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I have just calculated an odds ratio between the variable vaccine group (experimental and control) and the variable flu (got the flu or did not get the flu). I found the odds ratio to be 0.25. Is it correct to interpret this in the following way?

The odds of developing influenza are 0.25 times less for individuals who had the experimental vaccine than for individuals who had the control vaccine.

If this is incorrect, what is a proper way to write this sentence?

Alexis
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ally.williams
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    Why "0.25" is negative? – Zhanxiong Apr 14 '23 at 15:30
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    Wording like "times less" and "times more" always leads to confusion. Is 2 twice 1 or twice more? Try rewording your sentence to avoid it. – mdewey Apr 14 '23 at 15:39
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    0.25 is not negative, but from my understanding of odds ratios if the odds ratio is less than 1 (still greater than 0 though) that means the experimental group of the explanatory variable has a negative effect on the outcome of disease. But I am unsure how to properly express this in a sentence. – ally.williams Apr 14 '23 at 15:41
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    Drop the less and and say "The odds of developing influenza for individuals who had the experimental vaccine are $0.25$ times the odds for individuals who had the control vaccine." If you prefer, you might shorten this to "the odds for those who had the experimental vaccine are a quarter of the odds for the those who had the control vaccine" – Henry Apr 14 '23 at 16:46

1 Answers1

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First of all, obviously "0.25" is not negative, but you are correct that the fact that the OR is less than 1 means that there is a negative relationship between the independent and dependent variable.

Your interpretation is not quite correct though. The OR of 0.25 means that the odds of developing influence are 25% as high (or 75% lower) for the treatment group compared to the placebo group.

However, note that this is a statement about what happens to the odds of developing influenza. An OR of 0.25 does not mean the chance or probability of developing influenza are 25% as high for the treatment group. This is a very common misinterpretation of odds ratios, even in peer reviewed work, because everyone understand changes in terms of percentages but very few people (even statisticians) have good intuitions about "odds." If you want to express your results in terms of probabilities (i.e. as a risk ratio - "x% less likely) you will need to put in some extra work.

Graham Wright
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