# A beginner’s guide to interpreting odds ratios, confidence intervals and p-values

Posted on August 13, 2013 by Tim Hicks

## Who is it for?

Students of medicine or from the clinical sciences and professions allied to medicine wanting to enhance their understanding of medical literature they will encounter throughout their careers.

## What will I learn and how?

How to interpret odds ratios, confidence intervals and p values with a stepwise progressive approach and a ‘concept check’ question as each new element is introduced.

## How long will it take?

Approximately 20 minutes.

## What it is not

A statistical textbook reworded or how to calculate any of these statistics.

## Contents:

Introduction

Odds ratio

Confidence interval

P value

Bringing it all together – Real world example

Summary

Self test Answers

## Introduction

The first steps in learning to understand and appreciate evidence-based medicine are daunting to say the least, especially when confronted with the myriad of statistics in any paper. This short tutorial aims to introduce healthcare students to the interpretation of some of the most commonly used statistics for reporting the results of medical research.

The scenario for this tutorial is centred around the diagram below, which outlines a fictional parallel two arm randomised controlled trial of a new cholesterol lowering medication against a placebo.

## Odds ratio (OR)

An odds ratio is a relative measure of effect, which allows the comparison of the intervention group of a study relative to the comparison or placebo group.

So when researchers calculate an odds ratio they do it like this:

The numerator is the odds in the intervention arm

The denominator is the odds in the control or placebo arm = Odds Ratio (OR)

So if the outcome is the same in both groups the ratio will be 1, which implies there is no difference between the two arms of the study.

However:

If the OR is > 1 the control is better than the intervention.

If the OR is < 1 the intervention is better than the control.

#### Concept check 1

If the trial comparing SuperStatin to placebo with the outcome of all cause mortality found the following:

Odds of all cause mortality for SuperStatin were 0.4

Odds of all cause mortality for placebo were 0.8

Odds ratio would equal 0.5

So if the trial comparing SuperStatin to placebo stated “OR 0.5”

What would it mean?

A. The odds of death in the SuperStatin arm are 50% less than in the placebo arm.

B. There is no difference between groups

C. The odds of death in the placebo arm are 50% less than in the SuperStatin arm.

## Confidence interval (CI)

The confidence interval indicates the level of uncertainty around the measure of effect (precision of the effect estimate) which in this case is expressed as an OR. Confidence intervals are used because a study recruits only a small sample of the overall population so by having an upper and lower confidence limit we can infer that the true population effect lies between these two points. Most studies report the 95% confidence interval (95%CI).

If the confidence interval crosses 1 e.g. 95%CI 0.9-1.1 this implies there is no difference between arms of the study.

#### Concept check 2

So if the trial comparing SuperStatin to placebo stated “OR 0.5 95%CI 0.4-0.6”

What would it mean?

A. The odds of death in the SuperStatin arm are 50% less than in the placebo arm with the true population effect between 20% and 80%.

B. The odds of death in the SuperStatin arm are 50% less than in the placebo arm with the true population effect between 60% and 40%.

C. The odds of death in the SuperStatin arm are 50% less than in the placebo arm with the true population effect between 60% and up to 10% worse.

## P values

P < 0.05 indicates a statistically significant difference between groups. P>0.05 indicates there is not a statistically significant difference between groups.

#### Concept check 3

So if the trial comparing SuperStatin to placebo stated “OR 0.5 95%CI 0.4-0.6 p<0.01”

What would it mean?

A The odds of death in the SuperStatin arm are 50% less than in the placebo arm with the true population effect between 60% and 40%. This result was statistically significant.

B The odds of death in the SuperStatin arm are 50% less than in the placebo arm with the true population effect between 60% and 40%. This result was not statistically significant.

C The odds of death in the SuperStatin arm are 50% less than in the placebo arm with the true population effect between 60% and 40%. This result was equivocal.

## Bringing it all together – Real world example

A drug company-funded double blind randomised controlled trial evaluated the efficacy of an adenosine receptor antagonist Cangrelor vs Clopidogrel in patients undergoing urgent or elective Percutaneous Coronary Intervention (PCI) who were followed up for specific complications for 48 hrs as outlined in the diagram below (Bhatt et al. 2009).

The results section reported “The rate of the primary efficacy end point was…….(adjusted odds ratio with Cangrelor, 0.78; 95% confidence interval [CI], 0.66 to 0.93; P=0.005)”

What does this mean?

A The odds of death, myocardial infarction, ischemia-driven revascularization, or stent thrombosis at 48 hours after randomization in the Cangrelor arm were 22% less than in the Clopidogrel arm with the true population effect between 34% and 7%. This result was not statistically significant.

B The odds of death, myocardial infarction, ischemia-driven revascularization, or stent thrombosis at 48 hours after randomization in the Cangrelor arm were 34% less than in the Clopidogrel arm with the true population effect between 7% and 22%. This result was statistically significant.

C The odds of death, myocardial infarction, ischemia-driven revascularization, or stent thrombosis at 48 hours after randomization in the Cangrelor arm were 22% less than in the Clopidogrel arm with the true population effect between 34% and 7%. This result was statistically significant.

## Summary

This is a very basic introduction to interpreting odds ratios, confidence intervals and p values only and should help healthcare students begin to make sense of published research, which can initially be a daunting prospect. However it should be stressed that any results are only valid if the study was well designed and conducted, which highlights the importance of critical appraisal as a key feature of evidence based medicine.

I do hope you enjoyed working through this and would appreciate any feedback on the content, design and presentational aspects of this tutorial.

## Self test Answers

Concept check 1. The correct answer is A.

Concept check 2. The correct answer is B.

Concept check 3. The correct answer is A.

Bringing it all together – Real world example. The correct answer is C.

## You may also be interested in these blogs:

Why should students know about kappa value?

Efficacy of drugs: 3 examples to get you to truly understand Number Needed to Treat (NNT)

Key to statistical result interpretation: P-value in plain English

Surrogate endpoints: pitfalls of easier questions

How did they determine diagnostic thresholds: the stories of anemia and diabetes

## References:

Bhatt DL, Stone GW, Mahaffey KW, Gibson CM, Steg PG, Hamm CW, Price MJ, Leonardi S, Gallup D, Bramucci E, Radke PW, Widimský P, Tousek F, Tauth J, Spriggs D, McLaurin BT, Angiolillo DJ, Généreux P, Liu T, Prats J, Todd M, Skerjanec S, White HD, Harrington RA. CHAMPION PHOENIX Investigators. (2013). Effect of platelet inhibition with cangrelor during PCI on ischemic events. N Engl J Med. Apr 4;368(14):1303-13.

