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Gill and colleagues (1) correction is probably (? probability of 1
in 4 or 0.25) a typing error. The first figure “1” in the denominator is
redundant, however even with this error corrected, the formulas given are
not strictly correct.
The formulas given by Gill et are inconsistent. Probability and odds
can be expressed as a ratio or as a fraction. For example a risk of 1 in 4
can also be expressed as the fraction 0.25. It can be easily seen that
this represents an odds of 1:3 and as an odds fraction 0.33333 For
consistency and ease of understanding, if the expression requires odds to
be entered as a fraction then the result should be returned as a fraction.
The conversion from probability to odds given by Gill et al (2) is
odds = (1-P)/P
Entering the P as a fraction returns the correct odds result as the
second part of the ratio. (e.g. 1:X) The appropriate conversion formula is
P/(1-P) which returns the odds as a fraction.
For the “corrected” formula given by Gill et al
probability = 1/(1+odds)
only returns the correct probability as a fraction if the odds are
entered as the second part of the ratio.
e.g. for the above example
probability = 1/(1+3) = ¼ = 0.25
The correct conversion are
Probability = odds/(1+odds)
Odds = probability/(1-probability)
Using these formula the probability or odds are entered as a
fraction and the answer is returned as a fraction.
Why clinicians are NOT natural mathematicians.
Sir,
Gill and colleagues (1) correction is probably (? probability of 1
in 4 or 0.25) a typing error. The first figure “1” in the denominator is
redundant, however even with this error corrected, the formulas given are
not strictly correct.
The formulas given by Gill et are inconsistent. Probability and odds
can be expressed as a ratio or as a fraction. For example a risk of 1 in 4
can also be expressed as the fraction 0.25. It can be easily seen that
this represents an odds of 1:3 and as an odds fraction 0.33333 For
consistency and ease of understanding, if the expression requires odds to
be entered as a fraction then the result should be returned as a fraction.
The conversion from probability to odds given by Gill et al (2) is
odds = (1-P)/P
Entering the P as a fraction returns the correct odds result as the
second part of the ratio. (e.g. 1:X) The appropriate conversion formula is
P/(1-P) which returns the odds as a fraction.
For the “corrected” formula given by Gill et al
probability = 1/(1+odds)
only returns the correct probability as a fraction if the odds are
entered as the second part of the ratio.
e.g. for the above example
probability = 1/(1+3) = ¼ = 0.25
The correct conversion are
Probability = odds/(1+odds)
Odds = probability/(1-probability)
Using these formula the probability or odds are entered as a
fraction and the answer is returned as a fraction.
References
1. Correction BMJ 2005;331:323
2. Gill et al BMJ 2005;330:1390
Competing interests:
None declared
Competing interests: No competing interests