Smooth ROC curve estimation via Bernstein polynomials.

Dongliang Wang,Xueya Cai,Alan D Hutson

doi:10.1371/journal.pone.0251959

Abstract

The receiver operating characteristic (ROC) curve is commonly used to evaluate the accuracy of a diagnostic test for classifying observations into two groups. We propose two novel tuning parameters for estimating the ROC curve via Bernstein polynomial smoothing of the empirical ROC curve. The new estimator is very easy to implement with the naturally selected tuning parameter, as illustrated by analyzing both real and simulated data sets. Empirical performance is investigated through extensive simulation studies with a variety of scenarios where the two groups are both from a single family of distributions (symmetric or right skewed) or one from a symmetric and the other from a right skewed distribution. The new estimator is uniformly more efficient than the empirical ROC estimator, and very competitive to eleven other existing smooth ROC estimators in terms of mean integrated square errors.

Highlights

An extensive array of estimators for receiver operating characteristic (ROC) curve has been developed from perspectives of parametric, nonparametric, semiparametric and Bayesian statistics
One class of the smoothed ROC estimators is based upon the classic kernel density estimators with regards to F0 and F1, and includes those proposed by Sheather and Jones [6], Altman and Leger [7], Lloyd [8], and Hall and Hyndman [9]
A comprehensive simulation study conducted by Zhou and Harezlak [10] suggests that the ROC estimator developed by Altman & Leger [7] generally performs better within this class

Summary

Introduction

An extensive array of estimators for ROC curve has been developed from perspectives of parametric, nonparametric, semiparametric and Bayesian statistics. Empirical ROC (eROC) curve is a widely used nonparametric estimator based upon empirical distribution functions F^i; i 1⁄4 0; 1. Wang et al [19] proposed a nonparametric ROC estimator via smoothing the Bernstein polynomials (BP). In this study a novel Bernstein polynomial ROC estimator is derived from the framework of smooth quantile function estimation. The empirical performances of the new estimators are investigated and compared with a wide range of existing ROC estimators via extensive simulation studies. The rest of the paper is organized as follows: a new estimator of the ROC curve is proposed via directly smoothing the eROC curve with Bernstein polynomial approximation. Empirical performance of the BP estimators is further explored via extensive simulations

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Findings

Conclusion and discussion