Sharon,

I believe that you will find this two attached papers very helpful in interpreting correctly the OR. They definately helped me!

Kind regards,

Eleftheria

Thanks so much Chamara! Your explanation is very helpful.

The exposed have a 0.5 times odds of the outcome compared to the unexposed, when all other measured confounders are held constant, assuming no interaction terms, assuming no unmeasured confounding, no measurement error, no sampling error, and no selection bias.

If the controls were properly randomly sampled with incidence density sampling, the odds ratio will estimate the incidence rate ratio had a full cohort study been performed.

Sharon,

Because case-control studies (by definition) begin with the outcome and then investigate the presence or absence of an exposure, I would report the OR in terms of the exposure. The odds ratio addresses the exposure since you already know - in both groups - whether or not the outcome is present (it's how you originally determined your case group and your control group). The case group had the outcome and the control group did not. So, you want to determine how common the exposure was in each group.

An odds ratio of 0.5 means that the odds of the exposure being found in the case group is 50% less than the odds of finding the exposure in the control group. Thus, the control group was exposed to the variable of interest more than the case group. I am not sure what your study is about, but if this was a study where the outcome of interest is a specific disease and you are looking at an exposure to a drug that prevents that specific disease, then the control group (those who did NOT develop the disease) may have benefited from the exposure (the drug or treatment) because their group shows more of an exposure to the variable of interest and resulted in NO disease outcome. On the other hand, you could say that when the exposure (treatment or drug) is missing or not provided, it resulted in disease more often (as noted in the pre-identified case group).

So, for your cases, fewer of them received the exposure, which may have contributed to them being cases and not controls. More of the control group received the exposure, which may be what prevented them from being cases.

Hope this helps. :)

Additionally, you should also consider the type of case-control design, especially as the controls were selected. Example: If the case and controls were selected by density, as is done in a case-control study nested in a cohort, the OR approximates (is a good estimator) to the rate ratio. And there are many specific features. Although in any case interpertation should be done as you explained here. An interesting discussion on this, you cand find it in Rothman´s modern epidemiology

It is a prevalence ratio where the proportion of exposed among the cases with the proportion of exposed among controls compares.

Then we interpret the results of OR?

1) When the OR has a value equal to 1, we have a lack of association;

2) When the OR is less than 1, the association suggests that the factor studied would have a protective action;

3) When the OR is greater than 1, the factor studied had an association with the disease, and the higher, the greater the force of association between exposure and disease.

Dear Dr. Tracy,

In my opinion for your case-control study is correct this explanation  "the case patients had lower odds of the exposure than control patients" This means that analyzed factor has a protective role for your cases comparing to control subjects. Really it is the comparison between cases versus controls.

Wishing you continued fruitful and successful research.

Prof. Marianne Shahsuvaryan

I think I'm going to disagree with a few people here (sorry!). There is little point in using the odds ratio to say what the odds are of having being exposed, because although the study design is retrospective, the exposure presumably happened before the outcome. It's no good saying to somebody who died that they had x times the odds of having been exposed to something. In my view, that interpretation doesn't answer any useful question. More useful to say that people who were exposed have y times the odds of becoming a case. As Jason said, this is subject to a very long list of important caveats that you should not ignore. These are just associations, and we should be careful to avoid suggesting causality. Phrasing it in terms of cases having z times the odds of having being exposed doesn't avoid that issue.

Added later: I've just seen that my comment above has been downgraded (and that of someone else on the list with whom I agreed). Maybe this is something where there is different practice in different disciplines? I have to say that I've never seen a case-control study interpreting the odds ratio as the odds of having been exposed. Rothman's book was making the valid point that it is mathematically possible to interpret the OR that way. My point is that, whilst mathematically true, it doesn't answer any sensible clinical question, and I doubt it is the question that the original research was trying to answer. Rothman also says that you can interpret as odds of the outcome, and that's the way that most people do interpret it. So I still don't think there is any point to a case-control study if the only interpretation is about whether somebody has already been exposed. It's a valid answer to a question, but not a helpful one. In epidemiology, the whole point of using the odds ratio is that it is does not vary by changing the proportion of controls. There would be little point to that, if actually it were only the risk of being exposed that was of interest. I agree with you all, of course, that the retrospective nature of identifying the exposure is a major weakness of the design. But changing the interpretation to a clinically meaningless one does not get around that problem. I am also assuming that this really is a case-control study where the exposure occurs before the outcome, as this was the original question.

