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Understanding the Results: More About Odds Ratios: Gordon Guyatt, MD, discusses odd ratios.
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Understanding the Results: More About Odds Ratios: Gordon Guyatt, MD, discusses odd ratios.
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Segment:0 .
>> I'm Joan Stephenson, editor of JAMA's Medical News and Perspectives section. Today, I have the pleasure of speaking once again with Dr. Gordon Guyatt, this time about understanding study results that are framed in terms of odds ratios. Dr. Guyatt, why don't you introduce yourself to our listeners? >> I'm Gordon Guyatt. I'm a professor of medicine and clinical epidemiology at McMaster University in Canada. >> Dr. Guyatt, listeners might be familiar with the concept of odds in the context of sporting events or games.
What role do odds play in the context of the clinical setting? >> Right, so if you're betting on a boxing match or any kind of sporting event, you're likely to have the results presented, or the possible results presented as odds. So you won't hear that the likelihood or risk of your team winning is 75%. Instead of 75%, you'll have odds of 3 to 1, for instance.
In the medical context, we have relative measures of effect that include relative risks and odds ratios. And these are alternative measures for what we call dichotomous outcomes. You either die or you don't die. You have a myocardial infarction or you don't, or you have a stroke or you don't. So relative risk and odds ratios are two alternative measures. Historically odds ratios have been frequently used in the context of randomized trials and in systematic reviews, because if you are a statistician, it turns out they have very nice statistical properties.
So that was how things were presented. Odds and odds ratios, however, are much less intuitive for clinicians. So clinicians, while at the racetrack they may be using odds, if they're talking to their patients, they will not say your likelihood of being free of cancer in four years is 4 to 1. They will say that there is an 80% likelihood you're free of cancer. So while odds ratios historically have appealed a great deal to clinicians, we generally encourage our colleagues presenting results of trials -- individual trials or systematic reviews -- to use risks and relative risk, rather than the odds.
And indeed, one of my colleagues has said that clinicians can understand risks, and they probably can get their mind around a ratio of risks. Gamblers understand odds, and nobody understands a ratio of odds. So the appeal to the statisticians is not a great reason for using the odds. But there's one type of design, a case-control design, where the investigator picks the number of cases and the number of controls, and that's not naturally determined but rather by the investigator.
There you have to use odds ratios. But when odds ratios are used in other contexts, they present interpretational challenges. >> Can you please explain the relationship between risks and odds in medicine? >> Okay. So the odds is the risk over 1 minus the risk. So if your risk is 80%, then your risk to 1 minus the risk is 8 to 2, and your odds are 4.
If your risk is 67%, or two-thirds, it is 2 to 1, so your odds are 2. 50%, it's 1 to 1. If your risk is 40%, it's 2 to 3. And that's an odds of 0.67. By the time you get to a risk of 10%, the odds are 11%. So what you see there is that with high levels of risk, like 80%, the odds are very different.
Risk is 0.8, odds are 4. By the time you get to a very low risk, 0.1, the odds are 0.11. So in other words, high risk, the odds and the risk are extremely different. By the time you get to a low risk, the odds and the risk are very similar. And it then follows that the situations in which you can do what is intuitive, which is to pretend your odds ratio is a risk ratio, because we understand risk ratios which are synonymous to relative risks.
Under those circumstances, you can substitute without problems. When you're in a high-risk or high-prevalence situation, not so much. >> What is an odds ratio, and how can it help clinicians determine the benefit of a potential treatment? >> An odds ratio is a ratio of odds. So if you reduce your risk from 80% to 67%, you go from a 4 to 1 risk to a 2 to 1 risk.
And the ratio of odds in the treatment and control reduced by half, and the odds ratio is 0.5. Relative risk at those high levels will be quite different. So as I was saying, at low levels of risk, if you see the odds ratio presented as a clinician, you can just treat it as a relative risk. So in other words, you see an odds ratio of 0.75. You would ordinarily think that's a 25 relative risk reduction, when it's an odds ratio, it's a 25 relative odds reduction.
But with a low baseline risk, say, under 30%, certainly you can think of it intuitively as you would. You're reducing your risk by 25%. So in most situations in the trials we do, the risk of bad things happening, fortunately, is relatively low. And under those circumstances, you see the odds ratio, and you do what is intuitive. Think of it, odds ratio, 0.75. It doesn't really mean a 25% reduction in risk.
It means a 25% reduction in odds. But intuitively we think in risks, and you can get away with saying 25% reduction in risk. >> Dr. Guyatt, this may be another way of getting at the same issue. But when can we feel comfortable, assuming that the odds ratios give us the same information as the relative risks? >> And you're right. It's a way of asking the same thing. But I'll expand on it. So what are the situations in which we are typically at low risk?
So we're trying to prevent heart attacks. We're trying to prevent strokes. We are trying to prevent gastrointestinal bleeds. We are trying to prevent venous thrombosis. All of these situations, which are some of the typical situations of clinical trials, our risk is going to be relatively low, often under 10%, certainty under 30%. And it's easy to make the substitution of risk versus odds.
What are the situations, clinically, that clinicians will encounter when the risk is high? And as a result, interpreting an odds ratio as a relative risk may be misleading. Two situations that I can think of are, one, critically ill patients, and particularly subgroups of critically ill patients, such as those with adult respiratory distress syndrome, or ARDS, or sepsis in the ICU, who might have mortalities of around 50, 40 or 50%.
If you have a substantially effective treatment, your odds ratio is going to look somewhat different than your risk ratio. Similarly, cancer, where you have a very high rate of people dying, with many cancers, then it's going to be misleading. And the way it's misleading is that the odds ratio will always be farther from 1 than the risk ratio. So in the extreme situation, you will have an odds ratio of 0.5, a 50% reduction in odds, whereas if you looked at the same risk ratio, it would only be a 25% relative risk reduction.
So the situations in which you need to be careful are the high baseline risk, things like critically ill patients with bad prognosis or cancer patients with a poor prognosis. And under those circumstances, if you see an odds ratio, it will make the treatment effect look bigger than the one that most clinicians are used to, which is the relative risk reduction. >> Is there anything else you would like to tell our listeners about odds ratios? >> Well, perhaps repetition is a good thing.
The bottom line is it's hard to get your mind around exactly what an odds ratio is. It's much easier to get your mind around a risk ratio. So if we say seat belts cut your risk by 50%, we're thinking that if your risk was 20%, it's now 10%. Doesn't work that way with odds. And because odds are non-intuitive, they can be misleading. Fortunately, in most situation in medicine, event rates are relatively low, and you see an odds ratio, don't worry.
You're not going to be misled if you think of it as a risk ratio, which we as clinicians find it easier to get our mind around. If you see an odds ratio in a cancer situation, or critically ill, when the risks are high, then it may be misleading. And basically, a 50% reduction in odds, you will not be able to translate it into a 50% reduction in risk. And the treatment effect will, might be substantially smaller than the first impression.
>> Thank you, Dr. Guyatt, for your discussion of odds ratios and understanding what they convey in clinical studies. This has been Joan Stephenson of JAMA, talking with Dr. Gordon Guyatt for JAMAevidence.
