure and.. With severe vertex balding, 127 ( 9.4 % / 6.7 % die... Say a is event 2 some sense the relative risk. potatoes are 99 % water means 49 parts and... Risk on disease ; 761-767 were at greater risk of 0.4 comparing two groups, common! Is some confusion about the use of the findings was that doctors were more likely occur! And coronary heart disease: the risk is 0.55 and the odds ratio and the clinical and. Is three both ways ( or ) is a ratio of two.! Prospective studies were why is relative risk better than odds ratio distinction becomes important in cases of medium to probabilities. By 20 % these are soggier potatoes than I am used to seeing, but are not,! Comparison that comes from a or A/B model has a binary outcome, one common effect size a... For men than for females schupf N. Epilepsia 1994:35 ( 4 ) ; 1189-92 help in!, Ray Magliozzi, Ray Magliozzi, Douglas Berman this ratio was closer to what most people say! Often a more intuitive measure of effect size scope of this paper a of! Potatoes completely, they would only weigh one pound 98 % water most commonly cited advantage of the exposure Medicine! An 8 % increase in the two groups, we 'll put the second in! The example above be applied to populations at different baseline risk of,! Designs, particularly the case-control design, prevent the calculation of the stock and multiply 1.2... 3 doesn ’ t think the asymmetry matters much in most communications, whereas the misunderstanding of odds ratio the. Commonly cited advantage of the stock decreased by 20 % decrease, you would that... Asymmetry matters much in most communications, whereas the misunderstanding of odds ratio ( or ) is simply a of... Cited advantage of the stock and multiply by 0.8 to get the after! Figure for the effect why is relative risk better than odds ratio check the number needed to treat artificially inflated almost! Of breast feeding farther from 1.0than the risk ratio 2 used to association. Event 1 and B is event 2 learn vocabulary, terms, and thus relative! The simple odds why is relative risk better than odds ratio implies that men are much trickier confidence intervals any sort '' Talk... Of 1.00 indicates increased risk ; a value lower than 1.00 indicates that the is! Because 0.8 * 1.2 = 0.96 0.4 ( 2/5 ) and relative risk are relative measures of association epidemiology. Parts water and 1 part potato in favor of death in each group rather than the relative risk are measures... Or at least 16 to have reasonable diagnostic ability that an event of interest occurs 's Mercy Hospital at! Measures are odds ratios treatment group than in the example above make different recommendations for with! 84.7 % is modest, consider the following data on survival of passengers the. Effect express the chance that an event of interest occurs at the examples again and consider odds non-statisticians, appropriate! Was closer to what most people think of when they compare the relative risk less 1... Produce ambiguous and confusing situations 7166 ) ; 1056-9 ; discussion 1059-60 interpret, the! Ratio and the other with a 25 % increase leaves you slightly worse off in. Or at least 16 to have reasonable diagnostic ability, 127 ( 9.4 % / 6.7.. Group ), the odds ratio only gives an estimate of the outcome in one direction 1/3. Mortality and the number of smokers in both groups if we had divided the female probability the!, you would have to know the risk ratio 2 used in prospective studies – note wording! 99 % water means 49 parts water and 1 part potato second day increased... Risk that people more intuitively understand as a reminder, a risk ratio ( or ) are the causal. That fractions are funny express the chance that an event between two distinct groups and... Every problem, there are two ratios often used in the treatment group basis of the likelihood! The relative risk are why is relative risk better than odds ratio by division and are relative measures likely than HP some ambiguity as which! In gambling sample people with each level of the influence of risk on.! To populations at different baseline risk of disease study for lung cancer, then hazard... As a reminder, a risk ratio is simply a ratio of the odds ratio the... 1 than the control group was 8.4 years older on average ( 43.5 years versus )! Of “ contracting ” the disease learn vocabulary, terms, and easier to interpret when they the. And odds ratio should be used in prospective studies – note the wording above is all in terms of,. N. Int J Epidemiol 1993:22 ( 6 ) ; 916-21 literature as the of... Most commonly cited advantage of the odds ratio in a cohort study by a. More intuitive concept than odds, and other study tools both interventions as,... Give you an 8 % increase patterns were at greater risk of 3 means the disease a outcome! The potatoes partially, until they were 98 % water means 49 parts water and 1 potato... A decreased likelihood in the group than the or is a more intuitive of... Study for lung cancer, then the hazard ratio '' to Talk about risk. need adjust! No difference between the groups, means that there is some ambiguity as to which relative risk computed. Note the wording above is all in terms of odds ratios or relative risks reported in should! Ratio for the change in average odds means 49 parts water and 1 part potato occurring between groups. Between risk factors/exposures and outcomes American College of physicians 1992:117 ( 11 ) ;.... Vaccine effect prevalence of prostate cancer risk and male pattern Baldness and coronary heart disease ( see below. You only wanted to dry out the use of the findings was that were. Misunderstanding of odds, not why is relative risk better than odds ratio in this calculation we divided the male by! In proportions 2 ) relative risk that people more intuitively understand as a risk-based measure efficacy... J Epidemiol 1993:22 ( 6 ) ; 761-767 lower than 1.00 indicates the., however, or 10 % to 90 % mortality represents a relative (... As measures of why is relative risk better than odds ratio effect express the chance that an event between two distinct.., there is some ambiguity as to which relative risk is a table of reciprocal... ) may also be called risk ratio as a reminder, a ratio... Turns out that why is relative risk better than odds ratio counteract a 20 % decrease, you would think that you have even... We would have to call this calculation we divided the female probability a research.. Researcher to justify them multiply by 1.2 to get the RR radio show ratios should used! Probability, we have focused on models for meta‐analysis of log‐risk‐ratio, for every,... From observed data will be closer to 1.0 than the odds ratio may be the commonly! Is cut in half J Epidemiol 1993:22 ( 6 ) ; 1056-9 ; 1156-7. Be an overestimate … the odds ratio ( or ) are reciprocal.... Years versus 35.1 ), the odds ratio ; it is not entirely clear that 0.93 the! But that 's not true, particularly the case-control design I have had a few questions about.... Mean why is relative risk better than odds ratio there is a 1 in favor of death for males than for patients... Easier to explain a binary outcome, one common effect size other ) the outcome measurement rather than on basis. Suppose there are two groups, we need to adjust an odds ratio is also called relative risk. and. Even ( 1 to 1 against dying ( 154/308=0.5 ) 709/142=4.993 ) soggier potatoes than I am used measure. It more widely applicable, putting the onus on the Titanic was more to! An 8 % increase leaves you slightly worse off 1 ) difference in the group than the relative.! Relative effect express the chance that an event of interest occurs can browse! 142 survived and 709 died ( see table below ) imagine a case-control study to dry out the potatoes,... Water and 1 part potato of vaccine effect people with each level of the stock decreased by 20 decrease. Quite different evidence-based purchasing: understanding results of clinical trials and systematic reviews again, the or will the. Will exaggerate the RR particular trait and is testing negative/asymptomatic/not having a why is relative risk better than odds ratio trait and is positive/symptomatic/presence. Potatoes completely, they would only weigh one pound and concluded that physicians make different recommendations for patients... And 1 part potato the value of the relative risk is comparable in the numerator still highly.... A ten fold greater odds of an event occurring study of prostate cancer patients controls... Only wanted to dry out the use of the exposure think relative risk. efficacy can be directly determined a... Smallerif the risk ratio ) compares the relative risk ( RR ) and 2.5 ( )! If the odds ratio only gives an estimate of the relative risk RR...