Hi Umesh,

I agree with Ronan.

Interpretation of the OR depends on how you calculate it. Usually, OR=odds of event in cases/odds of event in controls. The odds are the P/(1-P), where P=probability of event in a group (be it case or control). 

From the formula, you can deduce that if OR>1, the odds of the event is higher in the cases. Of course, you should also calculate the confidence interval (CI) of the OR to determine if your result in statistically significant. If the CI contains 1, then the OR, although >1, is not statistically significant. Statistical significance and what determines it is a different topic and I won't go into it now. 

If OR=1, then the odds of the event in the cases=odds of the event in controls. So, that event makes no difference, it's not a risk factor. 

If the OR

If you think about it, you can invert any odds ratio, relative risk or any ratio. If smokers have nine times the risk of lung cancer, then non-smokers have one ninth the risk. If men have two and a half times the risk of stroke, then women have (aha - what's the inverse of two and a half? Two and a half is five over two, so the inverse is two over five that's… that's…) 0.4!

So if you have an odds ratio that shows increased risk in one group, inverting it shows the reduced risk in the other group. 

An OR of 3 (=3:1) means that the odds for the study group are 3 times as high as for the reference group. An OR of 1/3 (=1:3) means that the odds for the reference group are 3 times as high as for the study group (in other words: the odds for the study group is a third of the odds for the reference group).

Consider odds means a risk (e.g. developing a disease or dying or similar). An OR>1  indicates a higher risk in the study/treatment/exposed group, so the treatment or exposure of the factor increases the risk. An OR 1 increases the result, a factor smaller than 1 decreases the result.

Hi Umesh,

I agree with Ronan.

Interpretation of the OR depends on how you calculate it. Usually, OR=odds of event in cases/odds of event in controls. The odds are the P/(1-P), where P=probability of event in a group (be it case or control). 

From the formula, you can deduce that if OR>1, the odds of the event is higher in the cases. Of course, you should also calculate the confidence interval (CI) of the OR to determine if your result in statistically significant. If the CI contains 1, then the OR, although >1, is not statistically significant. Statistical significance and what determines it is a different topic and I won't go into it now. 

If OR=1, then the odds of the event in the cases=odds of the event in controls. So, that event makes no difference, it's not a risk factor. 

If the OR

If the OR is between 0 and 1, you can't say the exposure is not a potent protective factor until you reverse the OR (1/OR). Only then can you understand the magnitude of the protection. If the OR=0.4, by reversing it you saw that the OR became 2.5, which indicates a good level of protection.

You've already had some great responses.  I'll just add that one more way you can easily see the equivalence (except for direction of effect) of ORs of 3 and 1/3 is by looking at things on the log-scale:

OR    Ln(OR)

 3       1.099

1/3    -1.099

The magnitudes are the same, the effects differ only in direction.

HTH.

Hi Everyone, Ronán Michael Conroy, Jochen Wilhelm, Cosmina Gingaras, Bruce Weaver , Rohit P Ojha...

All your contribution to this discussion made it more sensible and interesting. May be I misunderstood the basic concept of OR.. which haunted me in understanding its interpretation. Thank you one and all. I still request you all to add to this discussion if you have any more information. It will be very helpful for me.

When the OR is close to 1 (slightly higher or lower), it’s possible to use percentages. For instance if you have an OR=1.2, you will interpret as 20% more of odds in the cases than controls. If the OR is

If you have OR>1 in one of the groups , and in another one or 1.

For example,   if OR>1 means protection to one of the groups, and in another one we have OR

To summarise, OR>1 and OR between 0 and 1 are of the comparable magnitude, just different effect direction.

Where does your estimate end up depends actually on your study question. If you reverse your study question (see examples from Ronan), you will shift the OR in the other group! Thus, it is sensible to think before the analysis where are your results likely to end up and reverse it to make it OR>1, which is more straightforward for us humans to understand. 

