Likelihood ratios of quantitative laboratory results in medical diagnosis: The application of Bézier curves in ROC analysis

Receiver operating characteristic (ROC) analysis is widely used to describe the discriminatory power of a diagnostic test to differentiate between populations having or not having a specific disease, using a dichotomous threshold. In this way, positive and negative likelihood ratios (LR+ and LR-) can be calculated to be used in Bayes' way of estimating disease probabilities. Similarly, LRs can be calculated for certain ranges of test results. However, since many diagnostic tests are of quantitative nature, it would be desirable to estimate LRs for each quantitative result. These LRs are equal to the slope of the tangent to the ROC curve at the corresponding point. Since the exact distribution of test results in diseased and non-diseased people is often not known, the calculation of such LRs for quantitative test results is not straightforward. Here, a simple distribution-independent method is described to reach this goal using Bézier curves that are defined by tangents to a curve. The use of such a method would help in standardizing quantitative test results, which are not always comparable between different test providers, by reporting them as LRs for a specific diagnosis, in addition to, or instead of, quantities such as mg/L or nmol/L, or even indices or units.