Comparison of the likelihood ratios of two diagnostic tests subject to a paired design: confidence intervals and sample size

TL;DR

This paper compares the likelihood ratios of two diagnostic tests in paired designs using confidence intervals, introduces methods for sample size determination, and applies findings to coronary artery disease diagnosis.

Contribution

It presents six approximate confidence intervals for the ratio of likelihood ratios and a new method for sample size calculation in paired diagnostic test studies.

Findings

Six approximate confidence intervals are proposed.

Simulation studies evaluate coverage probabilities and interval lengths.

Application to coronary artery disease diagnosis demonstrates practical utility.

Abstract

Positive and negative likelihood ratios are parameters which are used to assess and compare the effectiveness of binary diagnostic tests. Both parameters only depend on the sensitivity and specificity of the diagnostic test and are equivalent to a relative risk. This article studies the comparison of the likelihood ratios of two binary diagnostic tests subject to a paired design through confidence intervals. Six approximate confidence intervals are presented for the ratio of the likelihood ratios, and simulation experiments are carried out to study the coverage probabilities and the average lengths of the intervals considered, and some general rules of application are proposed. A method is also proposed to determine the sample size necessary to estimate the ratio between the likelihood ratios with a determined precision. The results were applied to the diagnosis of coronary artery disease.