Irena, I kindly disagree here: "and reverse it to make it OR>1, which is more straightforward for us humans to understand."

1) when a scientist (as a particular subset of "humans") is not able to grasp the concept of multiplicative changes / comparisons we have a severe problem anyway.

2) Reversing means to exchange target group and reference group. This may be ok when the "reference" has no specific meaning (example: when the risk of meals and females is compared; it would make no difference if the OR of "smoking" in Albania [1] is reported as OR(male vs. female) = 0.4/0.04 = 10 or if it is reported as OR(female vs. male) = 0.04/0.4 = 0.1).

It makes little sense - or is even confusing! - when there is a meaningful "reference". For instance if one tries to express the effect of meditation on the risk of getting migraine, comparing the the meditation group vs. the non-meditation group (which is the "reference"). Say that the OR is 0.2, that means that the risk for meditating people is lower. Just taking the inverse (1/0.2 = 5) would indicate the opposite. Correctly this would mean that avoiding meditation increases the risk of migraine by a factor of 5. What is usually wrongly interpreted as meditation decreases the risk by a factor of 5 (what is nonsensical and mathematically wrong, because the factor of decrease is 0.8 [i.e. 80 percent points: from 100% to 20%]).

[1] http://en.wikipedia.org/wiki/Prevalence_of_tobacco_consumption#Rates

Jochen, I was referring to Ronans examples, where reversing the study question is possible - your nr. 2.

We scientists usually hand over the results to non-scientists, decision makers and the media. These are other subsets of humans (as you call them) we normally collaborate with and it is better to make the results easy to understand for a broader public, in my opinion.

I have seen a lot of mistakes being made with interpretation of OR between 0 and 1 (also, if it was that easy to grasp, there would not be this debate here), so would still recommend to try to have the OR above 1 - if that is possible to do and easy to interpret. Most frequently however, we would get different directions of effect anyway if we are doing estimates in multivariable analysis. 

Umesh,

Odds ratio are related to probabilities in basic sets theory. If the probability of the event is X, then 1-X is the probability of not-event. This means that

x/(1-X)=R, so x=R-Rx, so x=R/(1+R) and 1-x = 1/(1+R) and their sum is 1.

When R=2 x=2/3 and 1-x=1/3

When R=0.25 x=0.2 , then 1-x=0.8 and it means that the probability of no-event is much higher.

The interpretation depends of event's meaning in your research and it is your task as researcher.  Statistics is highly related to sets theory and mathematics.

OK, hope it helps, emilio

There are so many great answers to the main question. I will add that Jochen and Irena have opened up a good debate about how to report, and whether it makes sense or not to 'flip the odds ratios'. While it's true that for most people an OR>1 is easier to understand, there are instances where they are better left as OR

Excellent point, Steve.  Age is such a great example to use too, because for many variables, the OR associated with a one year increment is tiny (i.e., very close to 1).  For that reason, I often use Age/5 or Age/10 (sometimes centered on a convenient value near the minimum) in logistic regression models.

@Steve: great comment.

@Bruce: not "age" is the unit but "year", I suppose. So instead of using year/5 ("Agre/5" as you wrote) you may consider taking months (weeks, days) as they are more common intervals that '0.2 years' or '0.1 years'. Just a note.

@Irena: I agree that results (sometimes/often) have to made understandable to a broader public. I am still of the opinion that clamin that (by a treatment or something)  "the odds are reduced to 20% of the odds in the reference group" (or, alternatively, "the odds are reduced by 80%"  is better and less prone to misunderastading than to say that "the odds are 5 times lower". Maybe I am nerdy here but for me this looks like thinking around two corners (it only seems simple but in fact is more complicated).

Or to get the symmetry better: as one can say that the treatment "multiplies the odds by 5" one could say that it "divides the odds by 5".

NB: the factor 5 or 1/5 is just an example. Take any other value you wish.

Sorry Jochen, I was probably not clear enough.  When I use Age/10 rather than Age, I use age in decades rather than age in years--e.g., 50 years / 10 = 5 decades.