## 120 Comments on A beginner’s guide to interpreting odds ratios, confidence intervals and p-values

Ben MI think it is an excellent idea to explain what statistical analysis actually means in a simplified manner this may be a little too simplified. Your explanation of odds ratio is just fine however it is important to look at how and if the researchers normalized the data. If there was no normalization for things like other health issues, differences in how skilled the surgical teams were, or the relative “smoothness” of the procedure then it is possible that these or other factors are responsible for some or all of the observed differences in outcomes. A confidence interval is actually a probabilistic statement about the repeatability of the trial as a whole (with a different set of patients who meet the same criteria) so saying that the confidence interval is 0.4-0.6 at a 95% level is actually saying there is if they performed this trial over and over they estimate that 95% of the trials will produce a result that is between .4 and .6. I know it sounds like I just said what you did but in a more complicated way but the way answer B is phrased discounts the 5% chance that the trial is actually an outlier which would result in misleading conclusions being drawn from its result. As far as P Value goes you are correct that a P Value of .05 is frequently stated and it is indeed often the threshold for statistically significant; however “statistically significant;” is closer to a legal term than a statement of fact. A P-Value of .05 simply means that assuming the individual data points are Normally distributed (which they almost always are) then there is at most a 5% chance that there is no correlation between the manipulated variables and the results observed. I don’t know if this will help or just confuse people all over again because statistics consistently cause smart people to have a logical but incorrect understanding of what a set of statistics mean in a practical sense.

January 18, 2014 at 3:16 pmTimThanks very much Ben,

This comment is very much appreciated and I’m sure will help visitors to the S4BE website.

Regards

Tim

January 20, 2014 at 6:46 pmmmaExcellent info. I’ve always been a little fuzzy on CI and crossing of *1*… etc. That was extremely helpful. Thanks!

March 5, 2014 at 12:03 pmTimVery pleased it’s been of some use. Please feel free to recommend the S4BE website as widely as possible and have a look at the many great articles and blogs in the site.

Regards

Tim

March 6, 2014 at 12:48 amRupyHi,

I’m trying to relate something I read in an article, to the way you have described it in your article.

…”an estimated odd ratio for response for anastrozole 1mg versus megestrol acetate was 1.95 (97.7% CI, 0.65-5.91)…”

Please may you kindly tell me what this means in plain english?

Thank you.

March 5, 2014 at 2:14 pmTimHello Rupy,

I think your quote comes from the study:

A Phase III trial comparing anastrozole (1 and 10 milligrams), a potent and selective aromatase inhibitor, with megestrol acetate in postmenopausal women with advanced breast carcinoma.

Available online at:

http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1097-0142(19970215)79:4%3C730::AID-CNCR10%3E3.0.CO;2-0/full

I think the plainest way to put it would be that there is no difference between anastrozole 1mg versus megestrol acetate for the outcome of “response”, which appears to be a combination of what the authors of the paper refer to as “Complete response” and “Partial response” of table 3.

Interestingly it’s a parallel three arm study looking at two different doses of double blind anastrozole and open label megestrol acetate. The total sample size is quite small at 386 participants, which perhaps goes some way to explaining the wide confidence interval (0.65-5.91), which are either side of 1 hence indicating there is not a significant difference. It is also a 97.5% confidence interval, which will also be wider than a 95% confidence interval, which I calculated (very roughly) as 0.75-5.07.

It’s also worth just keeping in mind that this is quite an old study with many of its references dating to the early to mid 90’s. So my first thought in considering the value of these drugs would be that no study stands in isolation and given that it’s quite old and has wide confidence intervals, it would be a good idea to look for a meta-analysis. Ideally start by looking for a Cochrane review and you may well find this study included in a meta-analysis, which could help with a more definitive answer to whether anastrozole or megestrol acetate is more effective for the type of patients you are interested in or perhaps they might be just as effective, but one may have more tolerable side effect or safety better profile?

So this might be of interest to you:

http://onlinelibrary.wiley.com/doi/10.1002/14651858.CD003370.pub3/abstract

I do hope this answer is of some help.

Thank you for your question, I quite enjoyed looking up this paper.

Tim

P.S. I’m conscious of the fact that this website is open to everyone not just healthcare students, so I would have to suggest that this shouldn’t be considered as medical advice and this topic is best discussed with a specialist in this field.

March 6, 2014 at 12:41 amrupyHi Tim,

Thank you for your reply, it was very helpful.

I just have a question regarding hazard ratios. Are these similar to odds ratio?

For instance, a disease free survival was longer for an anastrozole group compared to a tamoxifen group; and the statistic given was “hazard ratio 0.83 (95% CI 0.71-0.96, p value=0.013)

from this statistic I understand it is statistically significant, with a p value below 0.05. But would you be able to kindly explain what this hazard ratio means?

Thank you.

Rupy

March 16, 2014 at 6:13 pmTimHello Rupy,

Thanks for the feedback and I’m glad it was some use to you.

The interpretation of a hazard ratio is essentially the same as an odds ratio.

However it’s probably worth noting that whilst an odds ratio is derived from calculating the odds of an event in the intervention and the control arms expressed as a ratio.

The hazard ratio is derived from calculating the rate (number of events/time) in the intervention and the control arms expressed as a ratio. So there are some additional statistical considerations, but that would perhaps be more detail than is needed for basic interpretation.

Kind regards

Tim

March 24, 2014 at 4:57 pmdhaneswariplz tell me how to calculate CI

May 14, 2015 at 2:18 pmdhaneswarithanx .got some idea.

May 14, 2015 at 2:03 pmHarryThe sentence in my paper was :

The most active quartile of women had a similar risk of breast cancer as the least active (odds ratio [OR], 1.04; 95% confidence interval (CI), 0.73-–1.48). Additional adjust ment for randomized treatment assignment, body mass index, alcohol consumption, menstrual and reproductive characteristics, use of oral contraceptives and postmenopausal hormones, and family history of breast cancer did not materially change the find ings (OR, 1.10; 95% CI, 0.73–1.67)’

The way I interpreted this was :

This means the odds of having breast cancer among physically active women is 1.04 times higher/ 4% more than odds of breast cancer in females who are least active which indicates no relationship between decreased rates of breast cancer and physically active women. Because the study used a sample, we don’t know the true value is for the whole population but the best estimate is 1.04 and they are 95% confident that the true value lies within the range of 0.73 to 1.48. As the range of value includes 1 (equal odds) we can say that we don’t have statistically significant evidence that there is a bigger risk of cancer among least physically active women. Furthermore, 1.04 is close to 1 meaning the outcome is the similar in both groups, which implies there is no difference between the two arms of the study.

