M Hellmich1, W Lehmacher. 1. Institute of Medical Statistics, Informatics and Epidemiology, University of Cologne, Joseph-Stelzmann-Str. 9, 50931 Köln, Germany. martin.hellmich@medizin.uni-koeln.de
Abstract
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 posttest 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. 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.
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 posttest 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. 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.