Sharon,

I believe that you will find this two attached papers very helpful in interpreting correctly the OR. They definately helped me!

Kind regards,

Eleftheria

Thank you all for a wonderful discussion. I think the differing opinions listed here highlight the two schools of thought on how to interpret the OR. So we are limited by the design to interpreting: given an outcome what the odds are of having had a previous exposure, which has limited clinical usefulness. It seems that Jason and Darren have mentioned that there is a way to (given some important assumptions) calculate a risk ratio to get at the question of what are the odds of becoming a case. Does anyone have a good reference or procedure for how to do this?

Hi Sharon,

In response to your question regarding calculation of risk ratio for a case-control study: Since you have a case control study, you will not be able to calculate the risk ratio directly as the case-control study be definition starts with the outcome (i.e. the number of cases and controls are determined by the researcher and do not therefore reflect the probability of outcome in the source population. If the sampling fraction for both cases and controls is known then you will be able to calculate the risk ratio. If your case-control study is nested within a well defined cohort, the odds ratio will be a good approximation of the risk ratio if the sampling is done using the case-base method. Alternatively if the cases are selected using incidence density sampling or  risk-set method, the odds ratio will be a good approximation of the rate ratio. Modern Epidemiology (Rothman, Greenland and Lash) provide a more detailed discussion. For a simpler explanation see the attached  article by Pearce. 

http://csm.lshtm.ac.uk/files/2011/05/Pearce-1993.pdf

Use likely-hood ratios it seems better in this case.

A likelihood ratio test won't give you an estimate, only a p-value, so doesn't add much to the interpretation.

Sharon - I don't think anyone is suggesting that you can calculate a risk ratio from a case-control study. There are some situations where the odds ratio approximates to it, but it is never exactly the same. Best to avoid thinking of it in terms of risk, and think in terms of odds, knowing that the odds ratio will always be more impressive looking than the risk ratio, then you steer clear of the problem.

Dear All

Very interesting and instructive discussion. And for non-statisicians like me

it was very helpfull to read the 2 articles indicated above by Elefteria.

Arthur

Dear all

An alternative design, the case-base study (or case-reference study) can directly produce estimates of absolute risks and relative risks. See the following paper:

Chui TTT, Lee WC*. A regression-based method for estimating risks and relative risks in case-base studies. PLoS ONE 2013;8:e83275.

Wen-Chung

No question that the OR is weak, compared to other measures.  The case-control study design is very artificial, and the outcome-to-risk factor direction of the OR seems non-sensical.  If you have an alternative, don't use the case-control design or the OR.  The proper use of a case-control study is for a rare disease, where the researcher must collect up the few cases available, then match the best they can to similar controls.  Not a design that mimics life very well, but with a rare disease, it's about the only choice.  With a cohort study design (choose a population and follow them over time, measuring for the risk factor(s) of interest and then watching for the outcome to occur), the outcome measure (relative risk) is better, easier to understand and more accurate. 

I think the interpretation of the odds ratio is better explained with examples. Lets say that the exposure is smoking and the disease is lung cancer in a case-control study. If you get an OR of 1.50 for smoking you would conclude: "smokers have 50% more chance of getting lung cancer as compared to non-smokers", now lets say that  vitamin A is given to children to protect them agains upper respiratory infections (URI) and the OR in children taking vitamin A was 0.5, you conclude that "children taking vitamin A had 50% less chance of getting URI compared to children that did not take vitamin A

Because of the logic of case-control studies (start with cases and controls, look back to find the prevalence of potential causes) it's more correct to say the odds of the exposure given disease are X.  So if the OR is 0.5, the cases have half the likelihood of having had the exposure as the non-cases.  Obviously that's the opposite of the cause-and-effect time sequence we want to prove.  But that's what makes the odds ration, and the case-control study, less powerful.  if the OR is significant (i.e. its 95% confidence interval does not include one) there is a significant association.  But association is the correct descriptor, it shouldn't be interpreted as causation.  If I study a foodborne outbreak, and find that a certain item on the menu is associated with disease using a case-control format, it's just as likely that being diseased caused people to choose to eat that food item as it is to say that eating that food item caused disease.   Neither is disproved by the OR, only an association is demonstrated.