After adjusting for confounding factors, the odds ratio of physical activity is increased a little from 1.04 to 1.10. This result suggests that these variables were slightly strong confounders of the association between physical activity and breast cancer. But even after adjusting, the 95% confidence intervals still included 1 meaning the results weren’t statistically significant . However, Adjusting for the confounding factors gives us an odds ratio further from unity (1) which means that the protection afforded by physical activity, if any, is stronger than the initial result led us to think.

I was unsure whether I had interpreted this correctly.

March 16, 2014 at 4:47 pmshajahanexcellent

March 19, 2014 at 3:19 pmL. MurphyTim, thanks for the great, concise tutorial. You have filled in the gaps where my texts left holes in my understanding. Greatly appreciated.

March 21, 2014 at 7:25 pmpleaseI would like to ask how to interpret CI like (1;1,3) ?

TIA

March 25, 2014 at 6:35 pmTimHello,

Could you possibly give me a bit more detail and send me a link to where it comes from so I can see it in context.

Thanks

Tim

March 27, 2014 at 1:16 pmAndreaThanks for your example above. It helps a lot. Why do we take the odds ratio and -1 in order to get the %. Eg 0.78 would mean 22% less and 1.78 would mean 22% greater…

April 5, 2014 at 1:39 amAll comments have been very helpful thanks

TimHello Andrea,

The odds ratio is calculated by dividing the odds in the intervention arm by the odds in the control arm.

So if:

Odds in the intervention arm = 5

Odds in the control arm = 10

Then the odds in the intervention arm are 50% less than in the control arm.

So the OR is 0.5 therefore the outcome in the intervention arm is 50% less than the control arm.

Conversely if:

Odds in the intervention arm = 10

Odds in the control arm = 5

Then the odds in the intervention arm are 100% greater than in the control arm.

So the OR is 2 therefore the outcome in the intervention arm is 100% more than the control arm.

So in your example of OR 0.78 it would be 22% less and the example of 1.78 it would be 78% greater.

Remember though the importance of confidence intervals and interpreting data in the context of the totality of evidence.

Kind regards

Tim

April 14, 2014 at 8:14 pmSallyHi Tim, I am studying for a health technology exam… need to learn the formula for calculating a confidence interval but there seems to be a number of different formulas around and am a little confused. Any suggestions? Thanks

April 17, 2014 at 1:03 pmTimHi Sally,

Will you have to calculate the CI for an OR? Can you let me know what sort of thing you have an interest in and I will post a relevant worked example for you.

Tim

April 22, 2014 at 10:15 pmGemmavery helpful!!! thank you

April 17, 2014 at 9:41 pmKate DaultonHi there,

I’m trying to understand the confidence intervals of a study, and really struggling! Here is part of the study:

April 25, 2014 at 5:34 amBleeding time associated with ticagrelor was slightly reduced

following administration of desmopressin. On Day 5, at 25 h postticagrelor

dose, median bleeding time with ticagrelor plus desmopressin

(75 min; range 3–17 min) was slightly reduced compared

with ticagrelor alone (105 min; range 3–25 min). However, by

24 h post-ticagrelor dose, a difference between treatments was no

longer evident. Geometric least square (GLS) mean AUEC was

1751 min.h for ticagrelor plus desmopressin vs. 2208 min.h for

ticagrelor alone, difference in GLS mean 4465 (95% CI: 9047,

117) (Fig. 1).

Inhibition of platelet aggregation by ticagrelor was not affected

by co-administration of desmopressin (Fig. 2). Following ticagrelor,

mean final-extent IPA was >87% at all measured time points

(≤24 h post-dose) in the presence and absence of desmopressin.

Mean final-extent peak IPA (IPAmax) was 9932% for ticagrelor

plus desmopressin compared with 9937% for ticagrelor alone,

difference in GLS mean 005 (95% CI = 072, 063). IPAmax

measurements were calculated for 17 of the 18 volunteers (n = 17)

as one volunteer’s plasma samples were unsuitable for IPA

determination.

JudithHi, thank you very much for your help. I have try to find in many pages how can I interpret A mul- tivariate analysis demonstrated that the independent risk factors for developing nosocomial B. cenocepacia bacter- emia were hospitalization at the center for long-term sup- port (OR 28.8; 95% CI 1.83–453.4) and reduced use of antibiotics during the last month (OR 0.07; 95% CI 0.01– 0.40).

Also I don’t understand why this figures are so big. I’m not good at statistics and I will really appreciate your help.

In multivariate analysis, the independent risk factors for developing nosocomial B. cenocepacia bacteremia were hospitalization at the Long Term Support Center for chil- dren (OR 27.65; 95% CI 1.66–460.69) and reduced use of antibiotics during the preceding month (OR 0.05; 95% CI 0.09–0.35).

.Significantly more episodes of severe hypotension developed during the current admission among the cases (11/17) than among controls (40/44; p = 0.013). None of the patients with B. cenocepacia bacteremia died, while 7/44 of the controls died (p = 0.08).

Thank you very much for your help

April 27, 2014 at 3:50 amTimHi Kate,

I think this is the study:

The effect of desmopressin on bleeding time and platelet aggregation in healthy volunteers administered ticagrelor.

Available online at:

http://onlinelibrary.wiley.com/doi/10.1111/jcpt.12130/pdf

Thank you for this question, indeed the interpretation of the confidence interval is different with this study because the outcome was a continuous variable, which was time. This was calculated as the Geometric Least Square (GLS) mean, which for the purposes of this explanation we will consider to be simply a mean and ignore the GLS part.

So as outlined in the tutorial above an odds ratio is a relative measure of effect so the line of no difference is one. However a mean is an absolute measure of effect so the line of no difference is 0.

