Improving the biomarker diagnostic capacity via functional transformations

Abstract

The use of the area under the receiver-operating characteristic, ROC, curve (AUC) as an index of diagnostic accuracy is overwhelming in fields such as biomedical science and machine learning. It seems that a larger AUC value has become synonymous with a better performance. The functional transformation of the marker values has been proposed in the specialized literature as a procedure for increasing the AUC and therefore the diagnostic accuracy. However, the classification process is based on some regions (classification subsets) which support the decision made; one subject is classified as positive if its marker is within this region and classified as negative otherwise. In this paper we study the capacity of improving the classification performance of univariate biomarkers via functional transformations and the impact of this transformation on the final classification regions based on a real-world dataset. Particularly, we consider the problem of determining the gender of a subject based on the Mode frequency of his/her voice. The shape of the cumulative distribution function of this characteristic in both the male and the female groups makes the resulting classification problem useful for illustrating the differences between having useful diagnostic rules and obtaining an optimal AUC value. Our point is that improving the AUC by means of a functional transformation can produce classification regions with no practical interpretability. We propose to improve the classification accuracy by making the selection of the classification subsets more flexible while preserving their interpretability. Besides, we provide different graphical approximations which allow us a better understanding of the classification problem. KEYWORDS Area under the ROC curve; (Bio)markers; Generalized receiver-operating characteristic (gROC) curve; Receiver-operating characteristic (ROC) curve.

Confidence intervals for the length of the receiver-operating characteristic curve based on a smooth estimator

“…We considered here the potential discriminatory capacity of the Mode frequency. Given the observed particularities of the involved distributions, Martínez-Camblor et al 16 used this data for illustrating the complexity of the binary classification problem. In order to remove ties in the sample values, we have introduced some random contamination to the data.…”

“…In this case, it is known that the gROC curve provides the optimal solution and the estimation of the optimal transformation (recall T false( ⋅ false) = f false( ⋅ false) / g false( ⋅ false)) is direct from using a plug-in method over the involved means and standard deviations. 16 Bantis et al, 13 in an interesting study about the ℓ ROC properties, considered its estimation under certain parametric models, and explored the use of randomization tests based on the kernel density estimator (KDE) for doing inferences. In this article, we proposed to use the KDE for approximating the theoretical probability density functions, and directly plug-in them in order to obtain an approximation for the length of the ROC curve.…”

The length of the receiver operating characteristic curve and the two cutoff Youden index within a robust framework for discovery, evaluation, and cutoff estimation in biomarker studies involving improper receiver operating characteristic curves

“…However, in practice the likelihood ratio is not known. Martínez-Camblor et al 17 explore functional transformations to deal with this problem but as they note this practice can produce classification regions with no practical interpretation. An alternative would be to consider nonparametric estimation of the density ratio under the assumption of unimodality, but we leave this as the goal of future research.…”