My understanding is that the OR was originally devised to approximate the prospective Risk Ratio (which most of us would prefer to have, and would use if we could, unless we could have something potentially even more powerful like a rate ratio or a hazard ratio.)

Although we usually use the cross product ratio (a * d) / (c * b) as a short-cut , the OR is actually the ratio of the odds of exposure between cases and controls.  (I think it would be clearer if we called it 'Relative Odds' as it would align with calling the Risk Ratio the Relative Risk).  

How you phrase it depends on how methodologically sophisticated your audience is.  If you want to be technically correct, you'd say "the odds of exposure were half as large in the cases as in the controls", and people who understand odds and relative comparisons would get that it's a protective effect, especially if they also grasped that the study started with outcome and then compared exposures, rather than the other way around.  Because you sampled on the basis of outcome (case-control), I don't think your second interpretation is correct.   Perhaps in the spirit of clear communication, you could add a footnote to the effect that 'if this was replicated in a prospective study and the association is causal, it would indicate that exposure cuts the probability of the outcome by 50%.' 

Everybody accepts OR as a retrospective outcome indicator. It is assumed that control group will display a similar chance to get the outcome as open populations, thus it reflects the same probability against which we compare that observed in case group. By this means, the odds is a measure of how many times the result surpases the control group. In this case we call it "risk". But, on the opposite situation, the proportion in which is reduced the outcome is named "protection factor", which means the exposure factor "protects" the case sample to the putative factor. In this case, I agree with Hernandez-Garduño and Speechly. 

To be more objective I have cited literally a paragraph from Sackett's Clinical Epidemiology:

"Case–control studies (sometimes known as case comparison studies or

“trohoc” research (“Trohoc” is cohort spelled backwards, a term coined by Alvan Feinstein) are on the next step down the evolutionary ladder of evidence generation. Here “cases” are gathered, namely patients who already have the rheumatologic endpoint of interest. Controls, who definitely do not have the outcomes of interest, are then matched to cases, usually for age, gender, and any other important characteristic that might  be related to the outcome of interest, except for exposure to the putative cause, that is, breast implants. Both groups are then questioned or examined for possible exposure or records are checked to ascertain whether they had received implants. Of importance, to avoid bias, ascertaining exposure should be done by someone who is unaware of whether the participants have, or do not have, the outcome(s) of interest. This design is much easier and faster to implement than a cohort study because the bad outcomes have already appeared. However, a price must be paid for this ease of execution, and a large literature exists on examples of spurious associations found in case–control studies that were not borne out by subsequent cohort studies and/or randomized trials. But because of their simplicity, case–control studies can be a good place to start when generating and exploring causal hypothesis, especially for rare disorders. Traditional epidemiology texts provide detailed methods for doing such studies, and they are even described in some clinical epidemiology texts.

Alvan Feinstein provided a detailed analysis of the biases inherent in

this study design and how to avoid many of them. Indeed, advocates

of observational studies such as Feinstein claim that they can provide the

same answers as RCTs about causal effects if their biases and other limitations are understood and, where possible, overcome. 

We agree that a badly done RCT can give incorrect answers and a well done observational study can give correct answers—but a welldesigned and executed RCT trumps  a well done observational study every time, because it is least susceptible to the

many biases that can create false conclusions". 

Copyright © by R. Brian Haynes, David L. Sackett, Gordon H. Guyatt, and Peter Tugwell. Clinical Epidemiology: How to Do Clinical Practice Research. 

Dear Sharon,

In a case control study by the design we are really estimating the exposition OR. But if we calculate both of them, OR of exposition and OR of disease it is the same value as you can see in the attached file.

Thus, although we are estimating exposition OR it is proper and better to say "the exposure is associated with lower odds of the outcome compared with non-exposure" or that people exposed have a lower chance for the outcome.

Bless you.

Both formulations are correct. Purely and simply we can say :   subjects with exposure have a risk two times less likely to develop the disease (1/0.5) compared to subjects with not exposure.

Interesting