For example if a placebo controlled randomised controlled trial evaluated the effect of a new medication to reduce blood pressure, the results might show:

Intervention arm mean reduction in BP 10mmHg

Placebo arm mean reduction in BP 2mmHg

So the intervention arm has a reduced mean BP of -8mmHg compared to the placebo arm.

It’s worth noting at this point that if both had reduced BP by 10mmHg then the difference in mean reduction in BP between arms would be 0. That is there was no difference, hence the line of no difference in absolute measures of effect is 0.

Having now established the point estimate we can think about the confidence interval.

Therefore if:

The intervention arm has a reduced mean BP by -8mmHg compared to the placebo arm and the confidence interval is (95%CI: -12mmHg, to -4mmHg). Then this would indicate that the new blood pressure medication reduces mean blood pressure by 8mmHg in the population in the study and we can be 95% certain that the true population reduction is from 12mmHg lower to 4mmHg lower and because the confidence interval does not cross 0 it is statistically significant.

However if:

The intervention arm has a reduced mean BP by -2mmHg compared to the placebo arm and the confidence interval is (95%CI: -8mmHg, to 4mmHg). Then this would indicate that the new blood pressure medication reduces mean blood pressure by 2mmHg in the population in the study and we can be 95% certain that the true population reduction is from 8mmHg lower to 4mmHg higher and because the confidence interval does cross 0 it is not statistically significant.

I hope this example makes sense?

Back to your example:

“24 h post-ticagrelor dose, a difference between treatments was no longer evident. Geometric least square (GLS) mean AUEC was 175.1 min.h for ticagrelor plus desmopressin vs. 220.8 min.h for ticagrelor alone, difference in GLS mean -44.65 (95% CI: -90.47, 1.17)”

Therefore although GLS mean AUEC was lower in the ticagrelor plus desmopressin arm compared to ticagrelor alone arm the confidence interval is from a minus number -90.47 to a positive number 1.17 passing through the line of no difference 0 suggesting that there is no significant difference between arms for the outcome of bleeding time at the 24 hrs post ticagrelor dose.

The second example in your question can be interpreted in the same way.

Regards

Tim

May 21, 2014 at 12:14 pmTimHi Kate,

I think this is the study:

The effect of desmopressin on bleeding time and platelet aggregation in healthy volunteers administered ticagrelor.

Available online at:

http://onlinelibrary.wiley.com/doi/10.1111/jcpt.12130/pdf

Thank you for this question, indeed the interpretation of the confidence interval is different with this study because the outcome was a continuous variable, which was time. This was calculated as the Geometric Least Square (GLS) mean, which for the purposes of this explanation we will consider to be simply a mean and ignore the GLS part.

So as outlined in the tutorial above an odds ratio is a relative measure of effect so the line of no difference is one. However a mean is an absolute measure of effect so the line of no difference is 0.

For example if a placebo controlled randomised controlled trial evaluated the effect of a new medication to reduce blood pressure, the results might show:

Intervention arm mean reduction in BP 10mmHg

Placebo arm mean reduction in BP 2mmHg

So the intervention arm has a reduced mean BP of -8mmHg compared to the placebo arm.

It’s worth noting at this point that if both had reduced BP by 10mmHg then the difference in mean reduction in BP between arms would be 0. That is there was no difference, hence the line of no difference in absolute measures of effect is 0.

Having now established the point estimate we can think about the confidence interval.

Therefore if:

The intervention arm has a reduced mean BP by -8mmHg compared to the placebo arm and the confidence interval is (95%CI: -12mmHg, to -4mmHg). Then this would indicate that the new blood pressure medication reduces mean blood pressure by 8mmHg in the population in the study and we can be 95% certain that the true population reduction is from 12mmHg lower to 4mmHg lower and because the confidence interval does not cross 0 it is statistically significant.

However if:

The intervention arm has a reduced mean BP by -2mmHg compared to the placebo arm and the confidence interval is (95%CI: -8mmHg, to 4mmHg). Then this would indicate that the new blood pressure medication reduces mean blood pressure by 2mmHg in the population in the study and we can be 95% certain that the true population reduction is from 8mmHg lower to 4mmHg higher and because the confidence interval does cross 0 it is not statistically significant.

I hope this example makes sense?

Back to your example:

“24 h post-ticagrelor dose, a difference between treatments was no longer evident. Geometric least square (GLS) mean AUEC was 175.1 min.h for ticagrelor plus desmopressin vs. 220.8 min.h for ticagrelor alone, difference in GLS mean -44.65 (95% CI: -90.47, 1.17)”

Therefore although GLS mean AUEC was lower in the ticagrelor plus desmopressin arm compared to ticagrelor alone arm the confidence interval is from a minus number -90.47 to a positive number 1.17 passing through the line of no difference 0 suggesting that there is no significant difference between arms for the outcome of bleeding time at the 24 hrs post ticagrelor dose.

The second example in your question can be interpreted in the same way.

Regards

Tim

May 21, 2014 at 12:19 pmAmalhi Tim

April 26, 2014 at 10:47 pmfirst i would like to thank you for this amazing work its really helped me

I’m a senior medical student and i have an assignment to do about EBM I’ve been struggling with the critical appraisal especially calculating the confidence intervals around the ARR and NNT so i used a web for the calculation but now i cannot interpret the result so please may you kindly tell me what this results mean (95% CI around ARR is -0.001 to 0.073) and ( 95%CI around NNT is -782 to 14 )

Best Regards

Amal

TimThanks Amal,

This is a great question and an area I’m not so certain about, so if there are any statisticians that read this post any additional answer would be very welcome.

My suggestion on this is to first consider that the NNT is calculated as the reciprocal of the absolute risk reduction (ARR). This is easily done on a standard scientific calculator by entering the ARR and then hitting the (x-1) key then( =) . The confidence interval for the NNT is done the same way with the lower limit of the ARR 95%CI and subsequently the upper limit of the ARR 95%CI.

Its worth noting at this point that ARR is an absolute measure so the line of no difference is 0 (There is an explanation of this in a slightly different context in the reply i posted for Kates question). Essentially it means that if the upper and lower limit of the ARR 95%CI are either both positive or both negative then there is a significant difference between arms. Or if one is negative and one is positive it indicates that there is not a significant difference.

However the NNT confidence interval can produce some intriguing numbers, which at first seem quite baffling. This essentially arises from the fact that if:

NNT = the reciprocal of ARR

Then if the ARR 95%CI is from a lower limit which is a negative number to an upper limit which is a positive number it must therefore pass through 0.

