Last update: 

06Feb2001

Arch Hellen Med, 16(4), JulyAugust 1999, 394402
APPLIED MEDICAL RESEARCH
Ôhe concepts of odds and logit in applied medical research
L. SPAROS
Laboratory of Clinical Epidemiology,
Faculty of Nursing, University of Athens, Greece
The wide use of the probability theory in
applied medical research, and the frequent transformation of probability concepts
have permitted misunderstanding and misinterpretation of the results of research
studies. Two such concepts which have been misinterpreted are those of odds
and logit. If Y is a proportion having a range of from zero to one, then Y/(1–Y),
referred to as the “odds” of Y, has a range of from zero to infinity. In addition,
the logarithm of the odds, ln[Y/(1–Y)], referred to as the “logit”, has a range
of from minus infinity to plus infinity. The use of the odds and the logit facilitate
calculations and are used almost always in Bayesian diagnostic research, especially
after the introduction of computers. The discriminant capacity of a test result,
a sign, or a symptom may be expressed by the natural logarithm of the likelihood
ratio (LR) which is named “weight of evidence”. The numerical evaluation of
the weights of symptoms, signs, or test results has simplified the diagnostic
reasoning process, mainly because logarithms can be added, rather than using
numbers which have to be multiplied. For instance, if the LR of a symptom is
3, then the weight of evidence becomes 1.1 (ln3=109). In addition, to simplify
its use, this value is multiplied by 100 and rounded to produce a whole number
as the weight. This introduces the concept of the score which is equal to 100
lnLR. The cumulative score is then easily converted into the secondary diagnostic
probability.
Key words: Diagnostic values, Likelihood ratio, Logit, Odds, Odds ratio.