Odds, Probability and Likelihood Ratios

In this chapter, we describe the critical differences between odds and probabilities. We introduce the concept of the likelihood ratio (LR) in its positive ( \(\kappa \) ) and negative ( \(\Upsilon \) ) forms, providing a version of the screening equation using this parameter. Though no formal argument underpins the consensus that \(\kappa \) \(>\) 10 is considered to provide strong evidence for the presence of disease, we propose a mathematical argument in favor of this cut-off using the logit function.