So, the reciprocal of 0 is ∞ (infinity).

The next point to consider is that if the NNT indicates the number needed treat for a desirable outcome, for instance if a randomised placebo controlled trial of an antiplatelet therapy for the prevention of stroke with an outcome of mortality had an ARR 0.1 (95%CI -0.05, to 0.25).

Then NNT = 10, therefore 10 people would need to be treated to prevent 1 death.

However the reciprocal of -0.05 the lower limit of the ARR 95% CI was -20 that is for every 20 people treated there is one more death. This is of course the number needed to harm NNH.

And lastly the upper limit of the ARR 95% CI was 4.

This means that an ARR of 0.1 (95%CI -0.05, to 0.25) Gives an NNT of 10 (95%CI -20, to 4), which of course at first glance seems bizarre because it appears to exclude the point estimate of 10. However taking into account how it’s calculated it makes sense?

So a more precise way of writing this taking into account 0 would be. NNT = 10 (95% CI -20 to -∞, to 4 to ∞), which does include the point estimate of 10.

So in your example: “(95% CI around ARR is -0.001 to 0.073) and (95%CI around NNT is -782 to 14)”

The intervention point estimate is not mentioned, but the upper limit 95%CI indicates that in the true population we can be 95% certain that the benefit may be as much as NNT 14 and the lower limit 95%CI indicates that in the true population we can be 95% certain that the harm may be as little as NNH 782.

If anyone has any further comments on this i would be delighted to read them.

Many thanks

Tim

May 23, 2014 at 12:29 pmShemsu Gabisoplease I need to know what adjusted odds ratio,crude odds ratio,bivarate and multi varate analysis, logistic regression are.

May 15, 2014 at 3:13 pmTimHi Shemsu,

This reply might be a bit over simplified, but hopefully it helps.

Crude Odds Ratio – the odds ratio calculated using just the odds of an outcome in the intervention arm divided by the odds of an outcome in the control arm.

Adjusted Odds Ratio – is the crude odds ratio produced by a regression model which has been modified (adjusted) to take into account other data in the model that could be for instance a prognostic baseline variable.

Bivariate – analysis with two variables

Multivariate – analysis with more than two variables (it’s more complex than this, but don’t worry unless you want to be a statistician).

Logistic regression – a type of statistical model used to evaluate a binary outcome e.g. mortality (dead or alive).

Regards

Tim

September 9, 2014 at 12:44 pmTadesseI’m just want answer for my question.

June 11, 2014 at 10:14 amIs Odds Ratio always with in the CI (in between the interval)?

Tadesse

TimHi Tadesse,

Yes always, the OR is the estimate of an intervention effect in a study population, which is of course only a representative sample of the whole population.

The confidence interval is always either side of this because it represents the uncertainty around the intervention effect.

Regards

Tim

September 9, 2014 at 12:13 pmCelesteHi Tim

Thank you so much for your informative posts- you really explain this crazy terminology in a way that we can all understand.

Do you have any experience in working with Epi Info?

Many Thanks

June 14, 2014 at 9:45 pmCeleste

TimThanks Celeste,

Glad it’s been of use to you. I’ve not much experience of epidemiology, but if there was anything in particular you were stuck with let me know and perhaps if I didn’t know the answer it might be fun to find it out?

Kind regards

Tim

September 9, 2014 at 12:08 pmanujGood help . thanks

August 17, 2014 at 3:33 amMrPanda TanUh… if OR > 1 then exposure is giving the effect you are looking for that is better than the control. If OR < 1, then the exposure is worsening the patients' condition.

August 31, 2014 at 3:24 amLaura AndersonThanks, 3rd year mature student nurse doing my dissertation and this has really helped explain things to me.

September 2, 2014 at 11:42 pmJust one question though, when you say that the CI is 0.9 to 1.1 how do you calculate this to a 60 and 40 percentage value? Apologies, never remember doing anything like this at school so I’m a bit dim.

Thanks

TimHi Laura,

If the CI is 0.9 – 1.1 then it would be 10% less to 10% more, if you take a look at the question from Andrea and the reply I wrote to it, it will help with understanding why.

It’s great to see nursing students using the S4BE website, please be sure to let as many other students know about it as possible.

Best wishes

Tim

September 9, 2014 at 12:03 pmHollyMillwardThanks Tim! Did you know this blog has been viewed over 83,000 times since it was published!!!! :-)

September 9, 2014 at 1:15 pmTimWow, that’s great I didn’t expect that! I do hope they stayed for more than 83000 seconds!

Best wishes

Tim

October 19, 2014 at 12:17 pmLiawIf logistic regression analysis shown OR 1100. Does this OR correct? Does OR results can be range from zero to infinity ?

October 16, 2014 at 5:34 amThank you.

TimHello Liaw,

I’m not sure of the context of your result, but in principle a ratio can range from 0 to infinity. However 1100 is certainly an unusual result.

It’s perhaps worth noting that in regression analysis the OR is log transformed, for the purpose of the model, which means that the log transformed OR can range from minus infinity to plus infinity.

Once the model produces a result the log transformed OR antilog is calculated to convert it back into a ratio for interpretation.

Regards

Tim

October 19, 2014 at 12:19 pmMaqbool BalochHow to find odds ratio, adjusted odds ratio and crude odds ratio in stata??

March 5, 2016 at 5:11 pmSusmitvery useful Tim…thanks so much for your efforts!

October 26, 2014 at 12:25 pmBupeHi Tim,

November 24, 2014 at 12:32 amThank you very much for post. I has been helpful to me.

However, I am just new in using logistic regression, and doing my research in finance. My research is on effects of financial behaviour on the decision to use financial services. Therefore, the event is use or non use. I have run logistic regressions, some variables have OR more than 1.000. For instance saving behaviour has an OR of 4.0601. Would it be interpreted as saving behaviour increases the likelihood for using financial services by 406%. Would it make sense?

AliThat was very helpful. Thanks.

November 30, 2014 at 12:13 pmSuriyaHi Tim, great article.

I do have a question:

In a paper I am appraising it states that patients in the intervention arm had a greater likelihood of response at 24 hours vs the active control.

It reports an Odds Ration of 2.18.

So are they saying one thing, and letting their OR report that control was actually better? Or am I misunderstanding?

