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  What Is Odds Ratio?

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Table of Contents    
Year : 2020  |  Volume : 68  |  Issue : 1  |  Page : 163-164

Some more Measures of Effect Size

Department of Neurology, All India Institute of Medical Sciences, New Delhi, India

Date of Web Publication28-Feb-2020

Correspondence Address:
Prof. Kameshwar Prasad
Department of Neurology, All India Institute of Medical Sciences, New Delhi - 110 029
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/0028-3886.279670

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How to cite this article:
Prasad K. Some more Measures of Effect Size. Neurol India 2020;68:163-4

How to cite this URL:
Prasad K. Some more Measures of Effect Size. Neurol India [serial online] 2020 [cited 2020 Apr 4];68:163-4. Available from:

  Odds Ratio Top

The odds ratio is another measure of the effect size of interventions or exposures, and also a measure of association between exposure and outcome in observational studies. Case-control studies can express the strength of association between exposure and outcome only as odds ratio. Cohort studies and randomised trails can also express effects as odds ratio. Therefore, this note explains briefly what is the odds ratio.

  What Is Odds Ratio? Top

We often say odds of England team winning the cricket match is 1:4. What does it mean? It means: if there is one chance of winning, there are four chances of losing. In other words, one in five (20%) chance of winning and four in five (80%) chance of losing. Chance is a probability. Odds of 1:4 means a 20% probability of winning and 80% probability of losing. Thus, odds look at both sides of the coin – win vs lose, death vs survival, improvement vs deterioration. Odds of 1:4 is equal to ¼, that is 0.25 or 25%. You can see that 25% odds of winning means 20% probability of winning. You need not bother about this interrelationship. All you need to remember is that odds expression requires the probability of one side of the coin (winning, for example) in the numerator and probability of the other side of the coin (losing, in our example) in the denominator.

Consider an example. Let us say, 20% of the patients in the treatment group died, that means 80% survived in the treatment group. So, what is the odds of death in the treatment group? Remember, for odds, we will have to have chance (probability) of death in the numerator, that is 20%; and chance of survival in the denominator, that is 80%. So, odds will be 20%/80% (in decimals, 0.2/0.8). This is equal to ¼.

Now, let us say, 25% of the patients in the control group died, which means 75% survived. So, the odds of death in the control group is 25%/75%. (or 0.25/0.75) = 1/3.

Therefore, odds ratio (OR) which usually has odds of death (or any adverse event) in the treatment group as the numerator and odds of death in the placebo group in the denominator will be equal to 1/4/1/3 = 1/4 ÷ 1/3 = 1/4 × 3/1= ¾ = 0.75 (or 75%) Thus one of expressing the treatment effect is odds ratio = 0.75 (=75%). Again OR can be interpreted as 'Odds Remaining'. So the odds remaining is 75%. Therefore, odds reduction is (100-75)% = 25%.

The merits of OR is that:

  1. Like risk ratio (RR), it is applicable to all kinds of patients, irrespective of their level of risk without the treatment
  2. It is not a loaded concept. It's neutral. Odds of going home sounds as appropriate as odds of institutionalisation or death. Just as odds of winning or losing both sound acceptable
  3. It is symmetrical. In the stroke example, the odds of institutionalisation in the 'stroke unit' group is 50:50 = 1, whereas in the 'general ward' group it is 75:25 = 3. The odds ratio for institutionalisation with stroke unit vs general ward is 1/3. Now, let us see what happens if we measured the odds of going home. This is 50:50 (=1) with stroke unit group and 25:75 with the general ward group is 1/3. Therefore, odds ratio of going home is 1÷ (1/3) =1 x (3/1) = 3. Thus odds of institutionalisation with stroke unit care is 1/3 of that with general ward. Similarly, odds of going home with a stroke unit is three times that with general ward. The symmetry is clear and no matter what you measure – the favourable or unfavourable outcome, it gives the same impression
  4. The fourth merit of OR is that it can be used in one of the commonest forms of adjusted analysis (using logistic regression), whereas risk difference (RD) or RR cannot be
  5. It has certain mathematical properties that make it a favoured measure for some statistical calculations including effect estimates in a meta-analysis.

The demerits of OR are that:

  1. it is a difficult concept to understand and interpret for health professionals
  2. if interpreted like RR, it overestimates the treatment effects. OR and RR are similar only when events in the control and experimental group is 10% or less or when they are close to one
  3. Like that in RR, there is no way to calculate the confidence interval around OR, when there is zero events in both the treatment arms. The only RD lends itself to the calculation of C.I. in this situation.


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