Last update:
06-Feb-2001

Arch Hellen Med, 16(4), July-August 1999, 394-402

APPLIED MEDICAL RESEARCH

Τhe 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.