Any help would be great,

Thanks

Suriya

December 7, 2014 at 2:53 pmZoethank you so much, excellent

December 11, 2014 at 9:16 amPete WhiteDear Tim,

Very helpful information indeed! Thank you!

I have a brief question please. Can I calculate the odds ration between the main group given a drug and the comparison group if these groups have different total number?

For instance, in a RCT, we have group A which is given bromide compared to group B which is given phenobarbital. In group A, a total number of 20 people were included and 10 of them developed side-effects. In group B a total number of 30 people were included and 5 of them developed side effects.

Therefore, could I calculate the odds ratio for the side effects between these two groups?

Sorry if the question sounds silly. ;- )

Thank you in advance for your time.

Kind regards,

Pete

December 18, 2014 at 11:07 pmCelestine EnenduYour explanation was quite simple and understandable. I’m a med doctor but studying MPH @ University of Derby. I’ve been quite fascinated in rewarding fields other than clinical medicine, can u give me some hints of ur view oe experience? cheers

December 29, 2014 at 1:15 pmRubinHi Tim:

January 21, 2015 at 3:17 pmI have to organize a table to show data with odds ratio, confidence intervals: Which of these data goes fiest on the table: the P or Odds ratio? Does it depend of the journal (I will submit my paper to “Pediatrics” but I can’t figure out on the Author’s guide). Thank you.

Rubin

adathanks so much for this. i spent the most part of my lecture confused and frustrated until i stumbled across this website!

January 22, 2015 at 2:07 pmC Cruz“If the OR is > 1 the control is better than the intervention.

If the OR is 1 the intervention is effective, but if OR < 1, the intervention is not.

January 24, 2015 at 4:01 pmbehzadIf the OR =o ???

January 26, 2015 at 8:10 pmTheresaTim,

I am confused when the CI is >1 and the OR is also >1??

If OR is 1.16 and CI 1.11-1.25 (for low complication rate associated with inserting an IO needle) and is considered in the paper to be a positive result. Then the OR for inserting a needle causes pain is 0.99 with CI 0.91-1.06. How is this interpreted?

That “the odds of IO placement are 84% likely when IV access is unsuccessful for 75-89% of the population”?

I am confused because my paper shows OR’s >1 and CI between 1-2 for many.

article ISSN: 1069-6563. doi: 10.1111/acem.12329

Thank you!

February 21, 2015 at 10:40 pmTheresa

JulThanks. I like the simplicity of your presentation with the 3 quick check and then bringinging all together.

March 4, 2015 at 8:52 pmAngela GlaubTim, I have a question, if you were studying a drug against a comparator and you had clinical study go out to 3 years but then patients had option to continue to 7 years, some continued other’s were lost to f/u now you see that those that continued past 3 years show good results and you want to make a comparative claim, if you do f/u to see if the patients are alive on the studied drug would you be able to use KM+CI or KM(kaplan myer)+HR+CI or KM+HR+CI+pvalue to describe your results in your label?

March 9, 2015 at 7:00 amsamuel gbogbothanks for making my day bright, you have enable me now to interpret data

April 6, 2015 at 1:03 pmCiaraWhat would an odds ratio >1 mean then? For example 2.5?

April 8, 2015 at 11:22 amRuthHi

May 1, 2015 at 12:18 pmThanks so much for these explanation. But how does this relate to standardized coefficient Gotten when one does a binary regression on spss or other statistical package. E.g A logistic regression of factors associated with uptake of HIV counselling and testing in the study group; condom use (none use) Standardized coefficient B= -0.44, OR=0.65, sig.= 0.03, C.I;0.43,0.97.

wish I could paste a table of results I got when I did my analysis.Pls interprete this result. Thanks.

Abebaw, B. EubalewWhat about, if they are not using it properly?

September 5, 2015 at 3:06 pmAndemaryam Y.I was just working with Spss a while ahead of ma search to this very potent solution for odds ratio abd confidence interval. I thank you anyways. I am also Physiologist would you please suggest me from experience the area of physiology i shall continue for Phd program?

May 1, 2015 at 5:12 pmI love this anyways…

RubyThank you so much for the tutorial and explanations, Tim! They were so helpful for my EBM project. :)

May 2, 2015 at 4:18 pmwilbertDear Tim,

May 4, 2015 at 8:49 amI assure you that, you can be a wonderful professor. You can clearly present in a simple manner for a good learner to understand. Keep sharing

KayIn Bringing it all together – Real world example. The correct answer is C.

Can you explain where 22

7 and 34 came from in your answer

Thanks?

May 9, 2015 at 9:09 pmSurabhiHi i have a question it is related to statically significant for my assignment. I have an odds ration of 2.20 (1.16, 4.19) so how would i comment or workout on the statistical significance of this result.

May 15, 2015 at 9:07 amit would be really helpful.

thanks

Surabhithe name of the article is indoor air pollution from biomass combustion and acute respiratory illness in preschool age children in zimbabwe

and my question is

May 16, 2015 at 12:35 pminterpret in your own words the OR of 2.20 for the high pollution fuel and comment on the statistical “significance” of this result.

Jones Dorkenoo kwameI like the examples that you give

May 20, 2015 at 4:05 amHankUnless I’m mistaken, the equation explained above does not properly describe Odds Ratio, it describes Relative Risk. Odds Ratio is the odds that the diseased group was exposed, divided by odds that the non-diseased group was exposed (a/c)/(b/d) in the classic table. Relative Risk is the risk of developing disease in the exposed/intervention group, that is to say: the odds of disease in the intervention arm divided by the odds of disease in the placebo arm (which is what is described above).

May 27, 2015 at 6:58 pmEeroTeppoHi Hank

Odds ratio can be calculated either with odds of exposure or odds of outcome. In case-control design, you would only know odds of exposure like you described. In a different design, ratio of odds of outcome is the way to go. These are the same mathematically which can be seen by playing with the 2 x 2 -table. Relative risk, risk ratio, or ‘incidence proportion ratio’ differ from odds ratio so that odds are not used but proportions/probabilities.

