Summary
Objectives:
Bayes’ rule formalizes how the pre-test probability of having a condition of interest
is changed by a diagnostic test result to yield the post-test probability of having
the condition. To simplify this calculation a geometric solution in form of a ruler
is presented.
Methods:
Using odds and the likelihood ratio of a test result in favor of having the condition
of interest, Bayes’ rule can succinctly be expressed as ”the post-test odds equals
the pre-test odds times the likelihood ratio”. Taking logarithms of both sides yields
an additive equation.
Results:
The additive log odds equation can easily be solved geometrically. We propose a ruler
made of two scales to be adjusted laterally. A different, widely used solution in
form of a nomogram was published by Fagan [2].
Conclusions:
Whilst use of the nomogram seems more obvious, the ruler may be easier to operate
in clinical practice since no straight edge is needed for precise reading. Moreover,
the ruler yields more intuitive results because it shows the change in probability
due to a given test result on the same scale.
Keywords
Bayes’ rule - nomogram - likelihood ratio
