A new parametric method based on S‐distributions for computing receiver operating characteristic curves for continuous diagnostic tests

Abstract

Receiver operating characteristic (ROC) curves provides a method for evaluating the performance of a diagnostic test. These curves represent the true positive ratio, that is, the true positives among those affected by the disease, as a function of the false positive ratio, that is, the false positives among the healthy, corresponding to each possible value of the diagnostic variable. When the diagnostic variable is continuous, the corresponding ROC curve is also continuous. However, estimation of such curve through the analysis of sample data yields a step-line, unless some assumption is made on the underlying distribution of the considered variable. Since the actual distribution of the diagnostic test is seldom known, it is difficult to select an appropriate distribution for practical use. Data transformation may offer a solution but also may introduce a distortion on the evaluation of the diagnostic test. In this paper we show that the distribution family known as the S-distribution can be used to solve this problem. The S-distribution is defined as a differential equation in which the dependent variable is the cumulative. This special form provides a highly flexible family of distributions that can be used as models for unknown distributions. It has been shown that classical statistical distributions can be represented accurately as S-distributions and that they occur in a definite subspace of the parameter space corresponding to the whole S-distribution family. Consequently, many other distributional forms that do not correspond to known distributions are provided by the S-distribution. This property can be used to model observed data for unknown distributions and is very useful in constructing parametric ROC curves in those cases. After fitting an S-distribution to the observed samples of diseased and healthy populations, ROC curve computation is straightforward. A ROC curve can be considered as the solution of a differential equation in which the dependent variable is the ratio of true positives and the independent variable is the ratio of false positives. This equation can be easily obtained from the S-distributions fitted to observed data. Using these results, we can compute pointwise confidence bands for the ROC curve and the corresponding area under the curve. We shall compare this approach with the empirical and the binormal methods for estimating a ROC curve to show that the S-distribution based method is a useful parametric procedure.

Bivariate analysis of sensitivity and specificity produces informative summary measures in diagnostic reviews

“…Unlike other sources of variation, a difference in threshold leads to a particular pattern between sensitivity and specificity. This pattern is well known from studies showing the effect of different cutoffs in case of a biochemical test with a continuous outcome [21][22][23]. Lowering the cutoff value will then lead to more patients with a positive result, thereby increasing the number of true positives but also the number of false positive results.…”

New Scaphocephaly Severity Indices of Sagittal Craniosynostosis: A Comparative Study with Cranial Index Quantifications

“…We recognize the existence of alternative density estimation methods that could be used to generate smooth ROC curves (e.g., Silverman, 1986;Zou et al, 1998;Sorribas et al, 2002;Zhou and Harezlak, 2002), particularly nonparametric approaches such as kernel density estimation (Silverman, 1986;Zou et al, 1998). A comparative study of parametric and non-parametric methods for estimating ROC curves in the context of this work as well as comparisons with alternative severity measures such as intracranial volume are topics of a future investigation.…”

Biochemical Systems Theory: A Review

“…Different approaches were proposed by Sorribas' group, who proposed using receiver-operating characteristic curves [190], or nonlinear regression methods [191][192][193]. An advantage of BST models for all these estimation tasks is the fact that every parameter has a clear and direct meaning, which oen permits the de�nition of relatively small search ranges, especially for kinetic orders [3].…”

“…Sorribas' group used the S-distribution, as well as a generalized GS-distribution [748], in a clinical setting to analyze reference intervals of normalcy and receiver operating characteristic (ROC) curves, which offer an effective method for the evaluation of the performance of a diagnostic test [190,749,750]. ey also used the GS-distribution to study questions in survival analysis [751].…”