Simplifying likelihood ratios

Abstract

Likelihood ratios are one of the best measures of diagnostic accuracy, although they are seldom used, because interpreting them requires a calculator to convert back and forth between "probability" and "odds" of disease. This article describes a simpler method of interpreting likelihood ratios, one that avoids calculators, nomograms, and conversions to "odds" of disease. Several examples illustrate how the clinician can use this method to refine diagnostic decisions at the bedside.

Figures

FIGURE 1

The S-shaped curve describes the actual relationship between probability and log odds, and the straight line is the estimate of the nearly linear portion of this curve between probabilities of 10% and 90%. The S-shaped curve is the logistic function P = 1/(1 + e−z), where z = log odds.