September 2, 2015 at 4:09 pmNiek TaxYour interpretation of the Odds Ratio in Concept Check 1 seems to be wrong. The paper “The odds ratio: cal cu la tion, usa ge, and inter pre ta tion” by Mary L. McHugh (2009) states: “An OR of less than 1 means that the first group was less likely to experience the event. However, an OR value below 1.00 is not directly interpretable. The degree to which the first group is less likely to experience the event is not the OR result. It is important to put the group expected to have higher odds of the event in the first column. It is not valid to try to determine how much less the first group’s odds of the event was than the second group’s.” (page 5)

Paper available online:

May 30, 2015 at 2:31 pmhttp://www.researchgate.net/publictopics.PublicPostFileLoader.html?id=520cd99cd039b1c948496440&key=72e7e520cd99bf05e5

Carter NewtonExcellent work! Appreciated and very helpful

May 30, 2015 at 7:01 pmChrisThis really is awesome!!! Have had two semesters of biostatistics and epidemiology and this really puts everything together. Thank you for keeping it so straightfoward.

June 2, 2015 at 8:13 amProf Honey MabuzaI found it very useful.

June 14, 2015 at 2:52 pmAMIf you have a confidence interval that is between 0.4-1.3 obviously this crosses 1. If you increase the number of people in the study can this prevent the CI from crossing 1.

June 19, 2015 at 4:04 amAliyu LawanPlease is there an acceptable range for the confidence interval (CI) and the Odd Ratio (OR)

June 28, 2015 at 12:34 amMehrunnisa RajeHello Sir, Thank yoou very much. you have explaind odds ratio very nicely. no vague information (which makes me confuse) examples are also very easy to understand. you are very focused on what exactly you want to tell us. it was “to the point” and yes with that focus I also received.

July 31, 2015 at 11:52 amThank you very much for making me understand statistics.

Anastasia Iliwho AshiThanks Tim for your explanation. Why is it important to also look at the odds ratio after calculating chi square?

August 7, 2015 at 3:03 amPaul HTim,

August 13, 2015 at 4:58 pmThank you for a wonderfully simple and memorable explanation of something I should know but have always struggled to grasp ( until now!)

Graeme LittleThanks so much Tim- long time since I did eco stats in 1973. Great help and got 100% – Link In with me and see how Johnson and Johnson will be squirming soon.

August 30, 2015 at 11:29 amAbebaw, B. EubalewWas it, as simple as this? Thank you, you made it!

September 5, 2015 at 2:15 pmSergioHi Tim,

September 14, 2015 at 6:55 pmSorry to bother you, but my problem is with sample sizes to different experiments.

For example I’d like to know to calculate the sample size needed to use renal scintigraphy to evaluate glomerular filtration rate in cats with diabetes, I mean which should be the minimum sample of felines (healthy and with disease) to use to establish a baseline gfr?

Best regards

Sergio

ArulJothiHi Tim

September 15, 2015 at 6:41 amI got he odds value 0.984 for one study and 1.05 for another study, Should I equate it as OR = 1 and say there is no risk, or should I calculate the risk based on the observed values

Dr SadiaThank you so much…I have read enormous material to understand these concepts and didnt make sense…Really appreciate your info..it makes complete sense now…

October 22, 2015 at 11:09 amBest Regards….

Anikka SalandyCould you explain further that the p value is the estimated probability of rejecting the null hypothesis. I am abit confused

November 9, 2015 at 10:30 pmemmaHello Tim,

This made clear the CI, P value and odds ratio very quickly compared to a 2 hour uni lecture.

November 13, 2015 at 7:44 pmMany thanks,

Emma

Abdul Waheed KhanDear Tim,

November 21, 2015 at 8:27 amCan we calculate CI from total number of samples if we do not have the raw data for each individual person?

behzadhello

December 3, 2015 at 11:14 pmdifferent?

odds ratio=0

odds ratio=1

ekaI’m struggling with my epidemiology and statistics class, your video/youtube tutorials would be so helpful…

December 15, 2015 at 6:44 pmHollyMillwardHi that’s a really good point and I will see if one of the bloggers would like to make a video tutorial. Podlearn.com may have some videos on statistics

December 17, 2015 at 10:10 amEero TeppoHi eka

Have you searched odds ratio, p-value or any data analysis concepts you are struggling with in youtube? There seems to be a lot of attempts at least to teach them.

But if you still find these hard, someone really should figure out how to make these concepts more intuitive…

S4BE tutorial series could be fantastic :)

December 31, 2015 at 11:54 pmDinaThis tutorial has been very helpful. Now, i can interpret OR, CI and P value. Thank u so much. God bless u

December 26, 2015 at 10:54 pmvickieHi Tim,

December 29, 2015 at 9:45 pmI’m running a logistic regression & wonder if you could help me? This is not epi data though. In short, I’m wondering how to interpret large ORs (3 and 2) with P-values of var coefficients <.0001 BUT CIs include 1. The explanatory variable is a dummy with 3 levels. Originally, the explanatory variable was continuous but the OR was 1.000. I turned it into a categorical var the ORs increased but CI still includes 1.

Yunusa yahuzaVery simplefied..

January 2, 2016 at 9:16 pmAidaThank you Tim for explaining these concepts! I’m still getting used to what they mean but will be extremely useful in my understanding of tobacco cessation medication research. Great work!

March 1, 2016 at 3:51 amMulunehThis info given us help full information and given clue on 95%cl and odds. thank you!!!

March 17, 2016 at 8:17 amGanesan sundaramurthyVery easy and simple to understand .Thanks

March 21, 2016 at 4:43 amfarida yasmin shumithanks a lot! it was very helpful for me.

April 6, 2016 at 7:01 pmIndranil SahaOdds ratio? Can it be negative?

April 20, 2016 at 7:30 pmdianawell, you explained it well and very simply.thank you

May 25, 2016 at 11:33 amMeganthis was very helpful information, however, seeing as i am a high school student, some of the words were harder for me to understand. maybe you could consider using smaller words so that more people can develop a better understanding!

May 30, 2016 at 7:48 amRituIf we say OR is 4 in one group who was exposed to chemotherapy,and in the other group OR is 1.8,this group did not receive chemo.we are looking at the effect of chemo on fertility

June 2, 2016 at 4:15 pmeyasui know how to calculate crude odds ratio manually but how can i calculate adjusted odds ratio manually ?

June 10, 2016 at 9:49 amhamzahOdds Ratio (OR) is a measure associations between exposure (risk factors) and the incidence of disease; calculated from the incidence of the disease in at risk groups (exposed to risk factors) compared to the incidence of the disease in non-risk group (not exposed to a risk factor).

