Likelihood ratios of quantitative diagnostic test results

In diagnostic medicine, a likelihood ratio (LR) is the probability of getting a specific test result if diseased, divided by the probability of getting the same test result if not diseased. The clinician may use the LR to revise the probability of disease. For quantitative test results there is a distribution of likelihood ratios. Grouping quantitative test results into a few (2-10) intervals and calculating LRs for those intervals leads to loss of information. We argue that LR for a specific diagnostic test result can be estimated by any statistical procedure capable of estimating the probability of disease as a function of the quantitative test result. Using real-life data, we show that logistic regression with fractional polynomials, or nonparametric regression, may be preferred over ordinary logistic regression.