Nonparametric monotonic regression can illustrate how the likelihood ratio varies with a continuous test result without specifying a test threshold

Background: Interpretation of a ROC plot assumes that the continuous test result will ultimately be dichotomised at a single threshold. Likelihood ratios provide an alternative means of interpreting test results that do not require dichotomisation. However, traditional methods require that either categorisation of the test result or specification of a parametric model. Nonparametric monotonic (isotonic) regression provides an alternative which assumes only that higher tests results imply greater likelihood of disease. Objectives: 1. To illustrate the use of nonparametric monotonic regression for analysing continuous test results. 2. To show how a simple extension allows estimation of likelihood ratios for continuous tests without the need to choose cut-points or parametric forms. Methods and Results: We apply the methods of Lloyd (2002) to standard data sets from the literature to illustrate that nonparametric isotonic regression corresponds to drawing a series of straight line segments of decreasing slope (a “convex hull”) around the data on a ROC plot. We extend his work by constructing a plot of the likelihood ratio against the test result as a series of steps, and discuss the interpretation of such a plot and procedures for adding confidence bands to illustrate the degree of uncertainty.