In this present study, by cross sectional study, We got OR 2.8 for variable keep livestock such as goats, sheep and pigs. Is this meaning Respondents or household who keep livestock such as goats, sheep and pigs have a 2.8 times greater chance of contracting malaria compared to a respondents or household who do not raise cattle where the confidence interval [CI: 2.180 – 3492])?

What does different between OR and RR, for this case

Regards for your advice

July 22, 2016 at 9:12 amNancyWhen doing a lit review, I find that results are frequently presented in different ways. I’d like to be able to convert them to read the same way so that I can compare them.

I know that I can convert OR1 by using the equation 1/x, where x=OR<1, which then reverses the factors being compared. For example,

FB is less likely in rural [OR=.26 (.12, .50)] than urban areas

converts to:

FB is more likely in urban [OR=3.85 (2.00, 8.33] vs rural areas

My question is how to convert:

HB is more likely in rural [OR=22.8 (10.6, 49.4)] than urban areas

Is it correct to say:

FB is more likely in urban [OR=22.8 (10.6, 49.4)] than rural areas

Or is there some calculation that needs to be done? FB and HB are dichotomous outcomes.

Thank you.

September 20, 2016 at 7:17 pmSHHi Tim, your explanation is so much easy to understand. Just a question. Is Odds ratio the same as relative risk ratio?

September 30, 2016 at 5:55 amAlso I have difficulty understanding different study designs and ends up misinterpreting them.

Is there an easier way of understanding the difference between cohort studies, case control studys, retrospective cohort studies and cross-sectional studies

Oswald PeshMight you help me understand the following interpretation?:

“Group A reported significantly less difficulty in the instrumental activities of daily living (IADL) than the control group (effect size, 0.29; 99% confidence interval [CI], 0.03-0.55). Neither Group B (effect size, 0.26; 99% CI, −0.002 to 0.51) nor Group C (effect size, 0.20; 99% CI, −0.06 to 0.46) had a significant effect on IADL”

What is the basis for interpreting no significant effect in groups B and C?

October 2, 2016 at 7:09 pmReenafantastic resource, thanks so much!!

November 29, 2016 at 4:08 amnoi noi παπουτσιαDo you mind if I quote a feww of your articles as long as I provide credit and

February 5, 2017 at 5:59 amsources back to your webpage? My blog site is in the very same

niche as yours and my visitors would certainly benefit from some of

the information you proviude here. Pleae let mee know if this alright with you.

Thanks!

Selena Ryan-VigYou’re welcome to quote any of the articles if you provide credit and link back to the original source. Many thanks!

February 6, 2017 at 9:28 amSahana VLet us consider the relationship between smoking and lung cancer. Suppose exposure to cigarette smoke increases the incidence of lung cancer by 20% (i.e. the relative risk is 1.2). Lung cancer has a baseline incidence of 3% per year (in the non-exposed group). Suppose as well that baseline incidence in obese individuals is 1/3 less (i.e. 1%/yr.), and the relative risk associated with the exposure is 1.2. You follow up 1000 non-obese and 1000 obese subjects with the exposure, and an equivalent number without the exposure. The study lasts 25 years. Work with 25-year cumulative incidence and a denominator of 1000.

How to calculate this problem? Especially the construction of the table. Kindly help.

February 18, 2017 at 3:59 amKiraHi Tim,

I am a current post-graduate fellow working with the LA County Department of Public Health. While wrapping up my epidemiological research project I searched for a quick refresher or reference guide for this very topic. You awesome data came up. Thank you so very much for compiling this information in a quick and straight forward manner. It helped me expedite my review of ORs essential to completing the data analysis portion of my manuscript.

You’re so awesome!!!

March 21, 2017 at 9:31 pmCaitlinHi,

Can somebody please help me? Can somebody explain this (AOR= 0,04 95% CI 0,02-0,09)? It would mean that an anterior and an lateral posterior episiotomie would be the best intervention to prevent an intrapartumhemmorage. Kindly help.

September 3, 2017 at 4:00 pmFredrik NathHi Tim,

September 30, 2017 at 8:37 amFelt I should just say I thought this little intro to OR and CI was excellent.

I’m a 67-year-old (full-time) neurosurgeon down south and for years, I’ve always gone by p levels in assessing stats presented in papers. Never worried much about the niceties of CI. I read your very clear article and realise now I should have done this years ago! Well done and thanks.

MaheshThere is some nice introductory stuff here but I’m concerned that your explanation of p values feeds into popular misconceptions that are somewhat harmful (see comment 91 for a stark example).

The p value is the risk of obtaining the observed result, or a more extreme result, by chance if the null hypothesis were true. 0.05 was chosen by a researcher many decades ago and the entire biomedical science community followed suit. There is nothing magical about 0.05 that makes a result “significant”.

I think it’s much more important that students learn about the scientific method, hypothesis testing, trial design, data types and distribution etc. before worrying about significance testing. Otherwise the risk is that they go through their entire career mistakenly looking for the magical 0.05 like comment no.91

November 26, 2017 at 7:52 pmσχεσειςI read this article completely concerning the resemblance of most up-to-date and earlier

December 5, 2017 at 5:09 pmtechnologies, it’s awesome article.

P KoulHi Tim

I am running a Vaccine effectiveness study and wanted to calculate the Vaccine effectiveness from OR. The OR is 27 (CI 17-40). This translates to VE of 73 (calculated as 1-OR). Do the confidence intervals also get changed to 60-83?

December 21, 2017 at 5:44 pmThanks for your response.

Catherine WilliamsHi, I’m a little confused about the CI interval and your statement that even if it’s 95% if the interval “crosses” 1 it’s not statistically significant. I am reading a paper comparing the effects of declawing of cats on various adverse out comes as compared with non declawed cats. In all of the comparisons (OR were calculated) the CI was 95% but the values listed under the CI were often greater than 1. Examples include the following (1.99-7.84, 1.32 – 4.56)

February 14, 2018 at 3:47 pmRitika KaushalThank you ! This helped me understand aspect of biostats better than any book.

July 23, 2018 at 6:50 pmMLNeeded clear, concise help in a hurry and you provided it. Thank you!

August 20, 2018 at 2:26 amdr saimavery informative

August 29, 2018 at 7:44 pmdr ashutoshIt would have been good if the etymology of terms were added.

September 12, 2018 at 12:23 pmwhat does 95% mean ? Is it the measure of confidence meaning ;that we are 95% confident of the applicable range’s(between 40% and 60%) dependability for its application for general population?