I understand that medicine and biology research developed their own approaches to statistics to work out their particular problems, creating biostatistics as a branch of the discipline. OR is a function of probabilities created to interpret the relation of p(E)/p(notE). But saying that 1/OR is the value of the ratio p(notEvent)/p(Event) is a big mistake and it is normal that many of your students do not understand it and have problems applying it, as it happends with external observers like me. It is easier to speak in terms of percentages of Event and Not-event, that must add to unity, than to do it in terms of OR(of event) and OR(of not event). OR is an strange way of interpreting the propability of events using the word "chance". This would effect even more the studies of sequential analysis that are so important in biostatistics. I consider my duty to share these concerns with all of you. Thanks a lot for all I have learned from biostatistics research. emilio

I would not try to complicate things too much as it will create confusion to the original question. OR is a ratio of odds, not a ratio of probability. The odds of something happening vs. not happening is a ratio of probabilities. So an odds ratio is a ratio of two ratios (sorry if this sounds confusing). However I am not sure anyone has suggested that OR is p(e)/p(not e).

Emilio, perhaps I am misunderstanding your explanation. However it is safe to say that taking the inverse of an odds ratio and simply re-framing your exposure reference is 100% valid.

You mention also that the interpretations are easier in terms of proportions rather than odds (I agree) - this is part of the reason why I mentioned the risk ratio as something to consider, as it is something people have an easier time grasping - and sometimes the more appropriate measure.

Hi @Doucette, @Chaves, @Jochen, @Bruce, @Irena... thank you all for providing me insight about interpreting OR. However, I am still not able to understand it completely may be because of different opinions posted or my poor comprehending ability. I request u all to suggest or share few literature if you can. It will be helpful for people like us to understand it better. Thank you 

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2938757/

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1127651/

http://meds.queensu.ca/medicine/obgyn/pdf/Making.Sense.of.Odds.pdf

I am taking a course on Statistical Reasoning for Public Health 1: Estimation, Inference, & Interpretation by John McGready, PhD, MS (John Hopkins University).

Where they described that scaling of ratios is not symmetric around the value of 1 as it differs in magnitude. They suggest taking log of OR (As already suggested by @Bruce Weaver) will make the magnitude symmetric around value 1, & make interpretation of magnitude of OR simple in either direction. I have also attached the video lecture for those who need more clarification. Hope this discussion helped many of us..

Thank u all for your valuable suggestions and comments...Which helped me lot in understanding OR.

Hello Sir

there are two factors A and B, B is mutant responsible for disease, and C is wild type.

If OR is  1.02 and CI is (0.86,1.56), it means B is responsible for disease as OR is Greater than 0.1 but CI is not equivalent or greater than 1?????please answer

I have just pasted a paragraph from an article (see LINK).

Odds ratios are used to compare the relative odds of the occurrence of the outcome of interest (e.g. disease or disorder), given exposure to the variable of interest (e.g. health characteristic, aspect of medical history). The odds ratio can also be used to determine whether a particular exposure is a risk factor for a particular outcome, and to compare the magnitude of various risk factors for that outcome.

OR=1 Exposure does not affect odds of outcome

OR>1 Exposure associated with higher odds of outcome

OR

Sharanbasappa concluded his post by quoting this sentence (with emphasis added) from the link he posted: 

"Nevertheless, it would be inappropriate to interpret an OR with 95% CI that spans the null value as indicating evidence for lack of association between the exposure and outcome."

This is a very important point.  As Altman & Bland (and I'm sure many others) have put it, absence of evidence is not evidence of absence (see link below).

http://www.bmj.com/content/311/7003/485

Thanks for the valuable answers about explaining the OR differently. Interpretation of OR for a categorical variable in logistic regression is clear (i.e. cases and control/ diabetes group vs non diabetes). How to interpret the OR for a independent contentious variable when OR is greater than 1 and less than 1? 

