student tutorial

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

Posted on August 13, 2013

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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.

diagram 1

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 togetherReal 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).

diagram 2

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.

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.

Tim Hicks

Tim Hicks

I’m Tim, a fifth year medical student at The University of Aberdeen. Prior to studying Medicine I was a physiologist working in cardiology and also completed a masters in clinical trials. My Key interests are cardiology, the design conduct and analysis of clinical trials and e-learning. Please feel free to contact me with any feedback, suggestions or requests.

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118 thoughts on “A beginner’s guide to interpreting odds ratios, confidence intervals and p-values

  1. Ben M

    I 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.

    Reply
    1. TimTim

      Thanks very much Ben,

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

      Regards

      Tim

      Reply
  2. mma

    Excellent info. I’ve always been a little fuzzy on CI and crossing of *1*… etc. That was extremely helpful. Thanks!

    Reply
    1. TimTim

      Very 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

      Reply
  3. Rupy

    Hi,

    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.

    Reply
    1. TimTim

      Hello 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.

      Reply
      1. rupy

        Hi 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

        Reply
        1. TimTim

          Hello 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

          Reply
  4. Harry

    The 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.

    Reply
  5. L. Murphy

    Tim, thanks for the great, concise tutorial. You have filled in the gaps where my texts left holes in my understanding. Greatly appreciated.

    Reply
    1. TimTim

      Hello,

      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

      Reply
  6. Andrea

    Thanks 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…
    All comments have been very helpful thanks

    Reply
    1. TimTim

      Hello 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

      Reply
      1. Sally

        Hi 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

        Reply
        1. TimTim

          Hi 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

          Reply
    1. Kate Daulton

      Hi there,

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

      Reply
      1. Judith

        Hi, 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

        Reply
      2. TimTim

        Hi 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

        Reply
      3. TimTim

        Hi 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

        Reply
  7. Amal

    hi Tim
    first 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

    Reply
    1. TimTim

      Thanks 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

      Reply
  8. Shemsu Gabiso

    please I need to know what adjusted odds ratio,crude odds ratio,bivarate and multi varate analysis, logistic regression are.

    Reply
    1. TimTim

      Hi 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

      Reply
  9. Tadesse

    I’m just want answer for my question.
    Is Odds Ratio always with in the CI (in between the interval)?
    Tadesse

    Reply
    1. TimTim

      Hi 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

      Reply
  10. Celeste

    Hi 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
    Celeste

    Reply
    1. TimTim

      Thanks 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

      Reply
  11. MrPanda Tan

    Uh… 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.

    Reply
  12. Laura Anderson

    Thanks, 3rd year mature student nurse doing my dissertation and this has really helped explain things to me.
    Just 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

    Reply
    1. TimTim

      Hi 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

      Reply
  13. Liaw

    If logistic regression analysis shown OR 1100. Does this OR correct? Does OR results can be range from zero to infinity ?
    Thank you.

    Reply
    1. TimTim

      Hello 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

      Reply
  14. Bupe

    Hi Tim,
    Thank 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?

    Reply
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  16. Suriya

    Hi 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

    Reply
  17. Pete White

    Dear 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

    Reply
  18. Celestine Enendu

    Your 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

    Reply
  19. Rubin

    Hi Tim:
    I 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

    Reply
  20. ada

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

    Reply
  21. C 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.

    Reply
  22. Theresa

    Tim,
    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!
    Theresa

    Reply
  23. Jul

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

    Reply
  24. Angela Glaub

    Tim, 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?

    Reply
  25. Ruth

    Hi
    Thanks 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.

    Reply
  26. Andemaryam 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?
    I love this anyways…

    Reply
  27. Ruby

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

    Reply
  28. wilbert

    Dear Tim,
    I 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

    Reply
  29. Kay

    In 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?

    Reply
  30. Surabhi

    Hi 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.
    it would be really helpful.
    thanks

    Reply
  31. Surabhi

    the 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
    interpret in your own words the OR of 2.20 for the high pollution fuel and comment on the statistical “significance” of this result.

    Reply
  32. Hank

    Unless 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).

    Reply
    1. EeroTeppo

      Hi 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.

      Reply
  33. Niek Tax

    Your 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:
    http://www.researchgate.net/publictopics.PublicPostFileLoader.html?id=520cd99cd039b1c948496440&key=72e7e520cd99bf05e5

    Reply
  34. Chris

    This really is awesome!!! Have had two semesters of biostatistics and epidemiology and this really puts everything together. Thank you for keeping it so straightfoward.

    Reply
  35. AM

    If 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.

    Reply
  36. Mehrunnisa Raje

    Hello 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.
    Thank you very much for making me understand statistics.

    Reply
  37. Anastasia Iliwho Ashi

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

    Reply
  38. Paul H

    Tim,
    Thank you for a wonderfully simple and memorable explanation of something I should know but have always struggled to grasp ( until now!)

    Reply
  39. Graeme Little

    Thanks 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.

    Reply
  40. Sergio

    Hi Tim,
    Sorry 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

    Reply
  41. ArulJothi

    Hi Tim
    I 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

    Reply
  42. Dr Sadia

    Thank 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…
    Best Regards….

    Reply
  43. Anikka Salandy

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

    Reply
  44. emma

    Hello Tim,

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

    Reply
  45. Abdul Waheed Khan

    Dear Tim,
    Can we calculate CI from total number of samples if we do not have the raw data for each individual person?

    Reply
    1. HollyMillwardHollyMillward

      Hi 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

      Reply
    2. Eero TeppoEero Teppo

      Hi 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 :)

      Reply
  46. vickie

    Hi Tim,
    I’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.

    Reply
  47. Aida

    Thank 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!

    Reply
  48. Megan

    this 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!

    Reply
  49. Ritu

    If 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

    Reply
  50. eyasu

    i know how to calculate crude odds ratio manually but how can i calculate adjusted odds ratio manually ?

    Reply
  51. hamzah

    Odds 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

    Reply
  52. Nancy

    When 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.

    Reply
  53. SH

    Hi Tim, your explanation is so much easy to understand. Just a question. Is Odds ratio the same as relative risk ratio?
    Also 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

    Reply
  54. Oswald Pesh

    Might 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?

    Reply
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  56. Sahana V

    Let 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.

    Reply

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