When you look at a categorical predictor, the OR gives tha ratio of odds when your predictor changes from one category (A) to the other (B):

OR = "odds under cat.B"  / "odds under cat. A"

When the predictor is continuous (X), the OR gives you the ratio of the odds when the predictor changes (increases) by one unit (from x to x+1).

OR = "odds when X=(x+1)" / "odds when X=x"

HI Jochen, thanks for the answer. Can you please explain it further using an example? 

Interpretation of OR=1.3 and 0.7 for a contentious predictor

Example (just made up, no intention that the given values have to be meaningful!):

predictor = BMI [kg/m²]

response = probability p to get coronary heart disease (CHD)

odds = p/(1-p)

The odds for CHD at a BMI=22 may be 0.020

The odds for CHD at a BMI=23 may be 0.026

Then the OR for CHD by BMI is 0.026 / 0.020 = 1.3

Let's assume we conducted a logistic regression, dependent variable frail/not independent variable mean blood pressure. If we get a significant OR of 0.986, can we interpret it as for every 1.00 mmHg decrease in mean blood pressure, there is a 1.4% increase in the chance of being frail? 

...there is a 1.4% increase in the odds of being frail

Thanks Jochen. I know how to interpret OR as a percentage. However, I am not quite sure about the logic behind it (the calculation). I would much appreciate if you could explain it.

If I invert the odds ratio, do I have to invert the confidence intervals as well?

If you mean to invert the limits of the CIs, then: yes, for sure,

Thanks every one for this nice discussion..

What about the CIs! What are the methods of inverting the CIs of the odds ratio?

I also have a question about the OR. I conducted a study about adherence on oral oncolytics and found that the presence of a solid tumor (OR = 2,026; 95% CI 1,058-3,880; p=0,033) and cyclic dosage regimen (OR 9,457; 95% CI 3,909-22,877; p=0,000) were significantly associated with optimal adherence.

So does this also imply that a hematological tumor and a continuous dosage regimen are significantly associated with non-adherence?? 

Not necessary. The conclusion about the significance of any determinant is not straight forward. Confounders must be considered in logistic regression analysis or other statistical approach. Evidence on one variable or characteristics does not exclude and/or prove lack of evidence on other variables.

Dear

Concerning of our explanatory variable, the behavior of participants in dummy variable using Chi-Square test. We noted participants which given coded 1, who did not use mosquito nets 3.12% having malaria than participants which given coded 0 [reference] who used mosquito nets at night as much 3.84% having malaria. in binary logistic regression, we noted OR = 0.805; Pv < 0.0000. In addition, participants were not using insecticide-treated nets (ITNs) which coded 1, among 3.08% having malaria than participants which given coded 0 [reference] who use ITNs as much 5.89% contracting malaria. In binary logistic regression OR = 0.508; Pv < 0.0000.. as if, from this the percentage each group of participants is not relevant to basic theory. Please advice.

Regarding interpret odds ratios that are smaller than 1, is my interpretation below true?

We observed that variables mosquito nets have OR = 0.805 means that in one group the outcome is 19.5 less likely malaria. Variables Insecticide-treated bed nets (ITNs) have OR = 0.508 means that the first group (participants who use ITNs) was less likely to experience malaria 49.2 than who did not use ITNs with P < 0·001. The theory result of odd ratio is connected with basic theory

Sincerely,

I would like some advice from you long time experts--

I have a study in which some controls and some predictors are significant and in OPPOSITE directions. It seems to me that explaining to the lay-person it is easier to understand when you keep the discussion about the same. So how would you discuss odds being less than 1 and odds being greater than 1?

If I am going to say the odds of x are 3.8 times greater for young participants... how would I make a comparable point for an OR of 0.154? I would like to be able to say something "comparable".... like the odds of x are ??? times less for minority participants.

Is it possible to do that? How would you word this? Thanks!

Thank you all for valuable answers. I have estimated odds of death in chickens when challenged with a virus. The trial revealed OR 0.38 (vaccinated vs. control). Does it mean control birds have 2.6 (1/0.38 = 2.6) more risk (odds) of death relative to the vaccinated group, or vaccinated birds have 62% (1 – 0.38) reduced risk of dying compared to the non-vaccinated ones. Which is correct/right?

What if a odds ratio result is 0.00119, is that a zero, and how do I interpret that??

Whats the CI?

nice information

If OR is less than 1 , this factor will be preventive

How do we correlate OR, CI and P values. For example with reference to allele frequency, OR (95% CI); P value =

0.71 (0.46-1.10) ; 0.17 .. How can we interpret these results.

You would say: "whatever the OR may be, my data suggests that it won't be lower than 0.5 or larger than 1.1". If a relevant OR would be lower than 0.5, you would conclude that your data suggests that there os no relevant effect.

Thanks Jochen Wilhelm

OR < 1 interpretation is also simple. Suffice it to inverse number 1. that's mean (1/OR). Now interpret the resulting number, which is a number larger than one, inverted.

With your CI including one, it means no effect, even if your p value is statistically significant.

Umar Abdullahi, no, that's a wrong conclusion. Absence of significance does not imply absence of an effect. If the CI includes one then hypotheses abvove as well as below 1 would not be rejected, so the data is not sufficiently conclusive regarding the direction (above 1 vs. below 1).

To determine the effect or outcome of a treatment (or any other type of study) we calculate odds ratio. Say, we obtain OR to be 0.71 (as mentioned by Qurteeba Quadri). Now this data is not enough to make any conclusive statement unless we have a solid foundation to mark it significant/insignificant. This solid foundation is provided by the confidence interval (CI) which depends upon several factors, the most important being the sample size. If CI includes 1 then the association is not strong enough to reject the null hypothesis (and automatically p will be greater than 0.05). So, if you obtain OR which is far from one (either side) then you may get significant association but it again depends upon how good your sample size and study design is. In other words OR =0.71 may also indicate significant association of you have a huge sample size so that the CI narrows down and excludes one (eg. CI @95 = 0.66 to 0.85).

Thank you everybody for sharing all your knowledge, but I'm still unsure about my data. I'm currently writing my bachelor thesis and I'm kind of lost how to interpret and report my odds ratios. I calculated them for male and female. The male OR is 0.618 (CI 0.300 : 1.274) and the female OR is 0.861 (CI 0.440 : 1.683). The independent variable is wording (abolish vs. maintain) and the dependent variable is the answering behavior of male/female participants. Is it possible to write for the male participants: The odds of the event is 38.2% (1-0.618)x100 lower for the wording "abolish" than for the wording "maintain"? Hopefully you understand my question. Thank you in advance!

The OR tells you already the ratio of the odds (of the event) for "abolish" vs. "maintain": the OR of 0.62 for males means that the odds for "abolish" is 62% of the ods for "maintain". This is 38 percent points lower than 100%. I would not mix percentages (relations, like OR) with differences (of percent points). I find that confusing. It should be clear to the educated reader of your thesis what it means when you say that the OR was 0.62.

What is more important is that this is a sample value. It may be considerably different if you'd repeat the study. To my opinion, the best you can do is to report that "for males, the data obtained in my study is compatible with odds ratios from 0.3 to 1.3". (the range is the CI, interpreted as "compatibility interval"). With this, the results are completely reported without misinterpreting the relevance of a point-estimate and acknowledgeing the uncertainty. The interpretation should refer to this sentence. It is obvious that it is impossible to see from your data if one should believe in an OR above or below 1.0. However, it seems also clear that the data is not compatible with low (1.5) ORs. So one can at least exculde a strong effect. It might be interesting to report the odds itself as well.

Hopefully you understand my answer :)

Jochen Wilhelm thank you so much! Your answer helps me a lot :)

p value=0.000 OR=0.093 CI=0.028-0.311

How do we interprete this??

Taleb Salima Dr,